ABSTRACT
This chapter introduces a simple exponential model associated with nonnegative random variables through the life-testing problem. In various reliability models, often, one may want to test for constant failure rates against an increasing failure rate or a decreasing failure rate. In a renewal process setup, for exponential inter-arrival times, one encounters a counting process attracted by the classical Poisson process. Therefore, it is quite relevant to discuss some sequential inference procedures relating to such Poisson processes. Reliability engineers have a very special affection to exponential models, and the classical text of Barlow and Proschan is an excellent source of such reliability models. Bivariate or multivariate exponential models have been proposed by a host of workers. In the context of competing risk models too, such exponential distributions crop up in a natural manner, and moreover, there is a genuine need for sequential inference (which may have also a time-sequential flavor).
