A novel imprecise reliability prediction method for incomplete lifetime data based on two-parameter Weibull distribution

作者：Liu, Bi; Teng, Yunlong^*; Huang, Qi

来源：Proceedings of the Institution of Mechanical Engineers - Part O: Journal of Risk and Reliability , 2020, 234(1): 208-218.

DOI：10.1177/1748006X18799014

• Imprecise reliability prediction
• Weibull-Gamma model
• incomplete lifetime data
• Bayesian theory
• information-gapdecision theory

The two-parameter Weibull distribution has been widely used in practical reliability engineering due to its flexibility of capturing various characteristics of failure data and trend. For the limited data, it is difficult to estimate the accurate parameters of the Weibull model, but we can to gain imprecise ones. In this article, the parameters are regarded as random variables where the scale parameter is Gamma distributed and the shape parameter is uniformly distributed within a certain range determined by the information-gap decision theory. From the view of Bayesian theory and information-gap decision theory, this article proposed a new imprecise reliability prediction method called Weibull-Gamma model for incomplete lifetime data subjecting to the two-parameter Weibull distribution, which can make an imprecise reliability prediction at any time and calculate out the intervals of mean life. Moreover, the convergence of the width about the imprecise intervals with the increase in the available sample size is also proved in this article. The experimental results from the right-censored lifetime data demonstrate that, in comparison with the traditional nonparametric predictive inference method, the Weibull-Gamma model can not only obtain narrower interval of survival function by adjusting the parameter s (whose effect is illustrated in section "Inference of imprecise SF and mean life given shape parameter") but also can calculate the intervals of mean life. Furthermore, the lower and upper bound functions of survival function are continuous while the nonparametric predictive inference method is piecewise. Moreover, nonparametric predictive inference can only deal with the right-censored data, while the Weibull-Gamma model is working for all the limited lifetime data including incomplete data as long as the data obeys two-parameter Weibull distribution. Besides, nonparametric predictive inference cannot express the reliability imprecision in the case that there is no right-censored data in the segmented intervals, while the Weibull-Gamma model still works.

• 出版日期2020-2
• 单位电子科技大学