A Three-Component Additive Weibull Distribution and Its Reliability Implications

Abstract

We consider a new failure time distribution by combining three Weibull distributions. The proposed distribution exhibits decreasing, increasing, and bathtub-shaped failure rate functions. Some statistical properties of the proposed distribution are presented. The maximum likelihood method is used to estimate the parameters, reliability, and failure rate functions of the proposed distribution, and the uncertainties of the estimates are obtained by using asymptotic confidence intervals. The cross-entropy method, a stochastic optimization procedure, is used to find the maximum of the log-likelihood function. The superiority of the proposed distribution is demonstrated on two benchmark datasets.

Keywords

• asymptotic confidence interval
• bathtub-shaped failure rate function
• cross-entropy method
• maximum likelihood estimator
• Weibull distribution