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Bias correction for the least squares estimator of Weibull shape parameter with complete and censored data

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  • Zhang, L.F.
  • Xie, M.
  • Tang, L.C.

Abstract

Estimation of the Weibull shape parameter is important in reliability engineering. However, commonly used methods such as the maximum likelihood estimation (MLE) and the least squares estimation (LSE) are known to be biased. Bias correction methods for MLE have been studied in the literature. This paper investigates the methods for bias correction when model parameters are estimated with LSE based on probability plot. Weibull probability plot is very simple and commonly used by practitioners and hence such a study is useful. The bias of the LS shape parameter estimator for multiple censored data is also examined. It is found that the bias can be modeled as the function of the sample size and the censoring level, and is mainly dependent on the latter. A simple bias function is introduced and bias correcting formulas are proposed for both complete and censored data. Simulation results are also presented. The bias correction methods proposed are very easy to use and they can typically reduce the bias of the LSE of the shape parameter to less than half percent.

Suggested Citation

  • Zhang, L.F. & Xie, M. & Tang, L.C., 2006. "Bias correction for the least squares estimator of Weibull shape parameter with complete and censored data," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 930-939.
  • Handle: RePEc:eee:reensy:v:91:y:2006:i:8:p:930-939
    DOI: 10.1016/j.ress.2005.09.010
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    Cited by:

    1. Peng, Yizhen & Wang, Yu & Zi, YanYang & Tsui, Kwok-Leung & Zhang, Chuhua, 2017. "Dynamic reliability assessment and prediction for repairable systems with interval-censored data," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 301-309.
    2. Starling, James K. & Mastrangelo, Christina & Choe, Youngjun, 2021. "Improving Weibull distribution estimation for generalized Type I censored data using modified SMOTE," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    3. Yan Shi & Shanshan Shao & Xuexi Yang & Da Wang & Bingrong Chen & Min Deng, 2023. "Metabolic Process Modeling of Metal Resources Based on System Dynamics—A Case Study for Steel in Mainland China," Sustainability, MDPI, vol. 15(13), pages 1-22, June.
    4. Zhuang, Liangliang & Xu, Ancha & Pang, Jihong, 2021. "Product reliability analysis based on heavily censored interval data with batch effects," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    5. Regattieri, A. & Manzini, R. & Battini, D., 2010. "Estimating reliability characteristics in the presence of censored data: A case study in a light commercial vehicle manufacturing system," Reliability Engineering and System Safety, Elsevier, vol. 95(10), pages 1093-1102.
    6. Guo, Xueyi & Zhang, Jingxi & Tian, Qinghua, 2021. "Modeling the potential impact of future lithium recycling on lithium demand in China: A dynamic SFA approach," Renewable and Sustainable Energy Reviews, Elsevier, vol. 137(C).
    7. Renyan Jiang, 2022. "A novel parameter estimation method for the Weibull distribution on heavily censored data," Journal of Risk and Reliability, , vol. 236(2), pages 307-316, April.
    8. Guo, Haitao & Watson, Simon & Tavner, Peter & Xiang, Jiangping, 2009. "Reliability analysis for wind turbines with incomplete failure data collected from after the date of initial installation," Reliability Engineering and System Safety, Elsevier, vol. 94(6), pages 1057-1063.
    9. Acitas, Sukru & Aladag, Cagdas Hakan & Senoglu, Birdal, 2019. "A new approach for estimating the parameters of Weibull distribution via particle swarm optimization: An application to the strengths of glass fibre data," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 116-127.

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