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Defence Research andDevelopment Canada

Recherche et développementpour la défense Canada

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Forecasting training ammunitionrequirements across the Canadian ArmedForcesGeneralized statistical models and interactive reporting

A. SirjoosinghDRDC – Centre for Operational Research and Analysis

Defence Research and Development CanadaScientific ReportDRDC-RDDC-2019-R221December 2019

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Abstract

Forecasting ammunition requirements for training across the Canadian Armed Forces (CAF)is a recurring task for which the Directorate Materiel Group Operational Research (DM-GOR) has supported ADM(Mat) and the Strategic Joint Staff (SJS) for several years. Inthis report, we describe a new and general statistical framework by which DMGOR willbe able to provide subsequent forecasts using agnostic time series and zero-inflated countmodels. This approach is applicable to all environments across the CAF and will enableefficient and automated predictions that are expected to become more accurate as morehistorical expenditure data continue to become available. In addition, we describe initialefforts to increase the accuracy and efficiency of the forecasting procedure using unsuper-vised learning techniques and discuss the work we have done on generating and providingSJS and other stakeholder organizations with interactive reports to streamline ammunitionforecasting reporting.

Significance for defence and security

Accurate and efficient forecasting of ammunition for training requirements across the Cana-dian Armed Forces is important from both budgetary and readiness demand points of view.By developing a framework for regular cycles of ammunition forecasting, this work describesa generally applicable approach that is expected to become increasingly accurate in futureyear studies. We also highlight advances in interactive reporting whose outputs are intendedfor direct use by military client organizations that are responsible for reporting on trainingammunition expenditures and demand.

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Résumé

Depuis plusieurs années, le Directeur – Recherche opérationnelle (Groupe de matériels)[DRO GM] appuie le SMA(Mat) et l’État-major interarmées stratégique (EMIS) lorsqu’ilest question de prévoir les munitions nécessaires pour l’instruction au sein des Forces arméescanadiennes (FAC). Dans le présent rapport, nous décrivons un nouveau cadre statistiquegénéral qui permettra au DRO GM de fournir des prévisions ultérieures à l’aide de sérieschronologiques indépendantes et de modèles de dénombrement sans inflation. Cette ap-proche s’applique aux trois armées des FAC et permettra d’effectuer des prévisions efficaceset automatisées qui devraient devenir plus précises à mesure que les données historiquessur les dépenses seront accessibles. En outre, nous soulignons les efforts initiaux déployéspour accroître l’exactitude et l’efficacité du processus de prévision à l’aide de techniquesd’apprentissage sans supervision. Nous présentons également le travail accompli afin defournir à l’EMIS et aux autres organisations participantes des rapports interactifs qui sim-plifieront la production de rapports sur les prévisions des besoins en munition.

Importance pour la défense et la sécurité

Il est important de prévoir avec exactitude et efficacité les munitions nécessaires pourl’instruction au sein des Forces armées canadiennes, aussi bien sur le plan budgétaire que surcelui de la disponibilité opérationnelle. En élaborant un cadre pour les cycles réguliers deprévision des besoins en munitions, le présent document décrit une approche généralementapplicable qui devrait être plus précise dans les études des années à venir. Nous soulignonségalement les progrès en matière de rapports interactifs dont les résultats seront utilisésdirectement par les organisations clientes militaires qui sont chargées de rendre compte desdépenses et de la demande en munitions d’instruction.

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Table of contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Significance for defence and security . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Résumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Importance pour la défense et la sécurité . . . . . . . . . . . . . . . . . . . . . . . . ii

Table of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Data considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.1 Time series analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.2 Zero-inflated models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.3 Principal component analysis . . . . . . . . . . . . . . . . . . . . . . . . . 4

4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4.1 Forecasting using time series and count modeling . . . . . . . . . . . . . . 6

4.2 Principal component analysis validation . . . . . . . . . . . . . . . . . . . . 7

4.3 Interactive Reporting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Annex A: Classification of ammunition natures . . . . . . . . . . . . . . . . . . . . . 15

Annex B: Canadian Army Forecasts . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Annex C: Royal Canadian Air Force forecasts . . . . . . . . . . . . . . . . . . . . . . 31

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Annex D: Royal Canadian Navy forecasts . . . . . . . . . . . . . . . . . . . . . . . . 36

Annex E: Principal component analysis: simulated scenario . . . . . . . . . . . . . . 39

iv DRDC-RDDC-2019-R221

List of figures

Figure 1: Historical expenditures and associated forecasts for two ammunitionnatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Figure 2: A screenshot of the RCN forecast page of the offline interactive report. . 11

Figure 3: A screenshot of the CA forecast page of the Shiny interactive report. . . 12

Figure E.1: Errors (NRMSD) for ammunition expenditure predictions using twelveyears of historical data. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Figure E.2: Errors (NRMSD) for ammunition expenditure predictions using sixteenyears of historical and simulated data. . . . . . . . . . . . . . . . . . . . 41

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List of tables

Table 1: Errors (NRMSD) for ammunition expenditure predictions for timeseries, principal component and rolling mean models using historical data. 8

Table A.1: Log guide for ammunition natures considered in this report. . . . . . . . 15

Table B.1: Predicted ammunition expenditures for the CA for FYs 2019 to 2021. . . 26

Table C.1: Predicted ammunition expenditures for the RCAF for FYs 2019 to 2021. 31

Table D.1: Predicted ammunition expenditures for the RCN for FYs 2019 to 2021. . 36

Table E.1: Errors (NRMSD) for ammunition expenditure predictions for principalcomponent and rolling mean models using simulated data. . . . . . . . . 41

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Acknowledgements

The author thanks Dr Jérôme Levesque for advice and guidance on all aspects of this work.

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1 Introduction

The Directorate Materiel Group Operational Research (DMGOR) has been involved insupporting ADM(Mat) and the Strategic Joint Staff (SJS) Strat J4 with ammunition ex-penditure forecasts for training purposes for several years [1, 2, 3]. These forecasts enableSJS to predict and quantify ammunition requirements at the environment and unit level inresponse to unit requests and projected readiness levels.

Initial studies conducted by DMGOR focused on forming predictions around readinessplans affecting individual units and the corresponding ammunition natures to be used. Inparticular, two approaches were used (top-down and bottom-up methods) depending onthe nature of the data available for each service. In some cases these earlier studies usedhistorical expenditure data to help form the forecasts; for example, using a rolling meanto predict the expenditure of specific natures. However, at the time of those studies, onlyvery few years of historical data were available and so more general and agnostic time seriesmodels could not be accurately applied. Analyses were thus conducted independently forthe Canadian Army (CA), the Royal Canadian Air Force (RCAF) and the Royal CanadianNavy (RCN) using differing methodologies (see Reference [2] for example).

In the latest request by SJS for updated ammunition expenditure forecasts, DMGOR set outto explore the possibility of using modern statistical approaches that aim to predict futureusage based solely on historical expenditure data. To this end, we successfully applied timeseries analysis (TSA) and zero-inflated count (ZIC) modeling approaches to the forecastingof different ammunition natures across the Canadian Armed Forces (CAF) using a consistentand general approach for the three formations [3]. The success of these efforts was dueprincipally to having almost double the historical data upon which previous studies wereable to draw (this study utilizes twelve years of historical ammunition expenditure data).Furthermore, in future cycles of ammunition forecasting, it is assumed that this methodologymay become increasingly more accurate as more expenditure data are available to informnew model selections.

Beyond developing a new generalizable methodology for ammunition forecasting, we alsocreated a framework to generate interactive reports intended for direct use by SJS staff andother stakeholders from the three formations who report on ammunition expenditures [4].Previously, with each new update of forecasts, DMGOR would provide “static” reportswhich contained a snapshot of current predictions for future ammunition expenditure basedon the data available for that study, and working-level staff at SJS would consult tablesand figures in these single PDF documents. The advantage of the new interactive reports isthat staff can pull up the latest forecasts built from the most up-to-date historical data andsearch, filter and organize outputs interactively in a web browser. The added capability forSJS and other stakeholder military organizations is that their staff can have direct hands-on access to the latest forecasts with interactive search and visualization features, resultingpresumably in increased awareness and knowledge of forecasting methods and more efficientaccess to individual prediction queries.

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In addition to this previous work, we have also explored the possibility of using otheranalytical techniques to improve the accuracy and efficiency of predicting ammunition ex-penditures. One promising direction lies in the use of principal component analysis (PCA)techniques to incorporate some degree of correlation between ammunition natures in devel-oping the forecasting models. In our previous studies [3, 4], individual ammunition naturesare each described with their own model based on their respective historical expendituresand accordingly forecasted independently. The advantage of using PCA or other unsuper-vised learning techniques is that models are parameterized and associated forecasts gen-erated for several ammunition natures at once. This can lead to an improvement in theefficiency (fewer models need to be generated to produce all of the forecasted expenditures)as well as the accuracy (correlations in usage between two or more ammunition natures areincluded in the models). Further details of this technique and a statistical evaluation of itsfeasibility for forecasting ammunition expenditures are given later in this report.

In what follows, we expand upon the forecasts presented in Reference [3], providing the the-oretical background and reproducing the forecasts in the appendices in full. We also includea systematic study of the potential for using unsupervised learning techniques (e.g., PCA)to refine predictions by using the inherent correlations between expenditures of differentammunition natures. We also include an overview of the interactive reporting capabilitiesand discuss future directions for ammunition expenditure forecasting work.

2 Data considerations

The historical ammunition expenditure data were obtained through reports generated bySJS staff from the Ammunition Information and Maintenance System (AIMS). These re-ports contained allocation and expenditure values for each ammunition nature for eachunit in each fiscal year for the CA, RCAF and RCN. The goal of the forecasting work is topredict expenditures of each ammunition nature for each formation, so expenditures weregrouped by nature and summed over all units in the CA, RCAF or RCN. Upon preliminaryexamination of these data, we observed that the ammunition natures fell into two distinctgroups based on their historical usage. The majority of natures were identified as high usagein that they were used regularly over the extent for which historical data were availableand qualitatively seemed to be suited to time series analysis modeling. Examples includelow calibre ammunition rounds and other natures that are used regularly in training. Asignificant subset of natures were identified as low usage in that they were used on an “on-again, off-again” basis and qualitatively seemed to be suited to count modeling. Examplesinclude high-cost missiles and other natures that are used sporadically in training over thehistorical data range. A more detailed description of these classification groups and theirprecise definitions can be found in Reference [3].

At a recent meeting with representatives from SJS Strat J4 [5], it was determined thatfuture work should draw ammunition allocation and expenditure values from the DefenceResource Management Information System (DRMIS) as military units are being mandated

2 DRDC-RDDC-2019-R221

to enter information in the department system of record. SJS staff agreed to work withDMGOR to collect the data in future cycles of ammunition expenditure studies.

3 Theory

We include a brief exposition of the theory behind the forecasting methods we used topredict ammunition expenditures in the latest cycle. These statistical approaches are well-known and widely-used and the reader is referred to, e.g., References. [6, 7, 8, 9] for a moredetailed background on each subject. We include a summary here mainly to introduce termsand concepts that will be referenced in the evaluation of the applicability of these statisticalmethods to the ammunition forecasting problem described in subsequent sections.

3.1 Time series analysis

We perform ammunition expenditure forecasting by fitting the historical data for eachnature with an autoregressive integrated moving average (ARIMA) model. This approachis a general time series model which is able to encompass autoregressive (AR) behaviourwith moving average (MA) trends. We determined that using time series models would beappropriate for high usage ammunition natures, where expenditure in a particular year iscorrelated to expenditures in adjacent years.

