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

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.