Suppose that n individuals are scrutinized in an experiment. Each failure is accompanied by a fixed number of removals. The experiment terminates after r(<= n) failures. An explicit expressions for the likelihood function of the available is proposed. Under the conditional proportional hazard rate (CPHR) model, the maximum likelihood estimates (MLEs) of parameters are derived. Under the CPHR model and assumption that the baseline distribution belongs to the Weibull family of distributions, existence and uniqueness of the MLEs are investigated. Moreover, two general classes of lifetime distributions, as an extension of the Weibull distribution, are studied in a greater detail. An algorithm for generating PSOS data under the CPHR model, is proposed. Finally some concluding remarks are given.

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