For a time series {xt}, say describing the ammunition expenditure for a particular unitand nature in year t, an ARMA(p, q) model assumes the following relationship between thehistorical expenditures:

xt − φ1xt−1 − . . .− φpxt−p = �t + θ1�t−1 + . . .+ θq�t−q, (1)

where {�t} is a white noise sequence and the {φt} , {θt} are regression coefficients. TheARMA(p, q) model incorporates both autoregressive features (AR model of order p) andmoving average information (MA model of order q). The main advantage of this model isthat it provides a general model in which p and q can be optimally selected based on theirrespective regressions, for example, by comparing information criterion values. For details ofthe model and its assumptions, the reader is referred to References. [6, 7], but we commentbriefly on one condition required to apply Equation (1).

The ARMA approach assumes a stationary time series. This states among other things thatthe mean and variance are constant throughout the time series, which means that thereis no underlying drift or trend in the observed time series. For example, if ammunitionexpenditures on average have been increasing over the length of time for which we havehistorical data, strictly speaking the ARMA model is not readily applicable. In these cases,one may employ an ARIMA approach in which stationarity is achieved following a simpletransformation of the observed data (by differencing). Again, a detailed exposition of theARIMA model is beyond the scope of this report, but we will refer to an ARIMA(p, d, q)model where p and q carry the same meaning as in the ARMA(p, q) model of Equation (1)


and the additional parameter, d, describes the degree of differencing necessary to producean effective stationary time series. Usually p, d, q ∈ {0, 1, 2} and can all be selected bycomparing respective regressions, as discussed above. Additional details about the ARIMAformulation can be found in Reference [6], for example.

3.2 Zero-inflated models

Upon examining the low usage ammunition natures, we determined that using a zero-inflated count model would be more appropriate than applying the ARIMA formalismdescribed above. These types of models are used for count-type data, where each eventis assumed independent (i.e., previous years have no direct bearing on the current year’sexpenditure of the ammunition). Instead, a probability distribution is formed describing thelikelihood of a given expenditure for a given ammunition nature in any year. Two standarddistributions for count data are the Poisson and negative binomial distributions, given by

fp (x;µ) =µxe−µ

x! and (2)

fn (x;µ, θ) =Γ (x+ θ)µxθθ

Γ (θ)x! (µ+ θ)x+θ, (3)

respectively. In these equations, µ is the center of the distribution, θ is the dispersionparameter of the negative binomial distribution, and Γ is the gamma function.

In situations where there are many zeros present (i.e., many years in which a particularammunition nature is not used), these distributions (especially Poisson) become increasinglyinaccurate [8]. To account for the excess of zeros in the target distribution, hurdle or zero-inflated models can be applied. The hurdle model is a two-component model which takesthe following form for observed variables x, regressor variables y and center µ:

f (x; y, µ) =

fzero (0; y) if x = 0(1−fzero(0;y))fcount(x;y,µ)1−fcount(0;y,µ) if x 6= 0

. (4)

In our work, we use a standard binomial distribution for fzero and either a Poisson ornegative binomial distribution for fcount. In a zero-inflated model, the form of Equation (4)is slightly modified to account for the possibility of zero contributions from fcount. Furtherdetails of both models can be found in Reference [8].

3.3 Principal component analysis

Principal component analysis is a standard unsupervised learning technique that aims todescribe the variation in data through dimension reduction [9]. In the ammunition forecast-ing context, fluctuations in the expenditure of all of the ammunition natures can potentiallybe described by fewer variables than having to describe each nature individually. For ex-ample, usage of one type of small caliber munition might be inherently correlated with the


usage of another nature of a similar type if they are both used in the same sort of trainingexercises or if one is being phased out in place of the other. PCA aims to describe thesetypes of correlated natures simultaneously with fewer variables than the time series meth-ods described above. Put another way, applying PCA before time series modeling allowsone to take advantage of the ‘extra information’ present from the correlation in expenditureof two or more ammunition natures to more accurately describe their combined variationbefore attempting to predict future-year usage.

Given N different ammunition natures whose expenditures are observed over M years, letxkt denote the expenditure of nature k ∈ {1, . . . , N} in year t ∈ {1, . . . ,M}. Then, forminga matrix X ≡ (X)tk = xkt , the singular value decomposition of X is given by

X = UΣVt, (5)

where U (M ×M) contains left singular vectors of X, V (N ×N) contains right singularvectors of X and Σ (M ×N) contains the singular values {σi} of X on the diagonal. In theterminology of PCA, the principal component vectors or coordinates are given by the rowsof Vt and the principal component coefficients or scores are given by the columns of UΣ.

The dimension reduction of the PCA scheme arises upon analyzing the principal components/ singular values. The key quantity is termed the percentage of variance explained (PVE),which suggests the appropriate level of dimension reduction according to the amount ofvariance encompassed by a certain number of principal components [9]. The PVE by n ≤Mprincipal components is given as

PVE =∑ni=1 Var σiu(i)∑Mi=1 Var σiu(i)

, (6)

where u(i) is the ith column of U. Below, we will report the PVE and forecasting results for1, 2 and 3 principal components (the latter at which we achieve > 90% PVE) and observehow the fits improve.

Once a level of truncation is determined by selecting the number of principal componentsto carry forward, the expenditures of each individual nature may be reconstructed usingthe formula

Xn = (UΣ)n Vtn, (7)

where (UΣ)n is the submatrix of UΣ formed by preserving the first n columns (ammunitionnature “coefficients”) and Vtn is the submatrix of Vt formed by preserving the first nrows (ammunition nature “vectors”). Here, Xn (M ×N) contains modified ammunitionexpenditure values for each nature x̃kt for k ∈ {1, . . . , N} and t ∈ {1, . . . ,M} organized asin the original X.


4 Results and discussion

In this section, we describe the ammunition forecasting models developed by DMGOR topredict future-year usage based solely on historical expenditure. We then discuss the relevantimplications of using PCA to improve the forecasting models. Finally we give an overviewof the types of interactive reporting we have developed for use by client organizations.

4.1 Forecasting using time series and count modeling

Reference [3] contains the classification of all ammunition natures that appeared in theAIMS reports provided by SJS: in Annex A we list those natures that are either highor low usage natures to match the forecasted expenditure values in subsequent annexes.We note that natures not listed were classified as rare or special usage meaning that theirusage is so irregular that specialist knowledge would be required to predict their future-yearexpenditures accurately and a generalized statistical model is not appropriate for accuratemodeling.

We employ the TSA described in the previous section to analyze the high usage ammunitionnatures. In particular, for each nature, we fit an optimal ARIMA model to the historicaldata by varying the parameters {p, d, q} and minimizing the Akaike information criterion(AIC). We then use the resulting model to forecast future expenditure for upcoming years.An example of the forecasts for high usage natures is given in Figure 1a.

For the low usage ammunition natures, we apply the ZIC models described in the previoussection. These models are suited to a situation where predicted expenditure depends ontwo things: choice and value. The choice part is defined as the probability that a naturewill be used in a given year. The value part is defined in the case that it is used in orderto describe the distribution of expenditures. The choice part is described using a (I) zero-inflated or (II) hurdle model, and the value part is described using a (i) Poisson or (ii)negative binomial distribution. Of these four possible models {Ii, Iii, IIi, IIii}, the optimalone is determined by minimizing the AIC. An example of the forecasts for low usage naturesis given in Figure 1b.

In the left panel of Figure 1, a high usage ammunition nature is analyzed. Naturally, theblack line represents the past-year expenditure from the historical data, while the blue lineand shaded region show the predicted expenditure mean and 90% confidence interval forthe next three FYs.

In the right panel of Figure 1, a low usage ammunition nature is analyzed. The visualizationdiffers from the traditional view of time series expenditures due to the inherent assumptionsof the probabilistic model: instead of viewing expenditures as continuous in time, it is moreconsistent to visualize the probability of whether that nature will be used or not, and if itis, its expenditure distribution. In this case, the historical data are represented by the greyhistogram showing the number of FYs in which a certain amount of that ammunition was


(a) (b)

0

10000

20000

30000

2010 2015 2020FY

Exp

ende

d

Cartridge 9mm Ball, Luger 115 gr, FMJ

0

1

2

3

4

5

0 200 400 600Expended

Cou

nt

Cartridge 12 Gauge Rifled Slug

Figure 1: Historical expenditures and associated forecasts for two ammunition natures.(a) High usage ammunition nature with log number 73 used by the RCAF. The black line

represents historical expenditure while the blue line and shaded region represent theassociated forecast. (b) Low usage ammunition nature with log number 163 used by theRCN. The grey histogram represents historical expenditure while the green line and

shaded region represent the associated forecast.

expended. The predicted expenditures are described by the green shaded region, where theheight describes the choice part (the probability that the nature will be used in a given year)as a fraction of the tallest histogram bar, and the dashed line and shaded region representthe value part (if used, the predicted expenditure mean and 90% confidence interval).

The forecasted values of all high and low usage ammunition natures are given in An-nexes B,C,D for the CA, RCAF and RCN, respectively. We note that for entries withconfidence intervals corresponding to lower bounds below zero, the lower range of the fore-cast should be taken to be zero. Graphical representations of all of these forecasts can befound in Reference [3].

4.2 Principal component analysis validation

In this subsection, we present an analysis to assess the feasibility of using PCA to improvethe accuracy and efficiency of ammunition expenditure forecasting. To assess this approach,we conducted a straightforward error analysis comparing the performance of the PCA-derived projections with the actual expenditure values in a leave-future-out (LFO) scheme(a time-series-appropriate variant of the leave-one-out or LOO scheme). In this exercise, weuse subsets of the historical data with certain numbers of future years “left out” to derivemodels. These models, in turn, are used to predict the expenditure for the left out yearsand those forecasted values are compared to the actual historical usage. As we will see, thecurrent historical data are too few to properly assess any increase or decrease in accuracyof forecasts using a PCA scheme, but the following demonstrates that there are possibleefficiency gains in using PCA in future-year ammunition forecasting studies.


In Table 1, we present the errors (in this case, the normalized root-mean-square deviation,or NRMSD, is used1) as a function of the number of years used to fit the models in theLFO scheme. The TSA models correspond to fitting each time series model individually,as before. The rolling mean (RM) models correspond to predicting the expenditure of aparticular nature in a given year by taking the mean of the previous three years’ expenditurevalues. The PCA models correspond to fitting either one, two or three time series (numberof principal components) and then reconstructing expenditures for all ammunition natures.

As mentioned in the Introduction, we see that the errors are quite high for TSA as comparedto RM for the shorter time series models: only in the last row (corresponding to using allof the currently available historical data) does it outperform RM. Thus, it is likely worthpursuing agnostic TSA models for future ammunition expenditure forecasting built usingsolely historical data. The PCA errors are high and no noticeable improvement over TSAis observed within the range for which we have historical data. However, as the time seriesbecome longer, we observe that there might be an increasing improvement in the PCApredictions and thus future studies could analyze the potential use of PCA for accuracyimprovements. In Annex E, we attempt to investigate future-year applications of PCAby performing the error analysis against simulated data. and indeed, such improvementsbecome apparent; however, the necessity of using simulated data to assess this approachsignals that a validation of PCA for model improvement should be undertaken using carefulanalysis with additional historical data as they become available.

Table 1: Normalized root-mean-square deviation predicting ammunition expenditurepredictions in a leave-future-out scheme. The number of years column indicates the size ofthe total data set for which the last remaining years (up to 13) are left out for the errorcalculation. NRMSD values are reported for forecasts generated using individual timeseries models, 1–3 principal components as well as for those generated using a rolling

mean scheme.

