Reliability data analysis and standards like ISO 14224 help optimize maintenance and reduce costs. This document uses reliability data and the Poisson distribution method to estimate the number of spare centrifugal pump parts needed over two years for multiple installations. It determines that 10 pumps, 21 seals, and 12 valves are required to maintain 143 pumps with around 90% confidence based on failure rates from reliability data sources. The Poisson distribution provides an initial simplified approach to estimate spare part needs when detailed engineering data is limited.

1. 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

2. 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.

3. 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.

4. © Monaco Engineering Solutions
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%.

5. MINIMISING RISK
MAXIMISING PERFORMANCE
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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