Optimal Censoring Schemes

Abstract

Up to this point, we have considered mathematical properties and problems of inference for progressively censored samples when a particular censoring scheme is to be employed. In reading this far, perhaps you yourself have asked the question, “How does a practitioner decide what the censoring scheme should be?” Is the decision made strictly on the basis of convenience, or can we choose a scheme which makes the most sense in some more statistical or mathematical setting? The question of choosing optimal values of R1, R2, ⋯, Rm when considering a progressive Type-II right censoring scheme is certainly an important one to consider from a practical point of view, and as it turns out, it also gives rise to a number of interesting mathematical problems, in the areas of optimization, numerical analysis, simulation and programming, among others. We consider progressively Type-II right censored samples for the most part, since Type-II censored samples are far more tractable and interesting to consider from the point of linear inference and other mathematical properties, as we have already seen, and right censored samples will arise most frequently in life-testing applications, where it is possible and generally sensible to observe and monitor failures from the onset of experimentation at time t = 0.