everett fire department data analysis 2009 & 2012

City of Everett Fire Department Data Analysis (2009 & 2012)

Phil Engel / … / …

Math 370: Statistics for Engineers

December 11th, 2015

General Statistics for Response Times:

2009 (h:mm:ss) 2012 (h:mm:ss)Min. Response Time 0:00:00 0:00:00Max. Response Time 0:29:55 0:29:57Mean (Average) Response Time 0:05:43 0:06:07Median 0:05:12 0:05:30Standard Deviation 0:03:10 0:03:19Variance 0:10:00 0:10:59

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Table of ContentsAbstract:.........................................................................................................................................................3

Project Inception........................................................................................................................................3

Design of Experiments....................................................................................................................................4

Analysis of DOE...........................................................................................................................................4

Regression Analysis: Response Time vs. TOD and Year...............................................................................6

Interactions of Factors................................................................................................................................7

Extra: Response Times vs. Populaton Growth............................................................................................8

Conclusions of DOE...................................................................................................................................10

Appendix A...................................................................................................................................................11

Glossary....................................................................................................................................................11

Appendix B....................................................................................................................................................12

Years 2008-2013 Average Response Times...............................................................................................12

Appendix C....................................................................................................................................................13

Anova Analysis Figures..............................................................................................................................13

Appendix D...................................................................................................................................................18

DOE Analysis Graphs and Data..................................................................................................................18

Works Cited..................................................................................................................................................19

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Abstract:The purpose of this document is to provide statistical analysis of the Everett Fire Department response time data. Initiation of this project began by parsing the EFD response time data from the years 2007-2013. After sorting the data it was determined that the years 2006 and 2007 were unreliable data and thus they were then excluded from the project. After determination of the appropriate variance in order to ensure randomization in all of the samples, final analysis was performed on years 2009 and 2012, months of April and December, times of day morning, midday and evening, and the station response times inside and outside of the EFD fire zones. The tests performed were: an ANOVA (analysis of variance), a D.O.E. (Design of Experiments), an analysis of the station response times from inside and outside of the zones, and graphical interpretation of subsidiary data. The analysis was performed using the statistical analysis software Minitab.

Project InceptionAfter sorting the data there were several questions that needed answers. The first question asked was what are the independent and dependent variables? The dependent variable was clearly chosen to be the response time. By soft analyzing the data and through discussion with the Everett Fire Department, the independent variables were chosen to be Year, Month, and Time of Day. An additional statistical analysis was performed on individual fire stations and the zones they were in.

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Design of ExperimentsAfter performing an ANOVA analysis to determine the best years, months, and times of the day to use based on the variances and high and low values of the average response times, a Design of Experiments test can now be performed to find out what were the significant factors and what kind of effect they have on the response time data. Design of Experiments can help conclude which factors are the most significant in affecting the response time and if there are any direct relationships or interactions between all of the factors chosen from the analysis.

The Year, Month, and Time of Day were chosen as particular factors that affected the overall response time of Everett Fire Department. This is the table of how the DOE was broken down:

Factors (+) (-)

Year 2012 2009

Month April December

Time of Day Morning Afternoon

After determining that factors and each level for each factor, an experiment could now be performed. A ½ fractional factorial design was used as it minimized the amount of data points required. Here is a figure 1 shows the factorial design treatment combinations (randomized) and the corresponding data response times.

Figure 1 – Treatment combinations for the DOE experiment

Analysis of DOETwo example factors that are the biggest effects from the analysis of variance can be calculated by the equation:MainEffect (Wheren=number of replicates ):

A= 12n [a+ab−b−(1 ) ]B= 1

2n[b+ab−a−(1 )]

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The DOE results were as follows:

Coded Coefficients

Term Effect Coef Coef T-Value P-Value VIFConstant 5.987 * * *Year 0.4752 0.2376 * * * 1.00Month -0.03325 -0.01662 * * * 1.00TOD 0.3498 0.1749 * * * 1.00Year*Month 0.08325 0.04163 * * * 1.00Year*TOD -0.11675 -0.05837 * * * 1.00Month*TOD -0.10825 -0.05413 * * * 1.00Year*Month*TOD -0.12475 -0.06237 * * * 1.00

From these results, it can be concluded that Year and TOD (Time of Day) were numerically the largest effects in the factorial analysis of the response times. This can also be seen in the Pareto Chart that compares the effects and different treatment combination effects.

None of the combinations between the Year, Month, or TOD had a large effect on the response time data.

