Abstract: The Weibull distribution has been widely used in reliability fields. A mixed Weibull distribution represents a population that consists of several Weibull subpopulations. In this paper, a new approach which combines the least-squares method with Bayes’ theorem, takes advantage of the parameter estimation for single Weibull distribution is developed to estimate the parameters of each subpopulation. The estimates given by this paper also satisfy the maximum likelihood equation. The estimates of the failure rate of the mixed Weibull population are given. An actual test data is computed by using the proposed method. The Kolmogorov-Smirnov goodness-of-fit test turns out that the proposed method yields more accurate result.

Key words: Bayesian estimation, Failure rate, Least-squares method, Maximum likelihood principle, Mixed-Weibull distribution

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