The Beta Reduced Modified Weibull Distribution with Applications to Reliability Data

Abstract

In this paper, we introduce a new probability distribution with application in reliability called the beta reduced modified Weibull distribution. The proposed distribution presents a more flexible model and has the capability to capture decreasing, increasing, bathtub, unimodal (upside-down bathtub) and modified unimodal shaped hazard rates. Also, this distribution has a bathtub-shaped hazard rate function with a long useful life period, which is desirable property in reliability analysis. We obtain the expansions for the moments, quantile function, stress-strength reliability, density function of the order statistics and their moments. We use the method of maximum likelihood to estimate the model parameters for complete and right-censored data. We evaluate the performance of the maximum likelihood estimators in a simulation study. We analyze three reliability data sets, complete and censored, to examine the flexibility of the proposed model.