Estimation of Current Reliability in a Duane-Based Reliability Growth Model

Abstract

In this article, I investigate the statistical inference concerning the current (field-stage) reliability of a reliability growth model. The model, assuming a step-intensity structure, evolves from the physical consideration of the Duane learning-curve property and incorporates the effect of a testanalyze- and-fix program that is typically undertaken in a developmental testing program. Both exact and large-sample distributional results are derived for the maximum likelihood and the least squares estimators of the current intensity. Under the assumption that the step-intensity model represents the reality, I provide an assessment of the extent of “misspecification” when the widely used power law process model is fit to the failure data of a system experiencing recurrent failures. Extensive simulation results are carried out to supplement the theoretical findings. An illustration with a dataset is provided as a demonstration of the application of the inference results.

KEY WORDS:

• Asymptotics
• Exact inference
• Generalized linear model
• Least squares
• Maximum likelihood
• Misspecification effect
• Reliability growth