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

Celik N., Konyalıoğlu A. K.

21st International Symposium on Production Research (ISPR) - Digitizing Production System, ELECTR NETWORK, 7 - 09 October 2021, pp.541-549 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.1007/978-3-030-90421-0_46
  • Page Numbers: pp.541-549
  • Keywords: Failure process, Weibull distribution, Time-varying parameter, One-way ANOVA, MODEL
  • 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.