Estimation of Weibull Shape-Parameters for Two Independent Competing Risks

This paper presents a technique to estimate Weibull shape parameters of life distribution of two components in a series system. The data consist of lifetime of the system only, that is, it is not known which component caused the system failure. The relations among cumulative hazard functions of the system at virtual observation limit are used for estimation. This technique is useful for 1) analysing this common kind of life-test data, and 2) estimating parameters of the smallest extreme value distribution. A numerical example including the experimental data on electron tubes is discussed briefly.