Extended optimal age replacement policy with minimal repair. (English) Zbl 0792.90032

Sheu, Shey-Huei; Kuo, Chung-Ming; Nakagawa, Toshio

RAIRO, Rech. Opér. 27, No. 3, 337-351 (1993).

Summary: A generalization of the age replacement policy is proposed and analysed. Under such a policy, if an operating system fails at age \(y\leq t\), it is either replaced by a new system (type II failure) with probability \(p(y)\), or it undergoes minimal repair (type I failure) with probability \(q(y)= 1-p(y)\). Otherwise, a system is replaced when the first failure after \(t\) occurs or the total operating time reaches age \(T\) \((0\leq t\leq T)\), which occurs first. The cost of the \(i\)-th minimal repair of a system at age \(y\) depends on the random part \(C(y)\) and the deterministic part \(c_ i(y)\). The aim of the paper is to find the optimal \((t^*,T^*)\) which minimizes the long-run expected cost per unit time of the policy. Various special cases are included and a numerical example is finally given.

MSC:

90B25

Reliability, availability, maintenance, inspection in operations research

Keywords:

maintenance; age replacement policy; minimal repair