A new method to estimate expected number of failures for allocating spare parts and labor

In determining the optimal allocation of spare parts and labor in a machine shop, in addition to the planned inspections, the random failures must be considered. The expected number of failures must be therefore assessed. At present, literature on the subject mostly discusses minimal repairs and failure replacement, giving only a little attention to partial repairs. These models ignored the time period to perform repairs, when the equipment is idle. This paper includes a mathematical model in which partial repairs are considered, when at each repair the effective age decreases by a given constant multiplier. Times needed to perform repairs are also taken into account. Two integral equations are derived to find the expected number of failures in any time interval during the useful life of the machine. The first is an approximation, and the second is the exact solution. Based on this information, the allocation of spare parts and qualified labor can be appropriately planned.