Replacement policies for age and working numbers with random life cycle.

It has been modeled for several replacement policies in literatures that the whole life cycle or operating interval of an operating unit should be finite rather than infinite as is done with the traditional method. However, it is more natural to consider the case in which the finite life cycle is a fluctuated parameter that could be used to estimate replacement times, which will be taken up in this article. For this, we first formulate a general model in which the unit is replaced at random ageU, random timeYfor the first working number, random life cycleS, or at failureX, whichever occurs first. The following models included in the general model, such that replacement done at ageTwhen variableUis a degenerate distribution, and replacement done at working numbersNsummed by numberNof variableY, are optimized. We obtain the total expected cost until replacement and the expected replacement cost rate for each model. Optimal ageT, working numberN, and a pair of (T,N) are discussed analytically and computed numerically. [ABSTRACT FROM AUTHOR]