Inference for Type-I and Type-II Hybrid Censored Minimal Repair and Record Data

In this paper, hybrid censoring mechanisms are applied to minimal repair and record data. Based on the derivation of the joint distribution of such data under hybrid censoring, likelihood inference is discussed. For illustration, Type-I and Type-II hybrid censoring schemes are considered for exponential distributions. In particular, the exact (conditional) distribution of the maximum likelihood estimator is obtained for an exponential distribution. This result is used to construct exact (conditional) confidence intervals using the method of pivoting the cumulative distribution function. Finally, the results are illustrated using two data sets taken from the literature on minimal repair models. Although the discussion of the results is in terms of minimal repair models, the results can be applied directly to record value data. By utilizing a connection of minimal repair times to occurrence times of non-homogeneous Poisson processes, a nonparametric estimate for the intensity rate of the process and the underlying lifetime distribution under hybrid censoring is also proposed. The paper is supplemented by simulational results.