A comparison of different least-squares methods for reliability of Weibull distribution based on right censored data

Abstract

The linear least-squares method has been applied to Weibull distribution for analysing the reliability, and the exact confidence intervals for Weibull parameters can be constructed from both Type-I and Type-II censored data. However, this method changes the shape of theoretical linear fit and estimates are highly biased for heavily censored data. Therefore, the nonlinear method (NLLSM) and transformation-based least-squares methods (TBLSM) are proposed in the literature. In this paper, I address confidence intervals for Weibull parameters based on the two methods and discuss the reliability and remaining lifetime with the right censored data. I propose the exact confidence intervals from pivotal quantities for the Weibull parameters based on NSLLM and approximate ones based on TBLLM. Further, different methods are compared through a Monte Carlo simulation study. Finally, these methods are applied to a data set as an illustrative example.

Keywords:

• Weibull distribution
• least-squares method
• pivotal quantity
• confidence interval
• remaining lifetime

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant number 71801219] and the Natural Science Foundation of Hunan Province [grant number 2019JJ50730].