Inference for constant stress accelerated life test under the proportional reverse hazards lifetime distribution

• Published in: Quality and reliability engineering international Vol. 38; no. 8; pp. 4223 - 4235
• Main Authors: Wang, Xiaofei, Wang, Bing Xing, Liang, Wenjuan, Jiang, Peihua
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.12.2022
• Subjects: Accelerated life tests; Confidence intervals; constant stress accelerated life test; Exponential functions; Failure times; generalized confidence interval; generalized pivotal quantity; Hazards; Mathematical models; Monte Carlo simulation; Parameters; proportional reverse hazards family; Reliability; Statistical analysis; Statistical inference; Statistical methods; Weibull distribution
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.3201

In this paper, we consider small sample statistical inference methods for the constant stress accelerated life test (CSALT) under the proportional reverse hazards family (PRHF). The model parameters are assumed to be the exponential functions of the stress. The generalized confidence intervals (GCIs) are derived for the model parameters and some commonly used reliability metrics such as the quantile and the reliability function of the lifetime at the designed stress level. The generalized prediction interval (GPI) is also proposed for the future failure time (FFT) and the remaining useful life (RUL) at the designed stress level. The Monte Carlo simulation study for the generalized Lindley distribution (GLD) and the inverse Weibull distribution are used to illustrate the performance of the proposed GCIs and GPI. The simulation results indicate that the performance of the proposed GCIs and GPI is better than the Wald confidence intervals (CIs) and bootstrap‐p CIs in terms of the coverage probability (CP). Finally, a real example is used to illustrate the developed procedures.