Effective Optimization of Statistical Decisions for Age Replacement Problems under Parametric Uncertainty

Abstract

In this chapter, an innovative model for age replacement is proposed. The costs included in the age replacement model are not assumed to be constants. For effective optimization of statistical decisions for age replacement problems under parametric uncertainty, based on a past random sample of lifetimes, the pivotal quantity averaging (PQA) approach is suggested. The PQA approach represents a simple and computationally attractive statistical technique. In this case, the transition from the original problem to the equivalent transformed problem (in terms of pivotal quantities and ancillary factors) is carried out via invariant embedding a sample statistic in the original problem. The approach allows one to eliminate unknown parameters from the problem and to find the better decision rules, which have smaller risk than any of the well-known decision rules. Unlike the Bayesian approach, the proposed approach is independent of the choice of priors. For illustration, numerical examples are given.