Number of Years Time Series Analysis Principal Component Analysis Rolling Mean1 PC 2 PCs 3 PCs

4 2.70 2.95 2.97 2.15 1.026 1.96 2.03 1.73 1.38 0.9788 1.62 1.76 1.59 1.68 0.95410 0.971 1.09 1.08 1.05 0.96012 0.888 1.11 0.971 0.968 0.958

As described in the introduction, PCA could be a useful addition to ammunition forecastingin two respects. Firstly, improvement in efficiency would arise if a few principal componentswere able to adequately describe the large number of ammunition natures that are currentlyeach forecasted individually: we see that this could potentially be the case based on thetrends observed using historical data (and consistent with the projected behaviour using1 We normalize the errors of each ammunition nature prediction by the variance of the historical usage ofthat particular nature so as to be able to compare errors from different classes of ammunition.


simulated data as discussed in Annex E). Secondly, PCA could actually help to improve theaccuracy of ammunition forecasting by including the inherent correlations between severalammunition natures in the model parameterization without the need for a priori speci-fication of these relationships (the main advantage of unsupervised learning techniques).Subject matter experts have suggested that such correlations should be present amongstdifferent ammunition natures (e.g., the phasing in of one nature relative to the phasingout of another) [10]. However, we are not able to fully assess this aspect in this study asthe PCA error was too high when using only the twelve years of available historical data.Thus, a careful assessment of the accuracy of introducing PCA could be performed as morehistorical data become available in future-year studies.

4.3 Interactive Reporting

As described in the introduction, we developed interactive reports intended for use by SJSstaff and other interested stakeholders across the CAF formations. A full description of thetwo types of reports is provided in Reference [4] but we include a brief description of eachhere with some screen captures.

The first type of report (offline) was created with the intention of maximum flexibility indistribution: it requires no specialist software and runs in a web browser including the de-fault Internet Explorer on the Defence Wide Area Network (DWAN). It contains tabulatedand searchable historical data reporting ammunition expenditure by fiscal year, log numberand unit. It also contains searchable tables and plots of the latest round of forecasts in aninteractive dashboard format. Working-level staff can view these reports and consult themas needed to report on historical expenditures and associated forecasts, and we envisagethat these reports could be easily updated when new rounds of historical data become avail-able. An example screenshot of the offline report as viewed in a web browser in the DWANis given in Figure 2.

The second type of report (Shiny) was created for analysts placed in SJS or other clientorganizations that are familiar with running interactive applications with R Shiny. Thenecessary software is approved for use on the DWAN and stakeholders will not have toread or write code; they only need the software installed to view this report. As with theoffline report, the Shiny report contains dashboards of historical ammunition expenditureand associated forecasts in tables and plots but offers even more flexibility and interactivitywhich can offer even more advantage to working-level staff reporting on this area. We expectin the near future that ongoing efforts at the new organization ADM(Defence InnovationAnalytics) will enable the creation and maintenance of a centralized server from which we(and others) will be able to host interactive applications of this type at which point noadditional software demands on the client will be required. As before, we envisage thatthese reports could be updated when new data become available, and perhaps even moreadvanced features (like on-the-fly model selection) could be added. An example screenshotof the Shiny report as viewed in R Studio is given in Figure 3.


We note also that both types of reports were created entirely using open-source tools (inR, using the markdown, flexdashboard and shiny packages) at relatively low effort forexperienced analysts. We hope that the development of interactive reports for client usagebecomes more commonplace as these tools become more sophisticated and increasinglyeasier to use. One interesting addition could be to include sections in the reports thatdescribe and interactively calculate forecasts based on the introduction of PCA or relatedtechniques. Reference [11] provides more technical detail on how the two types of reportsdescribed here were created and could be extended.


Figure 2: A screenshot of the RCN forecast page of the offline interactive report.


Figure 3: A screenshot of the CA forecast page of the Shiny interactive report.


5 Conclusions

In this report, we have described recent efforts conducted by DMGOR in the area of train-ing ammunition expenditure forecasting. Encouraged by the ever increasing availability ofhistorical expenditure data, we set out to develop, apply and assess the feasibility of usingmodern statistical approaches to improve the generalizability and accuracy of forecastingexpenditure.

We successfully applied TSA and ZIC models to describe the expenditure of the majorityof ammunition natures used in the CAF, allowing the prediction of future year usage us-ing a general, consistent and systematic approach for the three formations. These modelsmay become more accurate in future year studies as more historical expenditure data con-tinue to become available, and their applicability should be analyzed in upcoming cycles ofexpenditure forecasting.

We also provided an analysis of the potential for using unsupervised learning techniques(PCA) in ammunition forecasting. We observe that currently, the data are insufficient toderive any improvement from using PCA. However, we determined that in upcoming cyclesof ammunition forecasting within the next ten years, PCA may offer significant efficiencygains in that significantly fewer models would need to be constructed in order to provideforecasts of all of the ammunition natures which are currently being described indepen-dently. Moreover, at that point we might expect potential improvements in the accuracy ofthe forecasts as predictions would include correlations between the expenditures of differentammunition natures. The basis of this conclusion is on simulated projections of expendi-tures as we currently have only twelve year of historical data; thus, a complete assessmentof the accuracy gains in using this approach would be appropriate in future studies.

Finally, we described the development of interactive reports created for direct use by militarystaff reporting on training ammunition expenditures. We expect that these reports will offeran advancement in capability for SJS and other organizations by providing hands-on accessto web pages or applications loaded with the latest historical data and associated forecastswith convenient search and filtering options. The ease with which analysts can use open-source tools to create these reports to engage military staff heralds the interesting possibilityof blending historical expenditure dashboards with on-the-fly analysis, serving to streamlineammunition expenditure reporting and forecasting.


References

[1] Pall, R. and van Bavel, G. (2010), Toward a determination of readiness-basedammunition allocations, (TR 2010-283) Defence Research and Development Canada –Centre for Operational Research and Analysis.

[2] Fang, M. and van Bavel, G. (2013), Using force posture and readiness to estimatetraining ammunition requirements, (TM 2013-099) Defence Research andDevelopment Canada – Centre for Operational Research and Analysis.

[3] Sirjoosingh, A. and Levesque, J. (2019), Forecasting ammunition requirements fortraining: A new analysis method and forecasts from 2019-2021,(DRDC-RDDC-2019-L056) Defence Research and Development Canada – Centre forOperational Research and Analysis.

[4] Sirjoosingh, A. (2019), Interactive Reports for Training Ammunition Forecasts,(DRDC-RDDC-2019-L055) Defence Research and Development Canada – Centre forOperational Research and Analysis.

[5] Strategic Joint Staff Strat J4 (2019). Personal communication. Meeting with SJSStrat J4 staff on 22 February 2019.

[6] Hamilton, J. D. (1994), Time Series Analysis, Princeton University Press.

[7] Box, G. E. P., Jenkins, G. M., Reinsel, G. C., and Ljung, G. M. (2016), Time SeriesAnalysis, 5 ed, Wiley.

[8] Zeileis, A., Kleiber, C., and Jackman, S. (2008), Regression Models for Count Data inR, Journal of Statistical Software, 27, 1–25.

[9] James, G., Witten, D., Hastie, T., and Tibshirani, R. (2013), An Introduction toStatistical Learning, 1 ed, Springer.

[10] MacCharles, H. J. (2018). Personal communication. E-mail dated 4 April 2018.

[11] Sirjoosingh, A. (2019), R Markdown and Interactive Reporting for TrainingAmmunition Forecasts, (DRDC-RDDC-2019-D039) Defence Research andDevelopment Canada – Centre for Operational Research and Analysis.


Annex A Classification of ammunition natures

This annex reports those natures that were identified as high usage or low usage and thatare forecasted in subsequent annexes adapted from Reference [3].

Table A.1: A list of all high and low usage ammunition natures sorted by formation andby log guide for all natures expended since FY 2006-07.

Formation Log Description Group

RCAF 61 Cartridge 5.56mm Linked 4 Ball C77 1 Tr C78 highRCAF 63 Cartridge 5.56 mm Blank C79 Clipped highRCAF 64 Cartridge 5.56mm Blank C79A1 Linked M27 Bandoleers highRCAF 65 Cartridge 5.56mm Ball C77 Linked lowRCAF 70 Cartridge 9mm Ball Cdn Mk1 highRCAF 72 Cartridge 9mm Hollow Point 147 Grain lowRCAF 73 Cartridge 9mm Ball, Luger 115 gr, FMJ highRCAF 81 Cartridge 9mm FX Red Marking lowRCAF 83 Cartridge 5.56mm FX Red, Clipped lowRCAF 90 Cartridge 7.62mm Ball C21 Clipped lowRCAF 100 Cartridge 7.62mm Linked 4 Ball C21A1 1 Tr C19 highRCAF 105 Cartridge 7.62mm Ball C21 Linked C1 lowRCAF 130 Cartridge 7.62mm Blank C24 Linked highRCAF 162 Cartridge 12 Guage No 00 Buckshot highRCAF 163 Cartridge 12 Gauge Rifled Slug highRCAF 166 Cartridge 12 Guage No 6 Shot (Steel) highRCAF 169 Cartridge 12 Guage No 7 Shot highRCAF 170 Cartridge 12 Gauge Bird Dispersing highRCAF 172 Cartridge .303 Ball SP Commercial lowRCAF 173 Cartridge Calibre 30-06 Springfield Ball Soft Point highRCAF 210 Cartridge .303 Ball Mk8Z Cdn lowRCAF 218 Cartridge .50 Cal Match, Anti-pers, 750 Gr lowRCAF 220 Cartridge .50 Cal Linked 4 Ball M2 1 Tr M17 highRCAF 1140 Grenade Hand Fragmentation HE highRCAF 1160 Grenade Hand Smoke No 4/1681 Blue highRCAF 1170 Grenade Hand Smoke No. 4/1679 Green highRCAF 1180 Grenade Hand Smoke No 4/1677 Red highRCAF 1190 Grenade Hand Smoke No 4/1675 Yellow highRCAF 1250 Training Grenade Smoke lowRCAF 1290 Fuze Grenade Hand Practice M228 highRCAF 1362 Flare Para Hand Fired highRCAF 1370 Flare Surface Trip M49A1 lowRCAF 1380 Thunderflash C1A1 highRCAF 1390 Simulator Projectile Ground Burst C1A1 highRCAF 1420 Signal Illumination Red lowRCAF 1421 Miniflare No1 Mk3 Red highRCAF 1430 Signal Illumination Green lowRCAF 1500 Riot Control Agent Capsules CS highRCAF 1530 Smoke Pot Ground Type,2.5 to 3.5 Min Orange highRCAF 1531 Smoke Pot Ground 3 Min White highRCAF 1550 Smoke Pot Ground No 24 Mk2 15 Min SC39 highRCAF 1570 Cap Blasting Electric No 12 high

Continued on next page




RCAF 1575 Cap Blasting Electric M6 w/12 ft Lead highRCAF 1580 Cap Blasting Non-Electric No 12 highRCAF 1582 Dummy Cap Blasting Non-Electric C2 lowRCAF 1584 Dummy Cap Blasting Electric C1 lowRCAF 1590 Charge Demolition Plastic Comp C4, 1.25 Lb highRCAF 1592 Dummy Charge Demolition Block 1.25 Lb C9 lowRCAF 1645 Tritonal Granulated (Trigran) HEBP lowRCAF 1656 Charge Demolition Deta Sheet .125 Inch, 25 Ft Roll highRCAF 1657 Charge Demolition Deta Sheet .042 Inch, 76 Ft Roll highRCAF 1690 Charge Explosive Training C2 lowRCAF 1700 Cord Detonating C3 highRCAF 1701 Dummy Cord Detonating C1 lowRCAF 1702 Det Cord 200 Gr, Commercial lowRCAF 1710 Fuse Blasting Time M700 highRCAF 1730 Igniter Time Blasting Fuse Electric C2 lowRCAF 1740 Igniter Time Blasting Fuse M60 highRCAF 1750 Match Fusee highRCAF 1910 Firing Device Demolition F1A1 lowRCAF 1921 Fusee Signalling Red highRCAF 1940 Coupling Base Firing Device F4 lowRCAF 1981 Cartridge 20mm Blank 70 Gr. For Neutrex Mk II highRCAF 1982 Cartridge 20mm Blank 75 Gr. For Neutres Mk II highRCAF 1983 CTG 20mm Blank 80 Gr. For Neutrex Mk II highRCAF 1984 CTG 20mm Blank 85 Gr. For Neutrex Mk II highRCAF 1985 CTG 20mm EOD Special (AVON) 70 Grain highRCAF 3012 Guided Missile Intercept Aerial RIM 7M(VL)(H Build) lowRCAF 3580 Signal Smoke Marine Mk3 Orange lowRCAF 3740 Signal Diver Recall SC-810 highRCAF 4041 Cartridge Calibre .50 Blank (Electrically Initiated) highRCAF 4175 Container Demolition Charge MK 7 Mod 6 lowRCAF 4177 Container Demolition Charge MK 7 Mod 8 lowRCAF 5016 Cartridge 20mm TP LD C144 highRCAF 5065 Fuze Bomb Aircraft highRCAF 5070 Bomb GP 500 Lb (IM) highRCAF 5073 Cup Support, App MK 80 Series Bomb highRCAF 5076 Fin Assembly Bomb highRCAF 5078 Nose Plug, Projectile, (Bomb GP MK 82 Mod 1) highRCAF 5081 Bomb 500 Lbs BDU-45/B, Mk 82, inert lowRCAF 5082 Bomb 500 lb BDU-50/A, Mk 82, Inert highRCAF 5084 Fin Assembly Bomb Mk 83 highRCAF 5086 Bomb GP Mk 83 Mod 4 1000 lb inert highRCAF 5087 Bomb GP Mk 84, Mod 7, 2000 lb, Inert lowRCAF 5089 Plug, Solid Nose Fuze, MXU-735/B P/N 30003-923AS148 highRCAF 5091 Initiator, FZU - 48/B highRCAF 5095 Lanyard, Firing, FZU - 61 / B highRCAF 5099 AFG GBU-12 and GBU-49 highRCAF 5111 Laser Guided Training Round, PN 137800 high





