Conditional reliability lower bound for Weibull distribution without estimating shape parameter

This paper presents and proves a procedure of using two-parameter Weibull distribution for reliability estimation. The procedure computes a confidence lower bound on conditional reliability without estimating or assuming Weibull shape parameter β. Therefore, it is a very valuable reliability estimation tool for highly reliable systems that generally have few or no failures. The applicability of the procedure is further extended to competing Weibull failure mode applications. The relationship of the computed worst-case shape parameter value and maximum likelihood estimate is revealed, which provides some additional insight to the conservatism and the physical essence of the procedure. Some real data examples are presented to illustrate the usefulness and power of the procedure. Mathematical proof is given in an appendix