q-Weibull Distributions: Perspectives and Applications in Reliability Engineering

Lifetime distributions, such as Weibull and log-logistic distributions, are critical for parametric and semi-parametric analysis in reliability engineering. This article promotes a promising but understated distribution, q-Weibull distribution, to the reliability engineering community by providing new perspectives and demonstrating potential applications. We interpreted the physical meanings of the parameter “q” from multiple perspectives, including internal interactions in nonextensive mechanics, dependence among components in a series system, and the frailty (heterogeneity) in field failure data. Also, we showed that q-Weibull distributions belong to a closed function family under three different operations: minimal ordered statistics, accelerated failure time and proportional hazards for modeling accelerated life test data. Then, q-Weibull distributions are found to be an interpolation between Weibull and log-logistics distributions, and an interpolation between Weibull and Power law distributions. Moreover, this article presented a new approach to estimating parameters more accurately and robustly, by combing maximum likelihood estimation and robust linear regression. Finally, q-Weibull distributions show superior performance for a list of reliability applications, such as modeling lifetime, material strength, accelerated life test, frailty in field failure data, repairable systems, and reliability growth. To promote wider usage of this lifetime distribution, we open source all the codes for parameter estimations and reliability applications and all the datasets collected.