RCAF 5131 Bomb Practice Modular Low Drag BDU 5002/B highRCAF 5160 Cable assy u/w FZU-48/B highRCAF 5214 Air Training Missile ATM-7M-5 lowRCAF 5216 Guided Missile TACT Sidewinder Aim 9M-6 highRCAF 5220 SONOBUOY SSQ536 BT lowRCAF 5230 SONOBUOY AN/SSQ 62B/C/D/E (DICAS) highRCAF 5241 SONOBUOY AN/SSQ 53D DIFAR highRCAF 5243 ICEPICK GEOBUOY SSC040 lowRCAF 5246 SONOBUOY 47B lowRCAF 5261 SUS MK84 MOD1 lowRCAF 5262 SONOBUOY AN/SSQ-53F lowRCAF 5265 Marker Buoy Self Locat Datum (SLDMB) lowRCAF 5280 Marker Location Marine highRCAF 5290 Marker Location Marine Mk 58 Mod 0 Red PH highRCAF 5300 Signal Illumination A/C Red 1.5 Inch lowRCAF 5305 Cartridge Signal Practice Bomb C1 Orange lowRCAF 5306 Cartridge Signal Practice Bomb C2 White highRCAF 5310 Signal Smoke A/C C7 Orange highRCAF 5311 Signal Smoke Drift Indicator C8 Orange highRCAF 5320 Signal Distress Day and Night No 1 Series highRCAF 5327 Signal Cartridge 19mm Single Star Red highRCAF 5328 Cartridge Signal 19mm Single Star Green highRCAF 5330 Flare A/C Parachute 5 min highRCAF 5331 Flare, IR, Decoy, ARM-002 (MJU 32/B) highRCAF 5333 Flare Decoy MJU 27A/B highRCAF 5335 Flare Decoy MJU8/B , MJU 38/B highRCAF 5336 Cartridge Impulse CCU-63/B highRCAF 5337 Cartridge Impulse CCU 136/A highRCAF 5340 Initiator Cartridge Actuated JAU 22/B highRCAF 5341 Cartridge Impulse BBU 35/B highRCAF 5342 Chaff, CM, RR-188/AL lowRCAF 5344 Chaff C/M CCU-129/AL (Trg) lowRCAF 5345 Chaff RR-144A/AL highRCAF 5346 Chaff RR-129/AL highRCAF 5347 Chaff RR-129A/AL highRCAF 5349 Ctge Impulse BBU-36/B highRCAF 5352 Cartridge Impulse CCU-45/B highRCAF 5353 Cartridge Impulse ARD 863 highRCAF 5354 Cartridge Impulse Mk 19 Mod 0 highRCAF 5356 Flare, IR, CM, MJU-53/B highRCAF 5357 Flare, CM, MJU-62/B highRCAF 5358 Decoy, IR, CM, MJU-50/B highRCAF 5359 Decoy, IR, CM, MJU-51A/B highRCAF 5380 Flare, IR, DSTL 73 highRCAF 5382 Flare, IR, DSTL 22 highRCAF 5383 Flare, 218 Mk4 highRCAF 5400 ECCG MAU-210 Series low





RCAF 5401 CCG MAU-169 Series highRCAF 5405 Safety Elec switch Mk 122 Mod 0 highRCAF 5407 Cable Assy Bomb M72 highRCAF 5960 Cartridge 5.56mm Ball C77 Clipped Combined highRCAF 6002 Actuator Assembly Explosive Rotary highRCAF 6012 Cutter, Cartridge Actuated, G1, 0.8 sec delay lowRCAF 6013 Cutter, Cartridge Actuated, G1, 0.1 sec delay lowRCAF 6016 Explosive Sequence Control DCU-241/A lowRCAF 6030 Initiator Cartridge Actuated MC50 lowRCAF 6031 Initiator Cartridge Actuated lowRCAF 6032 Initiator Cartridge Actuated lowRCAF 6035 Initiator Cartridge Actuated M27 lowRCAF 6040 Initiator Mechanical JAU-25/A highRCAF 6047 Initiator Explosive Actuated JAU-23A lowRCAF 6052 Initiator Cartridge Actuated PN 0113226-23 lowRCAF 6053 Valve One Way Transfer lowRCAF 6059 Remover A/C Canopy M1A3 lowRCAF 6061 Rocket Motor Mk109 Mod O lowRCAF 6065 Release Propellant Actuated M1A1 lowRCAF 6068 Thruster Cartridge Actuated highRCAF 6070 Thruster Cartridge Actuated w/o Cartridge lowRCAF 6071 Cord Detonating Shielded Mild, 41.073 in long lowRCAF 6073 Cartridge Impulse CCU-72A lowRCAF 6079 Cord Detonating Shielded Mild, 41.463 in long lowRCAF 6080 Cord Detonating Shielded Mild, 11.031 Inch Long lowRCAF 6081 Cord Detonating Shielded Mild,24.042 Inch Long lowRCAF 6082 Cord Detonating Shielded Mild, 8.664 Inch Long lowRCAF 6083 Cord Detonating Shielded Mild, 5.000 Inch Long lowRCAF 6085 Cord Detonating Shielded Mild, 35.224 Inch Long lowRCAF 6086 Cord Detonating Shielded Mild, 32.507 Inch Long lowRCAF 6087 Cord Detonating Shielded Mild, 9.176 Inch Long) lowRCAF 6093 Cord Detonating Shielded Mild, 18.545 Inch Long lowRCAF 6094 Cord Detonating Shielded Mild, 35.017 Inch Long lowRCAF 6139 Cord Assembly detonating(SMDC) lowRCAF 6144 Cord Detonating Kit No 16 (For CF 18) lowRCAF 6154 Cartridge A/C Fire Extinquisher highRCAF 6155 Cartridge A/C Fire Extinquisher highRCAF 6156 Cartridge A/C Fire Extinquisher highRCAF 6157 Cartridge A/C Fire Extinquisher CCU-94/A highRCAF 6158 Cartridge A/C Fire Extinguisher highRCAF 6159 Cartridge A/C Fire Extinquisher lowRCAF 6163 Cartridge A/C Fire Extinguisher lowRCAF 6166 Cartridge Impulse Mk 105 Mod 0 lowRCAF 6168 Cartridge Impulse Mk 24 Mod 0 lowRCAF 6172 Cartridge Powder Actuated Cutter highRCAF 6178 Cutter Cord and Flag Assembly lowRCAF 6193 Cartridge Impulse No 6100 low





RCAF 6217 Cartridge Fire Extinguisher CCU-126/A lowRCAF 6233 Initiator Explosive Actuated JAU-24A lowRCAF 6289 Cutter Cable Assembly lowRCAF 6318 Cord Assembly Detonating(TLX Transfer Line) lowRCAF 6319 Cord Assembly Detonating(TLX Transfer Line) lowRCAF 6330 Para Deploy Rkt Motor MK122 Mod 0 highRCAF 6333 Ctge Impulse CCU-105/A lowRCAF 6335 Ctge Impulse CCU-102/A lowRCAF 6336 Ctge Impulse CCU-118/A lowRCAF 6339 Initiator JAU-74/A highRCAF 6350 Ctge, Aircraft, Fire Exting. lowRCAF 7010 Body Practice Hand Grenade lowRCAF 7500 Dummy Cartridge 5.56MM C80A1 Clipped lowRCAF 7513 Dummy Cartridge 7.62mm lowRCAF 7514 Dummy Cartridge 9mm C14A1 lowRCAF 7517 Dummy Cartridge Calibre .50 CAL C51 lowRCAF 7566 Dummy Grenade Hand C7 lowRCAF 9015 Swivel & Link Assembly lowRCAF 9523 Dummy 20mm XM254 Oran Plast lowRCN 61 Cartridge 5.56mm Linked 4 Ball C77 1 Tr C78 highRCN 63 Cartridge 5.56 mm Blank C79 Clipped highRCN 64 Cartridge 5.56mm Blank C79A1 Linked M27 Bandoleers highRCN 65 Cartridge 5.56mm Ball C77 Linked highRCN 70 Cartridge 9mm Ball Cdn Mk1 highRCN 72 Cartridge 9mm Hollow Point 147 Grain highRCN 73 Cartridge 9mm Ball, Luger 115 gr, FMJ lowRCN 80 Cartridge 9mm Blank C30 highRCN 81 Cartridge 9mm FX Red Marking highRCN 83 Cartridge 5.56mm FX Red, Clipped highRCN 84 Cartridge 5.56mm FX White, Clipped highRCN 85 Cartridge 9mm FX White, highRCN 100 Cartridge 7.62mm Linked 4 Ball C21A1 1 Tr C19 highRCN 162 Cartridge 12 Guage No 00 Buckshot highRCN 163 Cartridge 12 Gauge Rifled Slug lowRCN 220 Cartridge .50 Cal Linked 4 Ball M2 1 Tr M17 highRCN 240 Cartridge Calibre .50 Linked AP-T C44 lowRCN 250 Cartridge Calibre .50 Blank C48 Linked highRCN 712 Igniter Friction Tube SC282 lowRCN 1160 Grenade Hand Smoke No 4/1681 Blue highRCN 1170 Grenade Hand Smoke No. 4/1679 Green highRCN 1180 Grenade Hand Smoke No 4/1677 Red highRCN 1190 Grenade Hand Smoke No 4/1675 Yellow highRCN 1362 Flare Para Hand Fired highRCN 1380 Thunderflash C1A1 highRCN 1390 Simulator Projectile Ground Burst C1A1 highRCN 1500 Riot Control Agent Capsules CS highRCN 1531 Smoke Pot Ground 3 Min White high