Since there were graphical and numerical conclusions that Year and TOD had the largest effects on the data, a regression analysis could now be performed to find out the accuracy in concluding that these are in fact affect-able factors in the response data. The regression analysis data table is as follows:

Regression Analysis: Response Time vs. TOD and Year

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Analysis of Variance

Source DF Seq SS Contribution Adj SS Adj MS F-Value P-ValueRegression 2 0.69638 87.67% 0.69638 0.34819 17.78 0.005 TOD 1 0.24465 30.80% 0.24465 0.24465 12.50 0.017 Year 1 0.45173 56.87% 0.45173 0.45173 23.07 0.005Error 5 0.09789 12.33% 0.09789 0.01958 Lack-of-Fit 1 0.02726 3.43% 0.02726 0.02726 1.54 0.282 Pure Error 4 0.07063 8.89% 0.07063 0.01766Total 7 0.79427 100.00%

Model Summary

S R-sq R-sq(adj) PRESS R-sq(pred)0.139925 87.67% 82.74% 0.250610 68.45%

Coefficients

Term Coef SE Coef 95% CI T-Value P-Value VIF Constant 5.9874 0.0495 (5.8602, 6.1145) 121.03 0.000TOD 0.1749 0.0495 (0.0477, 0.3020) 3.53 0.017 1.00Year 0.2376 0.0495 (0.1105, 0.3648) 4.80 0.005 1.00

Regression Equation

Response Time = 5.9874 + 0.1749 TOD + 0.2376 Year

As seen in the results, the T-Value has a high value and both the TOD and Year P-Values are less than .05 (with a selected alpha of .05), fitting the 95% confidence interval that these two factors have a significant effect on the response time.

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Interactions of FactorsA secondary analysis of the factors chosen could be to analyze interaction plots between the three factors. This tells us if any of the factors have an interaction with each other and if that is the case, a conclusion can be drawn. Here is the matrix plot of interactions between the factors Year, Month, and Time of Day.

There is direct interaction with Month and the Year as observed. What this could represent in an applicable style is that if continuing years are showing predictable data, then it can be concluded that the months within those years will also be normal/predictable. This could be beneficial for the Everett Fire Department if they are interested in scheduling firefighters in accordance with historically low or high months, in order to maximize their response efficiency.

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Extra: Response Times vs. Populaton Growth

It was interesting to note that the average response times per time of day were typically consistent with each other, minus the outlier of the response times in the afternoon of 2012. This could have been due to a data entry error however.

Another interesting note to mention is that when graphing the total population of Everett per year vs. the response time per year, the response times seemed to have a trailing and cubic effect against the population growth, significant seen after about 1-2 years after a large jump in population.

2007 2008 2009 2010 2011 2012 2013 20144.00

4.50

5.00

5.50

6.00

6.50

7.00

Comparison of Response Time with Time of Day

4pm-12am (Afternoon) 12am-8am (Morning)8am-4pm (Midday)

Tim

e (m

ins)

2007 2008 2009 2010 2011 2012 2013 20145.50

5.60

5.70

5.80

5.90

6.00

6.10

6.20

94000

96000

98000

100000

102000

104000

106000

Response Time and Population Growth

Average Reponse Time Per Year

Population Per Year

Tim

e (m

ins)

Popu

latio

n

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0 1 2 3 4 5 6 7 8 9 10 11 125.005.105.205.305.405.505.605.705.805.906.006.106.206.306.406.506.60

Responses Times per Month per Year

2008 2009 2010 2011 2012 2013

Month in Numbers

Resp

onse

Tim

e

Response Times per Month per Year had no significant observable patterns. This appears to be the most scattered data that was displayed over the course of the 5 years analyzed.

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Conclusions of DOEFrom the DOE test, it can be concluded that the year and months have strong interaction with each other. This means that if the year is following to be predictable in average response times, then the months concluding that year will also be predictable based on historical high and low months. An additional point to note is that the Time of Day that the Year that responses take place are the most significant effects and factors for response times, which mean that the Everett Fire Department should assign firefighters based on the average response time for the year up to date, and focus more on how to implement efficient scheduling based on specific times of the day rather than an arbitrary shift that crosses over the times analyzed (12am-12pm, 12pm-12am)

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Appendix A

Glossary

ANOVA – Analysis of variance, this refers to a procedure that uses the F statistic to test the statistical differences among the average values of two or more random samples of a population of data.

