Assurance for Sample Size Determination in Reliability Demonstration Testing

Abstract

Manufacturers are required to demonstrate that products meet reliability targets. A way to achieve this is with reliability demonstration tests (RDTs), where a number of products are put on test and the test is passed or failed according to a decision rule based on the observed outcomes. There are various methods for determining the sample size for RDTs, typically based on the power of a hypothesis test following the RDT or risk criteria. Bayesian risk criteria approaches combine the choice of sample size with the analysis of the test data while relying on the specification of acceptable and rejectable reliability levels. In this article, we offer an alternative approach to sample size determination based on the idea of assurance. This approach chooses the sample size to provide a specified probability that the RDT will result in a successful outcome. It separates the design and analysis of the RDT, allowing different priors for the producer and consumer. We develop the assurance approach for sample size calculations in RDTs for binomial and Weibull likelihoods and propose appropriate prior distributions for the design and analysis of the test. In each case, we illustrate the approach with an example based on real data.

Keywords:

• Bayesian inference
• Hardware product development
• Power calculations
• Prior elicitation
• Reliability analysis

Supplementary Materials

Appendices:Further details and explanation as follows. (pdf)

1. Bayesian acceptance sampling in quality assurance

2. Posterior risk criteria

3. Proof of Proposition 1

4. Choosing a prior distribution: binomial case

5. Sensitivity to the skeptical analysis prior

6. Parameter posterior distributions in the Weibull example

R code:This contains two R files:

1. Techno code.R—R code to run to reproduce the results in Example 4.1.

2. Techno.R—Two functions and the rjags model required for Example 4.1.