RCN 1575 Cap Blasting Electric M6 w/12 ft Lead highRCN 1580 Cap Blasting Non-Electric No 12 highRCN 1582 Dummy Cap Blasting Non-Electric C2 highRCN 1584 Dummy Cap Blasting Electric C1 lowRCN 1590 Charge Demolition Plastic Comp C4, 1.25 Lb highRCN 1592 Dummy Charge Demolition Block 1.25 Lb C9 highRCN 1656 Charge Demolition Deta Sheet .125 Inch, 25 Ft Roll highRCN 1657 Charge Demolition Deta Sheet .042 Inch, 76 Ft Roll lowRCN 1700 Cord Detonating C3 highRCN 1701 Dummy Cord Detonating C1 highRCN 1710 Fuse Blasting Time M700 highRCN 1711 Dummy Fuse Blasting Time C9 highRCN 1740 Igniter Time Blasting Fuse M60 highRCN 1750 Match Fusee highRCN 1760 Clip Cord Detonating highRCN 1981 Cartridge 20mm Blank 70 Gr. For Neutrex Mk II lowRCN 1982 Cartridge 20mm Blank 75 Gr. For Neutres Mk II lowRCN 1983 CTG 20mm Blank 80 Gr. For Neutrex Mk II lowRCN 1984 CTG 20mm Blank 85 Gr. For Neutrex Mk II lowRCN 1985 CTG 20mm EOD Special (AVON) 70 Grain lowRCN 1996 CTG Inj Kit PT 1062A (ABL 2000) lowRCN 3001 Cartridge 40mm HE-T, Clipped lowRCN 3002 Cartridge 40mm Practice (BL & P) L60 highRCN 3015 Guided Missile ESSM RIM 162C highRCN 3016 Guided Missile ESSM MK 79 Mod 1 highRCN 3025 Guided Missile Surface Attack Harpoon RGM-84D-4 highRCN 3026 Guided Missile, Practice Harpoon RTM-84D-4 lowRCN 3092 Charge Depth HE DM 211 Anti-Frogman highRCN 3122 Cartridge 76mm HE PFF lowRCN 3124 Cartridge 76mm HE PD lowRCN 3125 Cartridge 76mm TP-S (NFF) highRCN 3126 Cartridge 76mm TP-T highRCN 3160 Cartridge 57mm PFHE highRCN 3161 Cartridge 57mm 3P lowRCN 3165 Cartridge 57mm HE, HCER highRCN 3170 Cartridge 57mm TP (BL&P) highRCN 3175 Cartridge 57mm NFF (TP-S) highRCN 3214 Cartridge 20MM LKD, APDS, MK 244 highRCN 3230 Rocket 100mm Chaff Decoy (Shield) P8 Mk 1 C16 lowRCN 3232 Cartridge 100mm I.R. Decoy P6 Mk 1 Model C17 lowRCN 3233 Cart. 81mm MASS Omni Trap ER lowRCN 3235 Rocket, Practice Decoy Cal 82 x 810mm (DEURAS) lowRCN 3325 Torpedo Mk46 Mod 5A (SW) Warshot highRCN 3540 Signal Sound Marine Mk NC1 Mod 1 lowRCN 3561 Cartridge 5.56mm Line Throwing highRCN 3580 Signal Smoke Marine Mk3 Orange highRCN 3610 Cartridge Ignition .410 Inch high





RCN 3690 Flare Hand PinPoint Red Mk 7 highRCN 3731 Signal Smoke and Illumination Mk 121 Mod 1 highRCN 3740 Signal Diver Recall SC-810 highRCN 3795 Flare D4A2, RED, Submarine Launched lowRCN 3821 Signal Smoke and Illumination Mk 117 Mod 2 highRCN 3920 Cntr Demolition MK NC1 highRCN 3950 Device Rope Cutting Kit 2.5 Lb lowRCN 3952 Device Rope Cutting N2 Mk 1 highRCN 4041 Cartridge Calibre .50 Blank (Electrically Initiated) lowRCN 4176 Container Demolition Charge MK 7 Mod 7 lowRCN 4177 Container Demolition Charge MK 7 Mod 8 lowRCN 4270 Container Demolition Charge MK 1 Mod 0 lowRCN 4271 Container Demolition Charge MK 2 Mod 0 lowRCN 4280 Container Demolition Charge MK 8 Mod 1 highRCN 4290 Marker Man Overboard Smoke and Light Series III w/o mounting highRCN 4300 Cartridge .50 Blank C128 highRCN 4301 Cartridge 6 Pdr Blank Mk 1 highRCN 4307 Charge Blank Mini 32 Pdr ML Gun lowRCN 4340 Cartridge Limpet Mine Disposal N12 Mk 1 lowRCN 4341 Cartridge Limpet Mine Disposal N2 Mk 1 highRCN 5230 SONOBUOY AN/SSQ 62B/C/D/E (DICAS) lowRCN 5241 SONOBUOY AN/SSQ 53D DIFAR lowRCN 5246 SONOBUOY 47B highRCN 5259 Signal Underwater Sound Mk 400 series lowRCN 5260 Signal Underwater Sound Mk401/411 lowRCN 5261 SUS MK84 MOD1 highRCN 5267 SONOBUOY SSQ553G(B) DIFAR highRCN 5280 Marker Location Marine highRCN 5290 Marker Location Marine Mk 58 Mod 0 Red PH lowRCN 5300 Signal Illumination A/C Red 1.5 Inch highRCN 5301 Signal Illumination A/C Green 1.5 Inch highRCN 5302 Signal Illumination A/C Yellow 1.5 Inch highRCN 5320 Signal Distress Day and Night No 1 Series highRCN 5340 Initiator Cartridge Actuated JAU 22/B lowRCN 5960 Cartridge 5.56mm Ball C77 Clipped Combined highRCN 7500 Dummy Cartridge 5.56MM C80A1 Clipped lowRCN 7514 Dummy Cartridge 9mm C14A1 lowRCN 7517 Dummy Cartridge Calibre .50 CAL C51 lowRCN 8512 Dummy Cartridge 40mm C58 Dummy lowRCN 9001 Link, Cartridge, 20mm, MK 7, Mod 1 for gun 20mm MK 15 lowRCN 9520 Dummy 20mm M51 Series lowRCN 9522 Dummy 20mm C145 (Naval) lowRCN 9523 Dummy 20mm XM254 Oran Plast lowCA 10 Cartridge Calibre .22 Ball Long Rifle highCA 61 Cartridge 5.56mm Linked 4 Ball C77 1 Tr C78 highCA 62 Cartridge 5.56mm Tracer C78 highCA 63 Cartridge 5.56 mm Blank C79 Clipped high





CA 64 Cartridge 5.56mm Blank C79A1 Linked M27 Bandoleers highCA 65 Cartridge 5.56mm Ball C77 Linked highCA 70 Cartridge 9mm Ball Cdn Mk1 highCA 73 Cartridge 9mm Ball, Luger 115 gr, FMJ highCA 81 Cartridge 9mm FX Red Marking highCA 83 Cartridge 5.56mm FX Red, Clipped highCA 84 Cartridge 5.56mm FX White, Clipped highCA 86 Cartridge 5.56mm FX Red, Linked highCA 87 Cartridge 5.56mm FX White, Linked highCA 90 Cartridge 7.62mm Ball C21 Clipped highCA 100 Cartridge 7.62mm Linked 4 Ball C21A1 1 Tr C19 highCA 105 Cartridge 7.62mm Ball C21 Linked C1 highCA 120 Cartridge 7.62mm Blank C24 highCA 130 Cartridge 7.62mm Blank C24 Linked highCA 140 Cartridge 7.62mm x 39mm Ball (Soviet M43) highCA 141 Cartridge 7.62mm x 54mm Ball highCA 142 Cartridge 7.62mm x 54mm Ball Linked lowCA 143 Cartridge 9mm Ball (9x18mm) Soviet Pistol highCA 145 Cartridge 5.45mm x 39mm Ball highCA 150 Cartridge Calibre .308 Winchester Match highCA 153 Cartridge .338 Lapua Magnum highCA 162 Cartridge 12 Guage No 00 Buckshot highCA 163 Cartridge 12 Gauge Rifled Slug highCA 166 Cartridge 12 Guage No 6 Shot (Steel) highCA 169 Cartridge 12 Guage No 7 Shot highCA 172 Cartridge .303 Ball SP Commercial highCA 173 Cartridge Calibre 30-06 Springfield Ball Soft Point lowCA 210 Cartridge .303 Ball Mk8Z Cdn highCA 218 Cartridge .50 Cal Match, Anti-pers, 750 Gr highCA 220 Cartridge .50 Cal Linked 4 Ball M2 1 Tr M17 highCA 222 Cartridge .50 Cal Ball M2 Linked highCA 250 Cartridge Calibre .50 Blank C48 Linked lowCA 273 Cartridge 25mm TPDS-T C131 Linked highCA 275 Cartridge 25mm Subcalibre Practice Chg 0 Green highCA 276 Cartridge 25mm Subcalibre Practice Chg 1 Yellow highCA 277 Cartridge 25mm Subcalibre Practice Chg 2 Blue highCA 278 Cartridge 25mm Subcalibre Practice Chg 3 Red highCA 304 Cartridge 25mm TP-T C152 linked M28 highCA 309 Cartridge 40 mm, LV, HE/Fragmentation C149 highCA 312 Cartridge 40mm PCM C158 highCA 320 Cartridge 81mm HE C70A1 w/fuze PD DM111A3 or DM111A4 highCA 321 Fuze Proximity and Point Detonating PPD 323-B3 highCA 330 Cartridge 81mm Smoke Red Phosphorous M819 w/fuze M772 highCA 340 Cartridge 81mm Illuminating M77 Fzd FH55K highCA 369 Rocket 66mm HEAT w/ Graze action highCA 371 Rocket Practice 21mm Sub Calibre highCA 400 Cartridge 84mm HEAT RAP 551 high





CA 401 Cartridge 84mm HEDP 502 highCA 410 Cartridge 84mm TP RAP 552 highCA 415 Cartridge 7.62mm Tracer 553 Cap w/Holder FFV533B highCA 520 Guided Missile Surface Attack BGM-71D lowCA 560 Cartridge 105mm HE Comp B M1 dualgran w/Fuze PD M739 highCA 570 Cartridge 105mm HE Comp B M1 Dualgran w/o fuze highCA 590 Cartridge 105mm Illuminating M314 highCA 640 Cartridge 105mm Smoke BE DM15 W/Fuze MTSQ DM53(M501A1) highCA 700 Cartridge 105mm Blank M395 highCA 712 Igniter Friction Tube SC282 highCA 720 Projectile 155mm HE M107 highCA 730 Projectile 155mm Illuminating M485A2 highCA 740 Projectile 155mm Smoke HC DM45A1 highCA 800 Charge Propelling 155mm M4A2 highCA 805 Flash Reducer M2 highCA 811 Primer Percussion M82 highCA 820 Fuze Point Detonating M739 highCA 822 Fuze Electronic C32A1 highCA 840 Fuze Mechanical Time and Super Quick M582 highCA 870 Fuze Mechanical Time and Super Quick M577A1 highCA 1030 Cartridge 105mm HESH L35A2 Tank lowCA 1050 Cartridge 120mm TP, DM18A2 lowCA 1060 Cartridge 105mm Smoke WP-T, M416, Tank highCA 1071 Cartridge 105mm Tank, SR TPDS-T, C148 highCA 1081 Cartridge 105mm SH/P-T C109A1 highCA 1120 Cartridge 105mm Blank C1A3 highCA 1140 Grenade Hand Fragmentation HE highCA 1160 Grenade Hand Smoke No 4/1681 Blue highCA 1170 Grenade Hand Smoke No. 4/1679 Green highCA 1180 Grenade Hand Smoke No 4/1677 Red highCA 1190 Grenade Hand Smoke No 4/1675 Yellow highCA 1210 Grenade Hand Smoke HC C1A1 lowCA 1220 Grenade Launcher Smoke HC 76mm DM15 highCA 1250 Training Grenade Smoke highCA 1270 Grenade Hand No 518 CS Riot Control highCA 1290 Fuze Grenade Hand Practice M228 highCA 1340 Defensive Command Detonated Weapon C19 w/Accessories highCA 1345 Mine Anti Tank Heavy M15 highCA 1347 Mine Off Route C14 Assembly highCA 1350 Charge Spotting Mine C5 highCA 1362 Flare Para Hand Fired highCA 1370 Flare Surface Trip M49A1 highCA 1380 Thunderflash C1A1 highCA 1390 Simulator Projectile Ground Burst C1A1 highCA 1420 Signal Illumination Red highCA 1421 Miniflare No1 Mk3 Red highCA 1430 Signal Illumination Green high





