Small sample discrete reliability growth modeling using a grey systems model

Abstract

Purpose

When performing system-level developmental testing, time and expenses generally warrant a small sample size for failure data. Upon failure discovery, redesigns and/or corrective actions can be implemented to improve system reliability. Current methods for estimating discrete (one-shot) reliability growth, namely the Crow (AMSAA) growth model, stipulate that parameter estimates have a great level of uncertainty when dealing with small sample sizes. The purpose of this paper is to present an application of a modified GM(1,1) model for handling system-level testing constrained by small sample sizes.

Design/methodology/approach

The paper presents a methodology for incorporating failure data into a modified GM(1,1) model for systems with failures following a poly-Weibull distribution. Notional failure data are generated for complex systems and characterization of reliability growth parameters is performed via both the traditional AMSAA model and the GM(1,1) model for purposes of comparing and assessing performance.

Findings

The modified GM(1,1) model requires less complex computational effort and provides a more accurate prediction of reliability growth model parameters for small sample sizes and multiple failure modes when compared to the AMSAA model. It is especially superior to the AMSAA model in later stages of testing.

Originality/value

This research identifies cost-effective methods for developing more accurate reliability growth parameter estimates than those currently used.

Citation

Talafuse, T.P. and Pohl, E.A. (2018), "Small sample discrete reliability growth modeling using a grey systems model", Grey Systems: Theory and Application, Vol. 8 No. 3, pp. 246-271. https://doi.org/10.1108/GS-02-2018-0011