DOE – Design of experiment, a procedure for eliminating insignificant test variables to reveal and properly analyze the significant variables and their reactions.

F value – When used in the ANOVA, the obtained value of F provides a test for the statistical significance of the observed differences among the means of two or more random samples.

P value – The probability of the hypothesis being tested to be true.

Regression – In a graph with data points plotted from the horizontal and vertical values the regression is a line that predicts the vertical values for a given horizontal value.

Pairwise – Coupled together with another value

Factor – The value(s) chosen in a plot to perform a DOE on.

EFD – Everett Fire Department

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Appendix B

Years 2008-2013 Average Response Times

Year Overall Mean[h:mm:ss]

12am-8am (Morning)[in Mins.]

8am-4pm (Midday)[in Mins.]

4pm-12am (Afternoon)[in Mins.]

2008 0:05:48 6.483 5.550 5.7002009 0:05:43 6.483 5.400 5.6332010 0:05:45 6.467 5.467 5.6832011 0:05:51 6.550 5.733 5.6672012 0:06:07 6.717 5.917 6.8172013 0:05:58 6.667 5.767 5.817

Appendix C

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Anova Analysis FiguresOne-way ANOVA: 2008-2013

Method

Null hypothesis All means are equalAlternative hypothesis At least one mean is differentSignificance level α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels ValuesFactor 6 2013, 2012, 2011, 2010, 2009, 2008

Analysis of Variance of the Years

Source DF Adj SS Adj MS F-Value P-ValueFactor 5 0.9299 0.18599 5.44 0.000Error 66 2.2567 0.03419Total 71 3.1867

Model Summary

S R-sq R-sq(adj) R-sq(pred)0.184912 29.18% 23.82% 15.72%

Means

Factor N Mean StDev 95% CI2013 12 5.9597 0.1298 (5.8531, 6.0663)2012 12 6.0306 0.2989 (5.9240, 6.1371)2011 12 5.8583 0.0815 (5.7518, 5.9649)2010 12 5.7472 0.1468 (5.6406, 5.8538)2009 12 5.7111 0.0854 (5.6045, 5.8177)2008 12 5.7958 0.2520 (5.6893, 5.9024)

Pooled StDev = 0.184912

One-way ANOVA: 4pm-12am, 12am-8am, 8am-4pm

Method



Factor Information

Factor Levels ValuesFactor 3 4pm-12am, 12am-8am, 8am-4pm

Analysis of Variance Time of Day

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Model Summary


Means

Factor N Mean StDev 95% CI4pm-12am 6 5.886 0.460 ( 5.629, 6.143)12am-8am 6 6.5611 0.1063 (6.3038, 6.8185)8am-4pm 6 5.6389 0.1985 (5.3815, 5.8962)

Pooled StDev = 0.295757One-way ANOVA: Months

* NOTE * Cannot draw the interval plot for the Tukey procedure. Interval plots for comparisons are illegible with more than 45 intervals.

Method



Factor Information

Factor Levels ValuesFactor 12 Jan, Feb, March, April, May, June, July, Aug, sept, Oct, Nov, Dec

Analysis of Variance


Model Summary


Means

Factor N Mean StDev 95% CIJan 6 5.9889 0.2128 (5.8095, 6.1683)Feb 6 5.8222 0.0841 (5.6428, 6.0016)March 6 5.7361 0.1665 (5.5567, 5.9155)April 6 5.867 0.246 ( 5.687, 6.046)May 6 5.7861 0.2141 (5.6067, 5.9655)June 6 5.8167 0.1517 (5.6373, 5.9961)

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July 6 5.8278 0.2059 (5.6484, 6.0072)Aug 6 5.8333 0.1680 (5.6539, 6.0127)sept 6 5.8250 0.2046 (5.6456, 6.0044)Oct 6 5.8806 0.2115 (5.7012, 6.0599)Nov 6 5.9222 0.1277 (5.7428, 6.1016)Dec 6 5.900 0.443 ( 5.721, 6.079)

Pooled StDev = 0.219673

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor N Mean GroupingJan 6 5.9889 ANov 6 5.9222 ADec 6 5.900 AOct 6 5.8806 AApril 6 5.867 AAug 6 5.8333 AJuly 6 5.8278 Asept 6 5.8250 AFeb 6 5.8222 AJune 6 5.8167 AMay 6 5.7861 AMarch 6 5.7361 A