CA 1440 Signal Illumination Ground White lowCA 1500 Riot Control Agent Capsules CS highCA 1530 Smoke Pot Ground Type,2.5 to 3.5 Min Orange highCA 1531 Smoke Pot Ground 3 Min White highCA 1550 Smoke Pot Ground No 24 Mk2 15 Min SC39 highCA 1571 Adapter Priming M1A4 Plastic highCA 1575 Cap Blasting Electric M6 w/12 ft Lead highCA 1580 Cap Blasting Non-Electric No 12 highCA 1582 Dummy Cap Blasting Non-Electric C2 highCA 1584 Dummy Cap Blasting Electric C1 highCA 1590 Charge Demolition Plastic Comp C4, 1.25 Lb highCA 1592 Dummy Charge Demolition Block 1.25 Lb C9 highCA 1630 Charge Demolition Shaped M2A4 15 Lb highCA 1645 Tritonal Granulated (Trigran) HEBP highCA 1646 Charge Demolition Necklace L1A1 highCA 1647 Primer Detaprime highCA 1656 Charge Demolition Deta Sheet .125 Inch, 25 Ft Roll highCA 1657 Charge Demolition Deta Sheet .042 Inch, 76 Ft Roll highCA 1680 Charge Demolition Shaped M3 40 Lb highCA 1690 Charge Explosive Training C2 highCA 1700 Cord Detonating C3 highCA 1701 Dummy Cord Detonating C1 highCA 1702 Det Cord 200 Gr, Commercial highCA 1710 Fuse Blasting Time M700 highCA 1711 Dummy Fuse Blasting Time C9 highCA 1720 Fuse Blasting Instantaneous L1A1 highCA 1730 Igniter Time Blasting Fuse Electric C2 highCA 1740 Igniter Time Blasting Fuse M60 highCA 1750 Match Fusee highCA 1760 Clip Cord Detonating highCA 1780 Demolition Kit Bangalore Torpedo M1A2 highCA 1910 Firing Device Demolition F1A1 highCA 1921 Fusee Signalling Red highCA 1940 Coupling Base Firing Device F4 highCA 1981 Cartridge 20mm Blank 70 Gr. For Neutrex Mk II highCA 1982 Cartridge 20mm Blank 75 Gr. For Neutres Mk II highCA 1983 CTG 20mm Blank 80 Gr. For Neutrex Mk II highCA 1984 CTG 20mm Blank 85 Gr. For Neutrex Mk II highCA 1985 CTG 20mm EOD Special (AVON) 70 Grain highCA 1992 CTG Injector Kit EOD L46A1 (Pigstick) highCA 1993 Injector Kit L47A1 highCA 1994 CTG ABL3000 (30mm Recoilless) highCA 2318 Mine Accessories lowCA 2525 Ammo Tools (US, Can, UK, NATO) lowCA 3740 Signal Diver Recall SC-810 highCA 4041 Cartridge Calibre .50 Blank (Electrically Initiated) highCA 4171 Container Demolition Charge MK 7 Mod 2 low





CA 4306 Charge Blank 9 Pdr 6 Cwt RML Gun lowCA 4307 Charge Blank Mini 32 Pdr ML Gun highCA 5320 Signal Distress Day and Night No 1 Series highCA 5960 Cartridge 5.56mm Ball C77 Clipped Combined highCA 7010 Body Practice Hand Grenade highCA 7019 Mine Anti Personel Practice Nonmetallic C4 lowCA 7030 Mine Anti Personel Practice M18A1 Empty highCA 7057 Adapter Priming Mine A/P Practice M18A1 lowCA 7080 Mine Training Kit lowCA 7208 Fuze Point Detonating DM111A4 w/Booster DM 1008A1 lowCA 7213 Blasting Machine Lit ZEB/C 100S lowCA 7214 Liner C1, C/W Pins (Container Demolition C126) highCA 7216 Crimpers highCA 7499 Dummy Ctg 12 Gauge highCA 7500 Dummy Cartridge 5.56MM C80A1 Clipped highCA 7504 Display Cartridge 81mm C70A1 HE w/empty fuze DM111A4 lowCA 7506 Launcher Fired 66mm M72E5 lowCA 7507 Dummy Launcher 66mm LAW C4 highCA 7508 Dummy Cartridge 84mm C59 highCA 7513 Dummy Cartridge 7.62mm highCA 7514 Dummy Cartridge 9mm C14A1 highCA 7516 Cartridge 9mm Inspection MK 1 lowCA 7517 Dummy Cartridge Calibre .50 CAL C51 lowCA 7520 Display Cartridge 81mm Smoke L19A3 w/empty Fuze L35A1 lowCA 7530 Display Cartridge 81mm Illuminating M77 lowCA 7553 Dummy Mine A/P C10 lowCA 7554 Dummy Mine A/T C9 lowCA 7559 Dummy Guided Missile TOW C6 lowCA 7566 Dummy Grenade Hand C7 highCA 7570 Display Simulator Projectile Ground Burst C1A1 lowCA 7594 Dummy Cartridge 40mm P/N 10031C highCA 7596 Display Thunderflash C1A1 low


Annex B Canadian Army Forecasts

This annex contains forecasted expenditures for the CA reproduced from Reference [3].Lower bounds should be taken to be ≥ 0.

Table B.1: Predicted ammunition expenditures for the CA for FYs 2019 to 2021. Thenumbers reported are sorted by log guide and given as an average predicted value ± a

range derived from the 80% confidence interval.

Predictions

Log 2019 2020 2021

10 12,747 ± 16,964 14,724 ± 18,047 13,011 ± 20,71461 3,361,375 ± 577,970 3,361,375 ± 817,373 3,361,375 ± 1,001,07462 175 ± 1,919 175 ± 2,678 175 ± 3,26163 8,005,103 ± 1,204,812 8,005,103 ± 1,703,862 8,005,103 ± 2,086,79764 5,012,272 ± 688,039 5,012,272 ± 973,034 5,012,272 ± 1,191,71965 529,119 ± 204,636 529,119 ± 289,399 529,119 ± 354,44070 1,096,169 ± 306,424 1,096,169 ± 433,349 1,096,169 ± 530,74373 11,300 ± 14,910 11,300 ± 14,910 11,300 ± 14,91081 4,910 ± 49,692 4,910 ± 69,259 4,910 ± 84,27383 298,983 ± 80,948 298,983 ± 114,478 298,983 ± 140,20784 286,392 ± 75,406 286,392 ± 106,640 286,392 ± 130,60786 21,681 ± 14,009 21,681 ± 14,009 21,681 ± 14,00987 14,793 ± 10,929 16,540 ± 12,286 15,690 ± 14,77190 1,899 ± 1,242 1,899 ± 1,375 1,899 ± 1,497100 5,770,408 ± 1,345,238 5,770,408 ± 1,902,453 5,770,408 ± 2,330,020105 513,069 ± 304,713 513,069 ± 323,651 513,069 ± 341,540120 228 ± 363 388 ± 474 388 ± 637130 1,170,417 ± 412,975 1,170,417 ± 467,355 1,170,417 ± 516,035140 7,924 ± 5,878 7,924 ± 5,878 7,924 ± 5,878141 0 ± 150 466 ± 511 466 ± 511142 422 ± 600 422 ± 600 422 ± 600143 178 ± 281 503 ± 386 203 ± 364145 484 ± 685 484 ± 685 484 ± 685150 135,908 ± 10,632 115,351 ± 20,478 104,944 ± 20,503153 32,585 ± 11,541 34,256 ± 13,031 34,256 ± 20,673162 12,198 ± 4,691 9,756 ± 4,885 11,489 ± 6,143163 46,135 ± 8,359 41,251 ± 11,391 41,251 ± 11,391166 7,178 ± 5,763 7,178 ± 6,049 7,178 ± 6,322169 500 ± 1,201 500 ± 1,595 500 ± 1,898172 136,889 ± 73,734 173,661 ± 119,779 173,661 ± 129,951173 209 ± 35 209 ± 35 209 ± 35210 105,555 ± 39,979 105,555 ± 56,539 105,555 ± 69,246218 10,421 ± 4,603 10,421 ± 6,510 10,421 ± 7,974220 46,600 ± 121,618 46,600 ± 162,342 46,600 ± 193,592222 4,811 ± 8,621 8,657 ± 10,749 5,806 ± 11,055250 1,436 ± 979 1,436 ± 979 1,436 ± 979273 153,780 ± 42,056 153,780 ± 42,056 153,780 ± 42,056275 0 ± 621 0 ± 878 0 ± 1,076276 1 ± 779 1 ± 1,101 1 ± 1,349





Predictions

Log 2019 2020 2021

277 0 ± 156 0 ± 282 0 ± 396278 0 ± 301 0 ± 426 0 ± 522304 81,069 ± 33,006 81,481 ± 33,068 81,094 ± 45,402309 4,197 ± 2,929 3,205 ± 2,994 3,205 ± 3,808312 31,782 ± 13,281 31,782 ± 18,782 31,782 ± 23,004320 5,317 ± 2,220 5,266 ± 2,426 5,266 ± 2,576321 226 ± 196 226 ± 196 226 ± 196330 545 ± 569 545 ± 692 545 ± 787340 509 ± 525 509 ± 637 509 ± 723369 1,952 ± 1,893 1,952 ± 2,314 1,952 ± 2,615371 388 ± 890 388 ± 1,179 388 ± 1,400400 898 ± 790 898 ± 1,008 898 ± 1,133401 140 ± 104 140 ± 144 140 ± 160410 4,334 ± 1,828 4,334 ± 2,586 4,334 ± 3,167415 943 ± 1,341 943 ± 1,701 943 ± 1,978520 104 ± 113 104 ± 113 104 ± 113560 0 ± 4,363 0 ± 6,171 0 ± 7,558570 16,665 ± 8,716 16,665 ± 12,327 16,665 ± 15,097590 1,276 ± 307 1,251 ± 314 1,271 ± 404640 1,943 ± 362 1,943 ± 513 1,943 ± 628700 1,802 ± 237 1,802 ± 237 1,802 ± 237712 50 ± 30 50 ± 32 50 ± 35720 5,004 ± 1,756 5,744 ± 2,025 5,744 ± 2,025730 277 ± 192 277 ± 192 277 ± 192740 635 ± 226 667 ± 226 667 ± 295800 7,631 ± 2,543 7,294 ± 2,759 7,489 ± 3,363805 12,163 ± 2,484 12,416 ± 2,506 12,416 ± 3,499811 0 ± 342 21 ± 598 104 ± 740820 22,064 ± 8,305 21,607 ± 9,304 21,833 ± 11,197822 5,822 ± 2,518 5,822 ± 3,562 5,822 ± 4,362840 2,037 ± 2,926 2,037 ± 2,926 2,037 ± 2,926870 141 ± 490 597 ± 889 597 ± 8891030 200 ± 186 200 ± 186 200 ± 1861050 80 ± 36 80 ± 36 80 ± 361060 5 ± 251 5 ± 355 5 ± 4341071 69 ± 1,292 69 ± 1,813 69 ± 2,2131081 271 ± 1,194 194 ± 1,294 230 ± 1,5521120 175 ± 297 175 ± 542 175 ± 6961140 18,200 ± 4,301 18,200 ± 6,083 18,200 ± 7,4501160 4,444 ± 1,440 4,712 ± 1,532 4,541 ± 1,8901170 5,533 ± 1,865 5,533 ± 2,082 5,533 ± 2,2791180 5,860 ± 1,618 5,977 ± 1,875 5,929 ± 2,2411190 5,624 ± 1,480 5,624 ± 2,093 5,624 ± 2,5631210 5,413 ± 6,945 5,413 ± 6,945 5,413 ± 6,945





