Abstract
We consider optimal replacement policies with periodic imperfect maintenance actions and minimal repairs. The multistate system is minimally repaired at failure and imperfect maintenance actions are regularly carried out for preventive maintenance. The discrete modified Weibull distribution is introduced and some cost functions applied to this distribution are defined in order to be minimized. Moreover, we assume that the costs of preventive maintenance depend on the degree of repair via a Kijima type 2 model. For illustrative purpose, the obtained results are applied on sets of simulated data.
Highlights
In reliability theory, discrete failure data arise in several common situations
We considered an incomplete maintenance model; that is, the impact of preventive maintenance (PM) is not minimal (ABAO) and not perfect (AGAN) but lies between these boundary cases
We assumed that the reduction of the failure rate is done by using the Kijima’s type 2 virtual age model
Summary
Discrete failure data arise in several common situations. It is sometimes impossible to measure the life length of items with continuous scale. The repair may not yield a functioning item which is as good as new and the minimal repair assumption seems to be too pessimistic in repair strategies. From this it is seen that the imperfect repair is of great signification in practice. A false negative occurs when the inspection says the system is good when it is defective In this case, the system reliability will be reduced. We are concerned with the modeling of an imperfect maintenance model; that is, the impact of preventive maintenance is between the two boundary cases: (a) minimal (as bad as old) and (b) perfect (as good as new). At last some possible cost functions are proposed and optimal maintenance strategies are discussed
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