A Bayesian approach to the analysis of burn-in of mixed populations

The authors develop a Bayesian methodology for burning-in manufactured items to differentiate between two populations. The life distribution of items under some given type and magnitude of stress is assumed to be a mixed exponential distribution. The mixture parameter represents the proportion of the weak subpopulation in the total. It is modeled as a random variable for which prior information exists, and formulated as a beta distribution. A proposed criterion for separating the two subpopulations addresses the issue of unnecessary screening from the strong subpopulation as well as the required percentage of screening from the weak one. The posterior distribution for the mixture parameter is derived for the mixed exponential model. Simulation results show that when data support the prior estimation it results in a narrower posterior