Optimal tests for no contamination in reliability models

Inferences on mixtures of probability distributions, in general, and of life distributions, in particular, are receiving considerable importance in recent years. The likelihood ratio procedure of testing for the null hypothesis of no contamination is often very cumbersome and lacks its usual asymptotic properties. Recently, SenGupta (1991) has introduced the notion of an 'L-optimal' test for such testing problems. The idea is to recast the original several parametric hypotheses representation of the null hypothesis in terms of only a single hypothesis involving an appropriately chosen parametric function. This approach is shown to be both mathematically elegant and operationally simple for a quite general class of mixture distributions which contains, in particular, all mixtures of the one-parameter exponential family and also a very rich subclass of mixtures useful in life-testing and reliability analysis. It is also illustrated through two examples--one based on real-life data and the other on a simulated sample.