Optimal design of accelerated life tests for an extension of the exponential distribution

• Published in: Reliability engineering & system safety 2014-11, Vol.131, p.251-256
• Main Author: Haghighi, Firoozeh
• Format: Article
• Language: English
• Subjects: Accelerated life tests; An extension of the exponential distribution; Applied sciences; Asymptotic properties; Asymptotic variance; Computer simulation; Cumulative exposure model; Exact sciences and technology; Experimental design; Fisher information matrix; Fundamental areas of phenomenology (including applications); Mathematical models; Mathematics; Maximum likelihood estimation; Measurement and testing methods; Mechanical engineering. Machine design; Operational research and scientific management; Operational research. Management science; Physics; Probability and statistics; Probability distribution functions; Product life cycle; Reliability theory. Replacement problems; Sciences and techniques of general use; Solid mechanics; Statistics; Step-stress test; Stress concentration; Stresses; Structural and continuum mechanics
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2014.04.017

Accelerated life tests provide information quickly on the lifetime distribution of the products by testing them at higher than usual levels of stress. In this paper, the lifetime of a product at any level of stress is assumed to have an extension of the exponential distribution. This new family has been recently introduced by Nadarajah and Haghighi (2011 [1]); it can be used as an alternative to the gamma, Weibull and exponentiated exponential distributions. The scale parameter of lifetime distribution at constant stress levels is assumed to be a log-linear function of the stress levels and a cumulative exposure model holds. For this model, the maximum likelihood estimates (MLEs) of the parameters, as well as the Fisher information matrix, are derived. The asymptotic variance of the scale parameter at a design stress is adopted as an optimization objective and its expression formula is provided using the maximum likelihood method. A Monte Carlo simulation study is carried out to examine the performance of these methods. The asymptotic confidence intervals for the parameters and hypothesis test for the parameter of interest are constructed.