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference of Difference SE of AdjustedLevels of Means Difference 95% CI T-Value P-ValueFeb - Jan -0.167 0.127 (-0.598, 0.265) -1.31 0.974March - Jan -0.253 0.127 (-0.684, 0.179) -1.99 0.696April - Jan -0.122 0.127 (-0.554, 0.309) -0.96 0.998May - Jan -0.203 0.127 (-0.634, 0.229) -1.60 0.903June - Jan -0.172 0.127 (-0.604, 0.259) -1.36 0.967July - Jan -0.161 0.127 (-0.592, 0.270) -1.27 0.980Aug - Jan -0.156 0.127 (-0.587, 0.276) -1.23 0.985sept - Jan -0.164 0.127 (-0.595, 0.267) -1.29 0.977Oct - Jan -0.108 0.127 (-0.540, 0.323) -0.85 0.999Nov - Jan -0.067 0.127 (-0.498, 0.365) -0.53 1.000Dec - Jan -0.089 0.127 (-0.520, 0.342) -0.70 1.000March - Feb -0.086 0.127 (-0.517, 0.345) -0.68 1.000April - Feb 0.044 0.127 (-0.387, 0.476) 0.35 1.000May - Feb -0.036 0.127 (-0.467, 0.395) -0.28 1.000June - Feb -0.006 0.127 (-0.437, 0.426) -0.04 1.000July - Feb 0.006 0.127 (-0.426, 0.437) 0.04 1.000Aug - Feb 0.011 0.127 (-0.420, 0.442) 0.09 1.000sept - Feb 0.003 0.127 (-0.429, 0.434) 0.02 1.000Oct - Feb 0.058 0.127 (-0.373, 0.490) 0.46 1.000Nov - Feb 0.100 0.127 (-0.331, 0.531) 0.79 1.000Dec - Feb 0.078 0.127 (-0.354, 0.509) 0.61 1.000April - March 0.131 0.127 (-0.301, 0.562) 1.03 0.996May - March 0.050 0.127 (-0.381, 0.481) 0.39 1.000June - March 0.081 0.127 (-0.351, 0.512) 0.64 1.000July - March 0.092 0.127 (-0.340, 0.523) 0.72 1.000Aug - March 0.097 0.127 (-0.334, 0.529) 0.77 1.000sept - March 0.089 0.127 (-0.342, 0.520) 0.70 1.000Oct - March 0.144 0.127 (-0.287, 0.576) 1.14 0.991Nov - March 0.186 0.127 (-0.245, 0.617) 1.47 0.944

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Dec - March 0.164 0.127 (-0.267, 0.595) 1.29 0.977May - April -0.081 0.127 (-0.512, 0.351) -0.64 1.000June - April -0.050 0.127 (-0.481, 0.381) -0.39 1.000July - April -0.039 0.127 (-0.470, 0.392) -0.31 1.000Aug - April -0.033 0.127 (-0.465, 0.398) -0.26 1.000sept - April -0.042 0.127 (-0.473, 0.390) -0.33 1.000Oct - April 0.014 0.127 (-0.417, 0.445) 0.11 1.000Nov - April 0.056 0.127 (-0.376, 0.487) 0.44 1.000Dec - April 0.033 0.127 (-0.398, 0.465) 0.26 1.000June - May 0.031 0.127 (-0.401, 0.462) 0.24 1.000July - May 0.042 0.127 (-0.390, 0.473) 0.33 1.000Aug - May 0.047 0.127 (-0.384, 0.479) 0.37 1.000sept - May 0.039 0.127 (-0.392, 0.470) 0.31 1.000Oct - May 0.094 0.127 (-0.337, 0.526) 0.74 1.000Nov - May 0.136 0.127 (-0.295, 0.567) 1.07 0.995Dec - May 0.114 0.127 (-0.317, 0.545) 0.90 0.999July - June 0.011 0.127 (-0.420, 0.442) 0.09 1.000Aug - June 0.017 0.127 (-0.415, 0.448) 0.13 1.000sept - June 0.008 0.127 (-0.423, 0.440) 0.07 1.000Oct - June 0.064 0.127 (-0.367, 0.495) 0.50 1.000Nov - June 0.106 0.127 (-0.326, 0.537) 0.83 0.999Dec - June 0.083 0.127 (-0.348, 0.515) 0.66 1.000Aug - July 0.006 0.127 (-0.426, 0.437) 0.04 1.000sept - July -0.003 0.127 (-0.434, 0.429) -0.02 1.000Oct - July 0.053 0.127 (-0.379, 0.484) 0.42 1.000Nov - July 0.094 0.127 (-0.337, 0.526) 0.74 1.000Dec - July 0.072 0.127 (-0.359, 0.504) 0.57 1.000sept - Aug -0.008 0.127 (-0.440, 0.423) -0.07 1.000Oct - Aug 0.047 0.127 (-0.384, 0.479) 0.37 1.000Nov - Aug 0.089 0.127 (-0.342, 0.520) 0.70 1.000Dec - Aug 0.067 0.127 (-0.365, 0.498) 0.53 1.000Oct - sept 0.056 0.127 (-0.376, 0.487) 0.44 1.000Nov - sept 0.097 0.127 (-0.334, 0.529) 0.77 1.000Dec - sept 0.075 0.127 (-0.356, 0.506) 0.59 1.000Nov - Oct 0.042 0.127 (-0.390, 0.473) 0.33 1.000Dec - Oct 0.019 0.127 (-0.412, 0.451) 0.15 1.000Dec - Nov -0.022 0.127 (-0.454, 0.409) -0.18 1.000

