Improved time-censored reliability test plans for k-out-of-n gamma systems

Abstract

Relevant prior knowledge supported by historical data and expert judgments is common in many manufacturing processes. The classical viewpoint to the determination of acceptance sampling plans for k-out-of-n gamma systems is generalized to those situations in which the available previous information is appreciable. A beta distribution with a reduced parameter space is adopted to describe the stochastic behavior of the fraction of defective systems. An integer nonlinear programming problem is stated to find the inspection scheme that minimizes the required number of components to test and keeps the average producer and consumer risks below specified thresholds. First, lower and upper bounds, as well as an approximate solution, are derived. Then, an efficient step-by-step procedure, which finds the best acceptance sampling plan in a finite number of iterations, is provided. The inclusion of prior information into the decision process provides substantial savings in the sample size required for demonstrating system reliability, and also more accurate assessments of the actual producer and consumer risks. A system of five water pumps for cooling a reactor is analyzed for illustrative and comparative purposes.