Pooled parametric inference for minimal repair systems

Abstract

Consider two independent and identically structured systems, each with a certain number of observed repair times. The repair process is assumed to be performed according to a minimal-repair strategy. In this strategy, the state of the system after the repair is the same as it was immediately before the failure of the system. The resulting pooled sample is then used to obtain best linear unbiased estimators (BLUEs) as well as best linear invariant estimators of the location and scale parameters of the presumed parametric families of life distributions. It is observed that the BLUEs based on the pooled sample are overall more efficient than those based on one sample of the same size and also than those based on independent samples. Furthermore, the best linear unbiased predictor and the best linear invariant predictor of a future repair time from an independent system are also obtained. A real data set of Boeing air conditioners, consisting of successive failures of the air conditioning system of each member of a fleet of Boeing jet airplanes, is used to illustrate the inferential results developed here.