Predictions

Log 2019 2020 2021

1220 0 ± 241 0 ± 340 0 ± 4171250 902 ± 2,856 902 ± 3,852 902 ± 4,6171270 44 ± 65 29 ± 99 29 ± 1531290 13,827 ± 4,156 13,827 ± 5,878 13,827 ± 7,1991340 1,656 ± 600 1,656 ± 849 1,656 ± 1,0401345 28 ± 29 28 ± 36 28 ± 411347 1 ± 4 0 ± 3 0 ± 41350 144 ± 156 150 ± 190 121 ± 2391362 23,216 ± 5,252 23,216 ± 11,378 23,216 ± 15,2091370 3,856 ± 1,163 4,076 ± 1,225 3,929 ± 1,5241380 8,007 ± 11,234 8,007 ± 14,229 8,007 ± 16,5271390 25,215 ± 4,521 25,215 ± 6,393 25,215 ± 7,8301420 423 ± 268 423 ± 379 423 ± 4431421 0 ± 225 0 ± 318 0 ± 3901430 329 ± 362 360 ± 379 333 ± 4321440 42 ± 47 42 ± 47 42 ± 471500 2,835 ± 633 2,835 ± 896 2,835 ± 1,0971530 82 ± 95 82 ± 118 82 ± 1351531 624 ± 394 643 ± 430 632 ± 5231550 140 ± 93 145 ± 97 142 ± 1221571 269 ± 590 269 ± 590 269 ± 5901575 2,726 ± 617 3,225 ± 616 3,065 ± 7841580 2,400 ± 1,499 2,116 ± 1,642 2,273 ± 1,9931582 1,449 ± 645 293 ± 469 1,001 ± 6791584 469 ± 274 469 ± 274 469 ± 2741590 7,538 ± 1,351 7,538 ± 2,926 7,538 ± 3,9121592 662 ± 1,086 662 ± 1,400 662 ± 1,6401630 89 ± 41 89 ± 41 89 ± 411645 2,228 ± 1,086 3,087 ± 1,480 3,087 ± 1,4801646 0 ± 73 0 ± 103 0 ± 1261647 801 ± 229 771 ± 255 787 ± 3081656 324 ± 165 324 ± 165 324 ± 1651657 104 ± 85 104 ± 85 104 ± 851680 128 ± 35 181 ± 38 153 ± 421690 753 ± 812 731 ± 855 742 ± 9601700 46,577 ± 18,317 46,577 ± 25,904 46,577 ± 31,7261701 47,618 ± 15,853 26,549 ± 21,604 26,549 ± 21,6041702 176 ± 99 100 ± 117 100 ± 1171710 16,796 ± 7,439 16,796 ± 8,261 16,796 ± 9,0081711 4,015 ± 3,852 4,015 ± 3,852 4,015 ± 3,8521720 38 ± 782 38 ± 1,098 38 ± 1,3411730 1,052 ± 926 533 ± 950 533 ± 1,4001740 1,713 ± 482 1,546 ± 498 1,669 ± 6321750 351 ± 210 318 ± 224 318 ± 246





Predictions

Log 2019 2020 2021

1760 6,417 ± 3,312 6,417 ± 3,312 6,417 ± 3,3121780 51 ± 5 53 ± 6 53 ± 71910 14 ± 97 14 ± 135 14 ± 1641921 777 ± 384 408 ± 388 728 ± 7501940 10 ± 55 10 ± 75 10 ± 911981 0 ± 120 0 ± 170 0 ± 2081982 0 ± 131 0 ± 186 0 ± 2281983 0 ± 151 0 ± 214 0 ± 2621984 0 ± 91 0 ± 226 0 ± 3101985 76 ± 111 76 ± 111 76 ± 1111992 483 ± 70 497 ± 131 505 ± 1861993 429 ± 67 436 ± 82 436 ± 1321994 343 ± 103 343 ± 146 343 ± 1792318 2 ± 1 2 ± 1 2 ± 12525 1 ± 1 1 ± 1 1 ± 13740 250 ± 93 235 ± 102 243 ± 1244041 14 ± 23 14 ± 30 14 ± 354171 35 ± 46 35 ± 46 35 ± 464306 22 ± 8 22 ± 8 22 ± 84307 53 ± 13 47 ± 14 47 ± 195320 112 ± 16 129 ± 24 90 ± 285960 7,388,646 ± 1,034,430 7,388,646 ± 2,199,914 7,388,646 ± 2,934,1437010 186 ± 177 186 ± 218 186 ± 2477019 33 ± 44 33 ± 44 33 ± 447030 0 ± 20 0 ± 14 0 ± 207057 35 ± 54 35 ± 54 35 ± 547080 0 ± 1 0 ± 1 0 ± 17208 37 ± 34 37 ± 34 37 ± 347213 1 ± 1 1 ± 1 1 ± 17214 1 ± 8 2 ± 8 1 ± 117216 0 ± 6 0 ± 10 0 ± 107499 53 ± 77 88 ± 113 88 ± 1137500 3,089 ± 2,922 3,089 ± 2,922 3,089 ± 2,9227504 1 ± 2 1 ± 2 1 ± 27506 129 ± 187 129 ± 187 129 ± 1877507 77 ± 96 62 ± 90 73 ± 1127508 19 ± 18 19 ± 18 19 ± 187513 1,851 ± 1,725 2,396 ± 2,351 2,396 ± 2,3517514 404 ± 445 404 ± 445 404 ± 4457516 59 ± 48 59 ± 48 59 ± 487517 628 ± 657 628 ± 657 628 ± 6577520 1 ± 1 1 ± 1 1 ± 17530 1 ± 1 1 ± 1 1 ± 17553 4 ± 6 4 ± 6 4 ± 6





Predictions

Log 2019 2020 2021

7554 2 ± 4 2 ± 4 2 ± 47559 10 ± 10 10 ± 10 10 ± 107566 147 ± 108 147 ± 108 147 ± 1087570 3 ± 2 3 ± 2 3 ± 27594 52 ± 43 52 ± 43 52 ± 437596 4 ± 3 4 ± 3 4 ± 3


Annex C Royal Canadian Air Force forecasts

This annex contains forecasted expenditures for the RCAF reproduced from Reference [3].Lower bounds should be taken to be ≥ 0.

Table C.1: Predicted ammunition expenditures for the RCAF for FYs 2019 to 2021. Thenumbers reported are sorted by log guide and given as an average predicted value ± a


Predictions

Log 2019 2020 2021

61 14,300 ± 11,207 14,300 ± 11,207 14,300 ± 11,20763 97,040 ± 86,512 97,040 ± 95,070 97,040 ± 99,97964 2,093 ± 2,099 2,093 ± 2,099 2,093 ± 2,09965 4,365 ± 4,832 4,365 ± 4,832 4,365 ± 4,83270 176,406 ± 34,827 176,406 ± 49,253 176,406 ± 60,32372 33,896 ± 46,900 33,896 ± 46,900 33,896 ± 46,90073 10,578 ± 10,757 10,578 ± 10,757 10,578 ± 10,75781 2,652 ± 2,685 2,652 ± 2,685 2,652 ± 2,68583 1,689 ± 1,643 1,689 ± 1,643 1,689 ± 1,64390 269 ± 251 269 ± 251 269 ± 251100 394,550 ± 162,468 394,550 ± 173,493 394,550 ± 183,858105 17,343 ± 18,984 17,343 ± 18,984 17,343 ± 18,984130 4,252 ± 3,332 6,709 ± 3,748 7,379 ± 4,079162 701 ± 458 632 ± 499 671 ± 607163 1,239 ± 1,026 1,239 ± 1,345 1,239 ± 1,508166 825 ± 530 825 ± 750 825 ± 872169 323 ± 445 323 ± 445 323 ± 445170 310 ± 387 565 ± 475 362 ± 488172 99 ± 80 99 ± 80 99 ± 80173 926 ± 327 926 ± 327 926 ± 327210 65 ± 26 65 ± 26 65 ± 26218 225 ± 110 225 ± 110 225 ± 110220 51,475 ± 24,083 42,841 ± 32,312 42,841 ± 32,3121140 526 ± 318 526 ± 318 526 ± 3181160 32 ± 37 48 ± 52 48 ± 521170 37 ± 26 66 ± 33 44 ± 361180 45 ± 44 45 ± 44 45 ± 441190 35 ± 24 35 ± 24 35 ± 241250 28 ± 32 28 ± 32 28 ± 321290 234 ± 237 234 ± 287 234 ± 3261362 0 ± 36 127 ± 142 127 ± 1421370 17 ± 16 17 ± 16 17 ± 161380 192 ± 150 192 ± 150 192 ± 1501390 197 ± 102 197 ± 102 197 ± 1021420 303 ± 427 303 ± 427 303 ± 4271421 6,347 ± 2,351 2,647 ± 3,732 3,711 ± 4,4721430 15 ± 20 15 ± 20 15 ± 201500 467 ± 204 467 ± 204 467 ± 2041530 90 ± 42 95 ± 47 92 ± 57





Predictions

Log 2019 2020 2021

1531 142 ± 104 147 ± 142 147 ± 1421550 15 ± 15 15 ± 15 15 ± 151570 0 ± 32 0 ± 38 0 ± 381575 154 ± 111 172 ± 111 172 ± 1511580 169 ± 131 169 ± 131 169 ± 1311582 40 ± 33 40 ± 33 40 ± 331584 34 ± 42 34 ± 42 34 ± 421590 756 ± 251 931 ± 312 767 ± 3981592 15 ± 9 15 ± 9 15 ± 91645 451 ± 619 451 ± 619 451 ± 6191656 114 ± 69 114 ± 98 114 ± 1171657 13 ± 17 6 ± 14 12 ± 201690 24 ± 21 24 ± 21 24 ± 211700 2,935 ± 1,526 2,935 ± 1,526 2,935 ± 1,5261701 243 ± 224 243 ± 224 243 ± 2241702 87 ± 112 87 ± 112 87 ± 1121710 2,946 ± 1,489 2,946 ± 1,619 2,946 ± 1,7401730 26 ± 38 26 ± 38 26 ± 381740 82 ± 75 82 ± 75 82 ± 751750 58 ± 62 58 ± 62 58 ± 621910 21 ± 28 21 ± 28 21 ± 281921 38 ± 25 17 ± 21 29 ± 291940 17 ± 13 17 ± 13 17 ± 131981 0 ± 8 0 ± 12 0 ± 151982 13 ± 13 13 ± 13 13 ± 131983 3 ± 9 1 ± 9 2 ± 121984 14 ± 14 14 ± 14 14 ± 141985 1 ± 11 0 ± 12 1 ± 153012 13 ± 15 13 ± 15 13 ± 153580 8 ± 6 8 ± 6 8 ± 63740 86 ± 51 86 ± 51 86 ± 514041 8 ± 9 16 ± 16 16 ± 164175 6 ± 3 6 ± 3 6 ± 34177 11 ± 12 11 ± 12 11 ± 125016 79,199 ± 63,708 67,600 ± 79,848 66,898 ± 80,6035065 77 ± 56 85 ± 89 61 ± 795070 6 ± 60 6 ± 84 6 ± 1035073 66 ± 77 66 ± 77 66 ± 775076 25 ± 128 25 ± 176 25 ± 2135078 170 ± 131 213 ± 179 213 ± 1795081 13 ± 17 13 ± 17 13 ± 175082 162 ± 98 136 ± 134 136 ± 1345084 92 ± 58 148 ± 70 140 ± 715086 26 ± 30 59 ± 49 59 ± 49





