Assurance for sample size determination in reliability demonstration testing

TL;DR

This paper introduces an assurance-based method for determining sample sizes in reliability demonstration tests, separating test design from analysis and allowing flexible prior choices for more reliable planning.

Contribution

It proposes an alternative to Bayesian risk criteria by using assurance for sample size calculation, applicable to binomial and Weibull models with tailored priors.

Findings

Assurance approach provides a probabilistic guarantee of test success.

Method allows different priors for design and analysis stages.

Illustrated with real data examples for binomial and Weibull models.

Abstract

Manufacturers are required to demonstrate products meet reliability targets. A typical way to achieve this is with reliability demonstration tests (RDTs), in which a number of products are put on test and the test is passed if a target reliability is achieved. 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 can conflate the choice of sample size and the analysis to be undertaken once the test has been conducted and rely on the specification of somewhat artificial acceptable and rejectable reliability levels. In this paper we offer an alternative approach to sample size determination based on the idea of assurance. This approach chooses the sample size to answer provide a certain probability that the RDT will result in a successful outcome. It separates the design and analysis of the RDT, allowing different priors for each. 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.