Use of Bayes' theorem and the beta distribution for reliability estimation purposes

Abstract

The aim of a reliability group is to establish the product reliability level prior to volume shipment, then regularly measure reliability throughout the product lifetime. This will provide the producer with a level of confidence about his process and the expected performance level of its products. Using information gained from testing, reliability can be closely monitored and appropriate control measures put in place. However, when product reliability is high, lot acceptance type sampling requires very large sample sizes to uncover defective units. Testing large sample sizes therefore becomes a very lengthy task that utilises most of the test capacity. The effect of this is that fewer tests can be carried out and products cannot be tested as regularly as one would like. This means the producer runs the risk of shipping products in which he has little confidence. To use only current products to perform statistically sufficient tests is often impractical, hence the need to use past experience in drawing conclusions on current products. By applying classical statistical theory, current products are required to be used each time a test is carried out, which therefore makes testing a very lengthy task as no prior knowledge has been used as part of the decision making process. The answer to the problem is to use a more appropriate statistical approach for sample testing. One which fits the bill well is the Bayesian procedure using beta priors, enabling the amount of testing required to be minimised to a level which still allows the producer to draw valid statistical inferences from his test data. © 1990.