Analysis of optimal accelerated life test plans for periodic inspection: The case of exponentiated Weibull failure model

Abstract

Purpose

The aim of this research paper is to generalize the previous works on the design of accelerated life tests (ALTs) for periodic inspection and Type I censoring and to promote the use of an exponentiated Weibull (EW) distribution in accelerated life testing.

Design/methodology/approach

Statistically optimal ALT plans are suggested for items whose lifetime follows the EW distribution under periodic inspection and Type I censoring. It is assumed that the mean lifetime (scale parameter) is a log‐linear function of stress and that the shape parameters are independent of stress. Given shape parameters, design stress and high test stress, the test plan is optimized with respect to the low test stress and the proportion of test units are also allocated to this test stress. The asymptotic variance (AsVar) of the maximum likelihood estimator of log mean life at the design stress is used as an optimality criterion with equally spaced inspection times. A FORTRAN program was written to calculate the optimal plans. Procedures for planning of an ALT, including selection of sample size, have also been discussed. An illustration of the optimal ALT plans has been done through a numerical example.

Findings

Computational findings for various values of the shape parameters indicate that the AsVar of log mean life at the design stress is insensitive to the number of inspection times and to misspecifications of imputed failure probabilities at design and high test stresses. Computational findings also show that optimal designs of ALT previously obtained for exponential, Rayleigh, and Weibull distributions become special cases of the EW distribution. Thus, the EW distribution is a useful and widely applicable reliability model for optimal ALT plans.

Originality/value

The present investigation features the EW distribution of lifetimes of test items and it generalizes the previous works on accelerated life testing. Furthermore, the propose test plans can be applied to estimate the lifetime of highly reliable product or material, if a researcher designs a test under the assumption of this model.

Citation

Ahmad, N., Islam, A. and Salam, A. (2006), "Analysis of optimal accelerated life test plans for periodic inspection: The case of exponentiated Weibull failure model", International Journal of Quality & Reliability Management, Vol. 23 No. 8, pp. 1019-1046. https://doi.org/10.1108/02656710610688194