Predictions

Log 2019 2020 2021

5087 2 ± 2 2 ± 2 2 ± 25089 52 ± 55 52 ± 55 52 ± 555091 55 ± 80 55 ± 102 55 ± 1195095 58 ± 34 58 ± 48 58 ± 585099 43 ± 51 43 ± 51 43 ± 515111 341 ± 124 371 ± 136 355 ± 1655131 759 ± 255 570 ± 348 570 ± 3485160 62 ± 66 66 ± 83 66 ± 835214 6 ± 8 6 ± 8 6 ± 85216 7 ± 10 7 ± 10 7 ± 105220 183 ± 150 183 ± 150 183 ± 1505230 610 ± 694 610 ± 694 610 ± 6945241 158 ± 921 74 ± 969 118 ± 1,1855243 7 ± 3 7 ± 3 7 ± 35246 38 ± 30 38 ± 30 38 ± 305261 91 ± 69 91 ± 69 91 ± 695262 29 ± 7 29 ± 7 29 ± 75265 12 ± 16 12 ± 16 12 ± 165280 3,885 ± 1,058 3,885 ± 1,058 3,885 ± 1,0585290 399 ± 133 399 ± 188 399 ± 2315300 16 ± 5 16 ± 5 16 ± 55305 588 ± 382 588 ± 382 588 ± 3825306 467 ± 436 467 ± 436 467 ± 4365310 16 ± 17 16 ± 17 16 ± 175311 65 ± 32 65 ± 45 65 ± 555320 1,338 ± 242 1,332 ± 246 1,332 ± 3115327 249 ± 90 249 ± 90 249 ± 905328 280 ± 85 317 ± 88 264 ± 1035330 118 ± 229 118 ± 300 118 ± 3545331 944 ± 823 944 ± 823 944 ± 8235333 1,514 ± 1,762 1,514 ± 1,762 1,514 ± 1,7625335 32,566 ± 12,459 32,566 ± 17,620 32,566 ± 21,5805336 6,477 ± 4,458 8,178 ± 4,461 5,605 ± 5,6905337 49,919 ± 24,205 50,202 ± 28,152 59,931 ± 28,4655340 7,090 ± 3,354 6,660 ± 3,448 6,987 ± 4,4075341 2,879 ± 2,407 2,879 ± 3,141 2,879 ± 3,5245342 2,149 ± 2,308 2,149 ± 2,308 2,149 ± 2,3085344 3,810 ± 3,697 3,810 ± 3,697 3,810 ± 3,6975345 27,439 ± 12,729 27,439 ± 18,001 27,439 ± 22,0475346 0 ± 1,584 0 ± 2,241 0 ± 2,7455347 0 ± 3,456 0 ± 8,518 0 ± 11,7035349 541 ± 207 357 ± 278 357 ± 2785352 873 ± 560 873 ± 560 873 ± 5605353 888 ± 358 628 ± 488 628 ± 488





Predictions

Log 2019 2020 2021

5354 79 ± 45 72 ± 45 90 ± 575356 0 ± 50 0 ± 70 0 ± 865357 152 ± 97 152 ± 97 152 ± 975358 357 ± 154 290 ± 207 290 ± 2075359 136 ± 92 136 ± 92 136 ± 925380 845 ± 768 845 ± 768 845 ± 7685382 403 ± 218 428 ± 293 428 ± 2935383 602 ± 99 254 ± 151 220 ± 1565400 9 ± 8 9 ± 8 9 ± 85401 45 ± 55 45 ± 55 45 ± 555405 0 ± 41 0 ± 57 0 ± 715407 12 ± 17 12 ± 17 12 ± 175960 419,703 ± 81,650 419,703 ± 115,470 419,703 ± 141,4226002 7 ± 12 7 ± 12 7 ± 126012 22 ± 25 22 ± 25 22 ± 256013 22 ± 22 22 ± 22 22 ± 226016 1 ± 2 1 ± 2 1 ± 26030 41 ± 58 41 ± 58 41 ± 586031 70 ± 81 70 ± 81 70 ± 816032 5 ± 6 5 ± 6 5 ± 66035 17 ± 24 17 ± 24 17 ± 246040 12 ± 13 12 ± 13 12 ± 136047 4 ± 7 4 ± 7 4 ± 76052 7 ± 9 7 ± 9 7 ± 96053 25 ± 24 25 ± 24 25 ± 246059 3 ± 2 3 ± 2 3 ± 26061 24 ± 34 24 ± 34 24 ± 346065 3 ± 2 3 ± 2 3 ± 26068 4 ± 4 4 ± 4 4 ± 46070 2 ± 2 2 ± 2 2 ± 26071 2 ± 2 2 ± 2 2 ± 26073 3 ± 2 3 ± 2 3 ± 26079 0 ± 1 0 ± 1 0 ± 16080 0 ± 0 0 ± 0 0 ± 06081 0 ± 0 0 ± 0 0 ± 06082 1 ± 1 1 ± 1 1 ± 16083 1 ± 1 1 ± 1 1 ± 16085 0 ± 0 0 ± 0 0 ± 06086 0 ± 0 0 ± 0 0 ± 06087 1 ± 1 1 ± 1 1 ± 16093 0 ± 0 0 ± 0 0 ± 06094 0 ± 0 0 ± 0 0 ± 06139 0 ± 1 0 ± 1 0 ± 16144 4 ± 4 4 ± 4 4 ± 4





Predictions

Log 2019 2020 2021

6154 9 ± 10 9 ± 10 9 ± 106155 10 ± 12 10 ± 12 10 ± 126156 7 ± 8 7 ± 8 7 ± 86157 0 ± 3 0 ± 13 0 ± 206158 10 ± 9 6 ± 9 6 ± 96159 1 ± 2 1 ± 2 1 ± 26163 16 ± 21 16 ± 21 16 ± 216166 2 ± 2 2 ± 2 2 ± 26168 1 ± 2 1 ± 2 1 ± 26172 8 ± 5 7 ± 7 7 ± 76178 5 ± 5 5 ± 5 5 ± 56193 6 ± 7 6 ± 7 6 ± 76217 7 ± 7 7 ± 7 7 ± 76233 6 ± 7 6 ± 7 6 ± 76289 4 ± 2 4 ± 2 4 ± 26318 4 ± 2 4 ± 2 4 ± 26319 12 ± 12 12 ± 12 12 ± 126330 14 ± 26 14 ± 27 14 ± 276333 55 ± 83 55 ± 83 55 ± 836335 14 ± 21 14 ± 21 14 ± 216336 28 ± 41 28 ± 41 28 ± 416339 23 ± 29 23 ± 29 23 ± 296350 8 ± 13 8 ± 13 8 ± 137010 27 ± 28 27 ± 28 27 ± 287500 817 ± 474 817 ± 474 817 ± 4747513 354 ± 399 354 ± 399 354 ± 3997514 110 ± 41 110 ± 41 110 ± 417517 207 ± 213 207 ± 213 207 ± 2137566 22 ± 29 22 ± 29 22 ± 299015 70 ± 107 70 ± 107 70 ± 1079523 2,662 ± 1,298 2,662 ± 1,298 2,662 ± 1,298


Annex D Royal Canadian Navy forecasts

This annex contains forecasted expenditures for the RCN reproduced from Reference [3].Lower bounds should be taken to be ≥ 0.

Table D.1: Predicted ammunition expenditures for the RCN for FYs 2019 to 2021. Thenumbers reported are sorted by log guide and given as an average predicted value ± a


Predictions

Log 2019 2020 2021

61 1,000 ± 5,045 1,000 ± 6,928 1,000 ± 8,37363 209,582 ± 103,199 209,582 ± 145,946 209,582 ± 178,74664 22,721 ± 5,673 12,817 ± 8,353 12,123 ± 8,71665 109,396 ± 46,258 109,396 ± 65,419 109,396 ± 80,12170 516,842 ± 125,796 516,842 ± 177,903 516,842 ± 217,88672 0 ± 7,214 0 ± 7,690 0 ± 9,47573 30,618 ± 32,431 30,618 ± 32,431 30,618 ± 32,43180 30 ± 205 30 ± 284 30 ± 34581 21,019 ± 11,868 21,019 ± 16,784 21,019 ± 20,55683 72,416 ± 17,648 90,272 ± 19,419 90,272 ± 29,86684 0 ± 17,249 0 ± 24,394 0 ± 29,87785 4,784 ± 11,302 4,784 ± 14,993 4,784 ± 17,825100 25,664 ± 33,067 25,664 ± 33,067 25,664 ± 33,067162 150 ± 2,523 150 ± 3,537 150 ± 4,315163 266 ± 170 266 ± 170 266 ± 170220 116,381 ± 23,590 114,218 ± 23,669 116,203 ± 32,185240 6,342 ± 6,640 6,342 ± 6,640 6,342 ± 6,640250 45,601 ± 8,320 45,601 ± 11,767 45,601 ± 14,411712 138 ± 109 138 ± 109 138 ± 1091160 14 ± 72 19 ± 84 14 ± 811170 57 ± 83 50 ± 94 54 ± 961180 72 ± 86 72 ± 86 72 ± 861190 128 ± 95 128 ± 95 128 ± 951362 931 ± 121 721 ± 243 612 ± 2671380 0 ± 179 0 ± 253 0 ± 3101390 232 ± 87 232 ± 87 232 ± 871500 678 ± 197 428 ± 201 630 ± 2611531 144 ± 46 103 ± 47 97 ± 581575 418 ± 187 482 ± 216 498 ± 2171580 363 ± 178 363 ± 178 363 ± 1781582 317 ± 261 317 ± 261 317 ± 2611584 115 ± 79 115 ± 79 115 ± 791590 2,568 ± 637 2,568 ± 901 2,568 ± 1,1041592 509 ± 106 379 ± 196 202 ± 1971656 6 ± 14 1 ± 12 4 ± 131657 35 ± 30 35 ± 30 35 ± 301700 12,941 ± 5,772 12,941 ± 5,772 12,941 ± 5,7721701 5,465 ± 5,635 7,464 ± 6,293 6,301 ± 6,9881710 2,785 ± 813 2,785 ± 813 2,785 ± 813



Table D.1: Predicted ammunition expenditures for the RCN for FYs 2019 to 2021. Thenumbers reported are sorted by log guide and given as an average predicted value ± a


Predictions

Log 2019 2020 2021

1711 714 ± 341 992 ± 341 653 ± 4511740 370 ± 160 370 ± 226 370 ± 2771750 104 ± 76 104 ± 76 104 ± 761760 0 ± 204 0 ± 289 0 ± 3541981 27 ± 37 27 ± 37 27 ± 371982 27 ± 22 27 ± 22 27 ± 221983 29 ± 20 29 ± 20 29 ± 201984 32 ± 34 32 ± 34 32 ± 341985 8 ± 7 8 ± 7 8 ± 71996 57 ± 51 57 ± 51 57 ± 513001 1,007 ± 1,003 1,007 ± 1,003 1,007 ± 1,0033002 0 ± 504 0 ± 713 0 ± 8733015 60 ± 26 56 ± 29 58 ± 353016 15 ± 11 15 ± 15 15 ± 173025 5 ± 6 5 ± 6 5 ± 63026 1 ± 1 1 ± 1 1 ± 13092 92 ± 107 92 ± 133 92 ± 1533122 594 ± 473 594 ± 473 594 ± 4733124 228 ± 241 228 ± 241 228 ± 2413125 176 ± 198 176 ± 198 176 ± 1983126 0 ± 229 0 ± 324 0 ± 3973160 2,626 ± 1,566 1,731 ± 1,660 2,311 ± 2,0533161 97 ± 109 97 ± 109 97 ± 1093165 384 ± 444 384 ± 549 384 ± 6293170 2,796 ± 1,194 2,796 ± 1,194 2,796 ± 1,1943175 229 ± 121 209 ± 164 209 ± 1643214 22,397 ± 11,352 22,397 ± 16,055 22,397 ± 19,6633230 141 ± 167 141 ± 167 141 ± 1673232 41 ± 44 41 ± 44 41 ± 443233 151 ± 219 151 ± 219 151 ± 2193235 4 ± 2 4 ± 2 4 ± 23325 79 ± 29 79 ± 42 79 ± 513540 34 ± 31 34 ± 31 34 ± 313561 1,193 ± 1,165 1,193 ± 1,165 1,193 ± 1,1653580 331 ± 193 331 ± 203 331

forecasting training ammunition requirements across the … · 2020. 5. 11. · historical...

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