Individual confidence level = 99.88%

Tukey Pairwise Comparisons


Factor N Mean Grouping12am-8am 6 6.5611 A4pm-12am 6 5.886 B8am-4pm 6 5.6389 B



Difference SE of AdjustedDifference of Levels of Means Difference 95% CI T-Value P-Value12am-8am - 4pm-12am 0.675 0.171 ( 0.232, 1.118) 3.95 0.0038am-4pm - 4pm-12am -0.247 0.171 (-0.690, 0.196) -1.45 0.3438am-4pm - 12am-8am -0.922 0.171 (-1.365, -0.479) -5.40 0.000


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One-way ANOVA: 2008-2013 Tukey Pairwise Comparisons


Factor N Mean Grouping2012 12 6.0306 A2013 12 5.9597 A B2011 12 5.8583 A B C2008 12 5.7958 B C2010 12 5.7472 B C2009 12 5.7111 C



Difference Difference SE of Adjustedof Levels of Means Difference 95% CI T-Value P-Value2012 - 2013 0.0708 0.0755 (-0.1507, 0.2924) 0.94 0.9352011 - 2013 -0.1014 0.0755 (-0.3229, 0.1201) -1.34 0.7602010 - 2013 -0.2125 0.0755 (-0.4340, 0.0090) -2.81 0.0682009 - 2013 -0.2486 0.0755 (-0.4701, -0.0271) -3.29 0.0192008 - 2013 -0.1639 0.0755 (-0.3854, 0.0576) -2.17 0.2652011 - 2012 -0.1722 0.0755 (-0.3937, 0.0493) -2.28 0.2162010 - 2012 -0.2833 0.0755 (-0.5049, -0.0618) -3.75 0.0052009 - 2012 -0.3194 0.0755 (-0.5410, -0.0979) -4.23 0.0012008 - 2012 -0.2347 0.0755 (-0.4562, -0.0132) -3.11 0.0322010 - 2011 -0.1111 0.0755 (-0.3326, 0.1104) -1.47 0.6832009 - 2011 -0.1472 0.0755 (-0.3687, 0.0743) -1.95 0.3822008 - 2011 -0.0625 0.0755 (-0.2840, 0.1590) -0.83 0.9612009 - 2010 -0.0361 0.0755 (-0.2576, 0.1854) -0.48 0.9972008 - 2010 0.0486 0.0755 (-0.1729, 0.2701) 0.64 0.9872008 - 2009 0.0847 0.0755 (-0.1368, 0.3062) 1.12 0.870


Appendix D

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DOE Analysis Graphs and DataDescription: Normal probability plot of the effects Year, Month, and Time of Da

Description: Four-way analysis of the residuals vs. fits and normal graph for the regression analysis with TOD and Year as factors.

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Works CitedMontgomery, Douglas C., George C. Runger, and Norma Faris Hubele. Engineering Statistics, 5th Ed.: Student Solutions Manual. Hoboken, NJ: Wiley, 2011. Print.

https://www.google.com/publicdata/explore?ds=kf7tgg1uo9ude_#!ctype=l&strail=false&bcs=d&nselm=h&met_y=population&scale_y=lin&ind_y=false&rdim=country&idim=place:5322640&ifdim=country&hl=en_US&dl=en_US&ind=false

http://www.theurbanist.org/2015/01/05/how-fast-can-everett-really-grow/

everett fire department data analysis 2009 & 2012

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