Reliability data analysis provides a wide-range of benefits, including the

opportunity to optimize the timing of equipment overhauls and inspections,

the content of maintenance procedures, as well as the life cycle costing of

sparing and upgrade programs in operating facilities world-wide.

As data standardization can result in improved quality of data, the

International Standard ISO 14224 (Collection and exchange of reliability and

maintenance data for equipment) provides a comprehensive basis for the

collection of reliability and maintenance (RM) data in a standard format for

equipment in all facilities and operations during the operational life cycle of

equipment.

In this example, the number of spare pumps and most demanded

components necessary to maintain centrifugal pumps distributed in several

operating installations for two years is estimated using the RM data and the

Poisson Distribution. The following relevant definitions for this article were

extracted and adapted for this example from ISO 14224:2006.

Boundary: A clear boundary description is imperative for the data

analysis. Inlet and outlet valves and suction strainer are not within

the boundary. The pump drivers along with their auxiliary systems

are not included (electric motor, gas turbine or combustion engine).

Taxonomy: According to standard classification presented in Figure

1 shows RM data on levels 6 (equipment unit) to level 9 (parts).

Equipment Attributes: The centrifugal pumps are classified as

rotating equipment and are sub-divided (Refer to Figure 2).

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APPLICATION OF USING THE

POISSON DISTRIBUTION METHOD

TO CALCULATE NUMBER OF SPARE

PARTS

Fabio Oshiro

Principal Risk & Reliability Engineer

References

BS EN ISO 14224:2006 Collection and exchange of reliability and maintenance data for equipment, BSI, 2007.

OREDA Handbook 2015, 6th edition – Volume I.

USP, Producao, v.21, n. 4, out./dez. 2011, p. 656-666, “Spare parts inventor control: a literature review”, Rego, Jose Roberto; Mesquita, Marco Aurelio.

Croston, J.D.: Forecasting and Stock Control for Intermittent Demands. Operational Research Quarterly, Vol.23, No 3, pp. 289-303, September 1972

Figure 2— Equipment Attributes (adapted from BS EN ISO 14224: 2006)

Figure 1—Taxonomy (BS EN ISO 14224: 2006)

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Failure and maintenance parameters: The RM data for exploration and production equipment from a wide variety of geographic areas, installations, equipment types and operating conditions is presented in the Off-shore & Onshore Reliability Data (OREDA) Handbook.

Failure mechanism: the physical, chemical or other process or combination of processes that leads to the failure. They are divided in the following major categories: mechanical, instrumentation and electrical fail-ures; external influence; and miscellaneous. For the centrifugal pump, leakage, mechanical failure - general and faulty signal/indication/alarm are the main mechanisms of failure corresponding to 23%.

Failure mode is the effect by which a failure is observed on the failed item and for the purpose of this ex-ample it can simplistic be divided into three types:

Desired function is not obtained (e.g. failure to start);

Specified function lost or outside accepted operational limits (e.g. spurious stop, high output);

Failure indication is observed but there is no immediate and critical impact on the equipment-unit function.

The centrifugal pump failure modes with the highest failure rate are abnormal instrument reading (AIR), ex-ternal leakage - process medium (ELP) and external leakage - utility medium (ELU).

The Seals and valves are the maintainable items with the highest failure rates, after unknown and other items.

Poisson distribution method

The Poisson distribution is a method often applied to

forecast the number of spare parts using reliability analysis.

The demand for spare parts for replacement or due to

failure follows the Poisson distribution when the events

occur at a constant average rate and in any interval

independent of the number of events occurring, i.e. given

that a failure has just occurred, it has no influence on the

time elapsed until the next failure. The number of failures

in a given time would be given by .

Where: λ = failure rate,

t = length of time being considered,

x = number of failures.

