On Comparing the Reliabilities of Two Exponential Populations

Consider two populations, each of whose probability properties are described by the 2-parameter exponential probability density function. The two parameters are unknown in each case. Assuming that a random sample is available from each of the two populations, this paper shows how to calculate an approximation for the probability that one of the populations has a greater reliability than the other. The Bayesian theory of statistical inference is used and we assume a weak prior for the parameters involved.