Monitoring reliability for a three-parameter Weibull distribution


RELIABILITY ENGINEERING & SYSTEM SAFETY, vol.94, no.2, pp.503-508, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 94 Issue: 2
  • Publication Date: 2009
  • Doi Number: 10.1016/j.ress.2008.06.001
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.503-508
  • Keywords: Average run length, Control chart, Error analysis, Moment approximation, Threshold parameter, Three-parameter Weibull, TRANSFORMED EXPONENTIAL DATA, CONTROL CHARTS, FAILURE-DATA, PARAMETER, APPROXIMATIONS, MIXTURE, DESIGN, SHAPE
  • Middle East Technical University Affiliated: Yes


Control charts are widely used to monitor production processes in the manufacturing industry and are also useful for monitoring reliability. A method to monitor reliability has recently been proposed when the distributions of inter-failure times are exponential and Weibull with known parameters. This method has also been extended to monitor the cumulative time elapsed between a fixed number of failures for the exponential distribution. In this paper, we consider a three-parameter Weibull distribution to model inter-failure times, use a robust estimation technique to estimate the unknown parameters, and extend the proposed method to monitor the cumulative time elapsed between r failures using the three-parameter Weibull distribution. Since the distribution of the sum of independent Weibull random variates is not known (except in specific cases with known parameters), we give two useful moment approximations to be able to apply their scheme. We show how effective the approximations are and the usefulness of the method in detecting a possible instability during production. (C) 2008 Elsevier Ltd. All rights reserved.