Tools › Reliability › Maintainability and Availability › Spares Provisioning › Example

Pooled spares for ten modules: Poisson pipeline against the exact finite-fleet model (JPL Deep Space Network study, Table 1)

Tool	Spares Provisioning
Source	Eisenberger, I., Lorden, G., and Maiocco, F. (1973). "A Preliminary Study of Spares Provisioning for the Deep Space Network." The Deep Space Network Progress Report, Technical Report 32-1526, Vol. XVIII, Jet Propulsion Laboratory, Pasadena, CA, pp. 102–110. Table 1, p. 107.
Level	Professional

Problem

Ten identical modules operate continuously, each with a failure rate of 481.07 failures per million hours. A failed module is replaced from a common pool of spares and returns to the pool two weeks (336 hours) later. How many spares are needed for each operating position to hold a working module at least 99 % of the time, and what protection against a stock-out does that stock give?

Inputs to Enter

Systems 10, quantity per system 1, 24 operating hours per day
Failure rate 481.07 per million operating hours (MTBF 2,079 h); repairable, turnaround 14 days
Confidence of no stock-out 95 %; availability target 0.99

Open the Spares Provisioning tool (loaded with this example)

Answers

Demand 10 · 24 · 0.00048107 = 0.1155 per day (42.14 per year); pipeline m = 0.1155 · 14 = 1.616 units in repair on average
Poisson: 4 spares give P(no stock-out) = 0.9754 (3 spares 0.9189), fill rate 0.9189, expected backorders 0.03268; a 95 % fill rate needs 5 spares
Supply availability with 4 spares: 0.9967 by the Poisson model, 0.9970 by the finite-fleet birth-and-death chain; with 3 spares 0.9886 and 0.9897, below the target
Finite-fleet stock for an up-time ratio of 0.99: N = 4 (book: 4, Table 1, row λ = 481.07 × 10⁻⁶, 1/μ = 336 h, n = 10)
Wait per demand with 4 spares: 0.283 days

Notes

The tool's default inputs are this case; press Submit. The test script reproduces all 72 cells of the report's Table 1, the 84 cells of its Table 2 for (m, n) systems and the theoretical down-time ratios of its Tables 3 to 5. The Multi-item optimisation analysis opens on the six-module example of DSN Progress Report 42-42 (Eisenberger and Lorden, 1977, Table 1), whose printed package of 3, 2, 3, 4, 5 and 2 spares is the list the marginal analysis reaches at a cost of 43,794.