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Monitoring reliability for a three-parameter Weibull distribution

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  • Sürücü, Barış
  • Sazak, Hakan S.

Abstract

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.

Suggested Citation

  • Sürücü, Barış & Sazak, Hakan S., 2009. "Monitoring reliability for a three-parameter Weibull distribution," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 503-508.
    • Handle: RePEc:eee:reensy:v:94:y:2009:i:2:p:503-508
    DOI: 10.1016/j.ress.2008.06.001
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    References listed on IDEAS

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    1. Chen, Huifen & Cheng, Yuyen, 2007. "Non-normality effects on the economic-statistical design of charts with Weibull in-control time," European Journal of Operational Research, Elsevier, vol. 176(2), pages 986-998, January.
    2. M. F. Ramalhoto & M. Morais, 1999. "Shewhart control charts for the scale parameter of a Weibull control variable with fixed and variable sampling intervals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(1), pages 129-160.
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    Cited by:

    1. Zhang, Tian & Homri, Lazhar & Dantan, Jean-Yves & Siadat, Ali, 2023. "Models for reliability assessment of reconfigurable manufacturing system regarding configuration orders," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    2. Shamstabar, Yousof & Shahriari, Hamid & Samimi, Yaser, 2021. "Reliability monitoring of systems with cumulative shock-based deterioration process," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    3. Sabri-Laghaie, Kamyar & Fathi, Mahdi & Zio, Enrico & Mazhar, Maryam, 2022. "A novel reliability monitoring scheme based on the monitoring of manufacturing quality error rates," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    4. Heping Jia & Rui Peng & Yi Ding & Changzheng Shao, 2020. "Reliability analysis of distributed storage systems considering data loss and theft," Journal of Risk and Reliability, , vol. 234(2), pages 303-321, April.

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