Optimal Tests for No Contamination in Reliability Models

Inferences on mixtures of probability distributions, in general,and of life distributions, in particular, are receiving considerableimportance in recent years. The likelihood ratio procedure oftesting for the null hypothesis of no contamination is oftenvery cumbersome and lacks its usual asymptotic properties. Recently,SenGupta (1991) has introduced the notion of an `L-optimal' testfor such testing problems. The idea is to recast the originalseveral parametric hypotheses representation of the null hypothesisin terms of only a single hypothesis involving an appropriatelychosen parametric function. This approach is shown to be bothmathematically elegant and operationally simple for a quite generalclass of mixture distributions which contains, in particular,all mixtures of the one-parameter exponential family and alsoa very rich subclass of mixtures useful in life-testing and reliabilityanalysis. It is also illustrated through two examples—onebased on real-life data and the other on a simulated sample.