Prediction Intervals for Reliability Growth Models with Small Sample Sizes

Abstract

The first section of this chapter provides an introduction to the types of test considered for this growth model and a description of the two main forms of uncertainty encountered within statistical modelling, namely aleatory and epistemic. These two forms are combined to generate prediction intervals for use in reliability growth analysis.

The second section of this chapter provides a historical account of the modelling form used to support prediction intervals. An industry-standard model is described and will be extended to account for both forms of uncertainty in supporting predictions of the time to the detection of the next fault.

The third section of this chapter describes the derivation of the prediction intervals. The approach to modelling growth uses a hybrid of the Bayesian and frequentist approaches to statistical inference. A prior distribution is used to describe the number of potential faults believed to exist within a system design, while reliability growth test data is used to estimate the rate at which these faults are detected.

After deriving the prediction intervals, the fourth section of this chapter provides an analysis of the statistical properties of the underlying distribution for a range of small sample sizes.

The fifth section gives an illustrative example used to demonstrate the computation and interpretation of the prediction intervals within a typical product development process.

The strengths and weaknesses of the process are discussed in the final section.