When tailor-made systems are introduced into fields, markets, or factories, the replacement parts or subcomponents for maintenance are produced and purchased simultaneously so as to keep the quality and reliability of those parts homogeneous against the parts installed into systems at the beginning. Those parts are then kept in stock at yards and will be kept waiting for their turns. Furthermore, the maintenance records of such systems are often window censored, under which the records are both left and right censored. In this talk, we model such situations as a renewal process with incomplete repairs, in which a failed subcomponent is replaced with an unused-but-not-new subcomponent. The statistical inference of the failure time distribution and the effect of in-stock term are implemented using stochastic EM algorithm, which is needed to solve the maximization problem of the incomplete data likelihood under window censoring. A real case is analyzed using the proposed model and the effect of in-stock-at-yards term on the total lifetime is assessed by assuming Weibull distribution. We also examine the sampling properties of the estimators for Weibull distributions.
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