Comparing the times between successive failures by using the Weibull distribution with time-varying scale parameter

In this study, we propose a method for comparing three or more means of time between two failures (TBF) for different systems or processes. Traditionally, one-way ANOVA is used to compare the means of three or more group, however, this method is based on the normal distribution assumption. For this reason, we propose one-way ANOVA model whose error distribution is the Weibull distribution with time-varying scale parameter. Since, in reliability analysis, the TBFs are generally not identically and independently distributed and the Weibull distribution with time-varying scale parameter has been proposed to analyse the TBFs. We obtain the estimations of the unknown parameters with the maximum likelihood methodology. We also propose a new test statistic for testing the difference mean time failures. A Monte Carlo simulation study is performed for comparing the power of this proposed test statistics with the traditional ones. Simulation results show that the proposed methodologies are more preferable.