This study proposes an alternative to the weighted least-squares (WLS) procedure for estimating the shape parameter of the Weibull distribution. Bergman (Journal of Materials Science Letters 1986; 5:611–614), Faucher and Tyson (F&T) (Journal of Materials Science Letters 1988; 7:1199–1203) suggested using different WLS approaches for Weibull parameters. However, the simulation results show that the novel approach is better than that of Bergman, and is not significantly different from that of F&T. Furthermore, the novel approach is also simpler and easier to comprehend.
Quality and Reliability Engineering International 20(6), pp.579-586