The probability of failures (n) in time (t) is given by R(t):

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Calculations:

N = 143 centrifugal pumps

λpumps = 51.66 failures / 106 hours (from OREDA)

Components: assuming 12.22% and 6.24% of the critical

pump failures are caused respectively by seals and valves

λseals = 0,1222 λpumps = 6,31 failures / 106 hours

λvalves = 0,0624 λpumps = 3.22 failures / 106 hours

t = 2 years trepair = 27 hours

For the calculation, the spare parts are divided in repairable

and non-repairable.

Non-repairable items:

In this example, seals and valves for the centrifugal pump

are considered non-repairable items. For the Poisson

Distribution equation, the number of failures (x) is equal to

number of spares. Using the Poisson distribution, the

results obtained are presented in Table 1.

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Seals

n f R

0 0.00000 0.00 %

1 0.00000 0.00 %

5 0.00112 0.16 %

10 0.03651 8.39 %

15 0.10027 48.51 %

20 0.05333 87.82 %

21 0.04017 91.84 %

22 0.02888 94.73 %

23 0.01986 96.71 %

Valves

n f R

0 0.00031 0.03 %

1 0.00251 0.28 %

3 0.02729 3.01 %

5 0.08900 18.44 %

10 0.10113 80.82 %

11 0.07425 88.25 %

12 0.04997 93.25 %

13 0.03104 96.35 %

14 0.01791 98.14 %

Table 1—Poisson Distribution—Seals and Valves

The fill rate or confidence level is the required probability of having a spare part in inventory when required

(90% =< R =< 95%). The recommended number of spare parts (only for seals and valves) for 143 centrifugal pumps

based on Poisson distribution and assuming a required confidence level between 90% and 95% is 21 seals and

12 valves.

Repairable items: For repairable parts, a stock level of spares is calculated to compensate for items undergoing the

process of repair (trepair = 27 hours).

Pumps

n-1 f R

0 0.819174 81.92 %

1 0.163392 98.26 %

2 0.016295 99.89 %

3 0.001083 99.99 %

Table 2—Poisson Distribution—Pumps Since the time to repair centrifugal pumps is relatively

short, the probability of a second pump failing while the

first one is in repair is fairly low. As a result, considering the

fill rate (≥90%), the recommended number of spares is two

pumps. The result obtained is presented in Table 2, where

n = 2 (n-1).

Scrap and condemned items: Additional spare parts need

to be considered in order to compensate for the

condemnation or scrappage of repairable items. Calculating

the number of failures during the period, it is possible to

determine this number. In this example, the scrap rate

considered is 5%.

M I N IMI SING RISK

MAXIMISING PERFORMANCE

Monaco Engineering Solutions

Americas ● Europe ● Middle East ● Africa ● Asia Pacific

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Pumps

n f R

0 0.000000 0.00 %

50 0.000000 0.00 %

100 0.001055 0.42 %

120 0.025596 21.80 %

140 0.022128 83.51 %

141 0.020312 85.54 %

142 0.18513 87.39 %

143 0.016756 89.06 %

144 0.015060 90.57 %

145 0.013443 91.91 %

Table 3—Poisson Distribution—Pump failures

Using the Poisson distribution, it is estimated that 144 failures

(see Table 3) may occur and 8 additional pumps are

recommended.

In summary, 10 centrifugal pumps, 21 seals and 12 valves are

necessary to maintain the 143 centrifugal pumps in operation for

two years with approximately 90% confidence.

The annual cost of equipment unreliability in the petroleum,

natural gas and petrochemical industries is significant. As a result,

analyses of reliability and maintainability data (RM) have become

of increased importance. As a consequence, the application of

standards, such as ISO 14224, is highly recommended to obtain

better quality of data.

As presented, RM data can also be used to estimate the quantity

of spare parts demanded during a determined period of time by

means of the application the Poisson distribution method.

The Poisson distribution is a simplified approach to estimate the

number of required spares when little process information is

known. If detailed engineering data is available a detailed

approach using Monte Carlo methods is recommended. © Monaco Engineering Solutions