Comparing the Times Between Successive Failures by Using the Weibull Distribution with Time-Varying Scale Parameter

Çelik N., Konyalıoğlu A. K.

in: Digitizing Production Systems Selected Papers from ISPR2021, Numan Durakbaşa,Güneş Gençyılmaz, Editor, Springer Nature, Zürich, pp.541-549, 2021

  • Publication Type: Book Chapter / Chapter Research Book
  • Publication Date: 2021
  • Publisher: Springer Nature
  • City: Zürich
  • Page Numbers: pp.541-549
  • Editors: Numan Durakbaşa,Güneş Gençyılmaz, Editor
  • Istanbul Technical University Affiliated: Yes


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.