Bayesian Decision Analysis of the Hazard Rate for a Two-Parameter Weibull Process

A two-parameter Weibull distribution is assumed to be the appropriate statistical life-model of an engineering device. The hazard rate of this device is the relevant quantity in terms of which statistical decisions are to be made. A Bayesian decision model is constructed around a conjugate probability density function for the Weibull hazard rate. Prior, posterior, and preposterior analysis of this decision model are discussed. The results indicate the rational decision before and after sampling, and permit the optimization of sequential single-item sampling schemes. Such schemes are of particular importance in the reliability testing of high-cost equipment.