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İlerleyen Sansürlü Örneklemlere Dayalı Olarak Weibull Dağılımının Şekil Parametresinin Sağlam Tahmin Edicileri

Year 2021, Volume: 25 Issue: 2, 410 - 418, 20.08.2021

Arzu Altin Yavuz

https://doi.org/10.19113/sdufenbed.882152

Abstract

Yaşam modellerinde parametre tahmini oldukça önemli bir konudur. Uygulamada karşılaşılan veri tipi genellikle ilerleyen sansürlenmiş veri şeklindedir. İlerleyen sansürlü örneklemlere dayalı parametre tahmini, klasik tam örneklem durumundan farklıdır. Bu çalışmanın amacı ilerleyen sansürlü veriye dayalı olarak Weibull dağılımının şekil parametresini tahmin etmektir. Bu amaçla Weibull dağılımının şekil parametresi basit doğrusal regresyon modeli kullanılarak tahmin edilmiştir. Tahmin yöntemi olarak En Küçük Kareler (EKK) ve sağlam (robust) tahmin yöntemi olan M (Huber, Tukey ve Hampel) tahmin edicileri ele alınmıştır. Bu tahmin yöntemlerinin etkinlikleri veri setinin aykırı değer içerip içermeme durumuna göre Monte-Carlo simülasyon çalışmasıyla karşılaştırılmıştır. Sonuç olarak, ilerleyen sansürlü örnekleme dayalı olarak Weibull dağılımının şekil parametresinin tahmini için en etkili tahmin edicinin M tahmin ediciler olduğu belirlenmiştir.

Keywords

İstatistik Güvenilirlik analizi Weibull dağılımı İlerleyen sansürlü örneklem Sağlam tahmin edici

Supporting Institution

Eskişehir Osmangazi Üniversitesi Bilimsel Araştırma Projeleri Komisyonu

Project Number

2018-1935 kodlu

Thanks

Teşekkür ederiz.

References

  • [1] Amstedter, B. L. 1971. Reliability Mathematics. McGraw-Hill, New York.
  • [2] Lewis, E. E. 1987. Introduction to Reliability Engineering. John Wiley & Sons, Canada.
  • [3] Shafer, S. M., Meredith, J. R. 1998. Operations Management. John Wiley & Sons, New York.
  • [4] Bentley, J. P. 1993. An introduction to Reliability and Quality Engineering. Logman Scientific and Technical. John Wiley & Sons, Inc, New York.
  • [5] Andrews, J. D., Moss, T. R. 2002. Reliability and Risk Assessment. Second Edition. Professional Engineering Publishing Limited: London and Bury St. Edmunds, UK, 540s.
  • [6] Hahn, G. J., Shapiro, S. S. 1967. Statistical Models in Engineering. John Wiley & Sons, Inc. New York, Chichester, Brisbane, Toronto.
  • [7] Moss, T. R. 2005. The Reliability Data Handbook. Professional Engineering Publishing Limited: London and Bury St Edmunds, UK, 287s.
  • [8] Klein, J. 2003. Survival analysis: techniques for censored and truncated data. 2nd ed. New York, London: Springer.
  • [9] Li, W. 2004. Evaluating Mean Life of Power System Equipment with Limited End-of-Life Failure Data. IEEE Transactions on Power Systems, (18), 236-242.
  • [10] Maciejewski, H., Anders, G., Endrenyi, J. 2011. On the use of statistical methods and models for predicting the end of life of electric power equipment. International Conference on Power Engineering, Energy and Electrical Drives (POWERENG).
  • [11] Abernethy, R. 2006. The New Weibull Handbook. 5th ed. Florida.
  • [12] Genschel, U., Meeker, W. 2010. A Comparison of Maximum Likelihood and Median-Rank Regression for Weibull Estimation. Quality Engineering, (22), 236-255.
  • [13] Olteanu, D., Freeman, L. 2010. The Evaluation of Median-Rank Regression and Maximum Likelihood Estimation Techniques for a Two- Parameter Weibull Distribution. Quality Engineering, (22), 256-272.
  • [14] Abernethy, R. 2010. Discussion of the Papers by Olteanu and Freeman and Grenshel and Meeker. Quality Engineering, (22), 281-283.
  • [15] Zhou, D. 2013. Comparison of Two Popular Methods for Transformer Weibull Lifetime Modelling. International Journal of Advanced Research in electrical, Electronics and Instrumentation Engineering, 2(4), 2320-3765.
  • [16] Cacciari, M., Montanari, G. C. 1987. A method to Estimate the Weibull Parameters for Progressively Censored Tests. IEEE Transaction on Reliability, (36), 87-93.
  • [17] Montanari, G. C., Mazzanti, G., Cacciari, M., Forhergill, J. C. 1997. Optimum Estimators for the Weibull Distribution of Censored Data. IEEE Transactions on Dielectrics and Electrical Insulation, (4), 462-469.
  • [18] Ng, H. K. T., Chan, P. S., Balakrishnan, N. 2004. Optimal Progressive Censoring Plans for the Weibull Distribution. Technometrics, (46), 470-481.
  • [19] Zhang, L. F., Xie, M., Tang, L. C. 2006. Robust Regression using Probability Plots for Estimating the Weibull Shape Parameter. Quality and Reliability International, (22), 905-917.
  • [20] Boudt, K., Caliskan, D., Croux, C. 2011. Robust Explicit Estimators of Weibull Parameters. Metrika, (73), 187-209.
  • [21] Olteanu, D., Freeman, L. 2010. The Evaluation of Median-Rank Regression and Maximum Likelihood Estimation Techniques for a Two-Parameter Weibull Distribution. Quality Engineering, (22), 256-272.
  • [22] Genschel, U., Meeker, W. Q. 2010. A Comparison of Maximum Likelihood and Median-Rank Regression for Weibull Estimation. Quality Engineering, (22), 236-255.
  • [23] Asgharzadeh, A., Valiollahi, R., Raqab, M. Z. 2011. Stress-strength Reliability of Weibull Distribution based on Progressively Censored Samples. SORT, (35), 103-124.
  • [24] Mohan, C. R., Rao, A. V., Anjaneyulu, G. V. S. R. 2013. Comparison of Least Square Estimators with Rank Regression Estimators of Weibull Distribution-A Simulation Study. Journal of Statistics, (20), 1-10.
  • [25] Lawson, C., Keats, J. B., Montgomery, D. C. 1997. Comparison of Robust and Least Squares Regression in Computer-Generated Probability Plots. IEEE Transactions on Reliability, 46(1), 108-121.
  • [26] Huber, P. J. 1981. Robust Statistics. John Wiley: New York.
  • [27] Hoaglin, D., Mosteller, F., Tukey, J. W. 1983. Understanding Robust and Exploratory Data Analysis. John Wiley & Sons, Inc.: New York.
  • [28] Tobias, P. A., Trindade, D. C. 1995. Applied Reliability (Second Edition), Van Nostrand Reinhold.:New York.

Robust Estimators of the Shape Parameter of Weibull Distribution Based on Progressively Censored Sample

Year 2021, Volume: 25 Issue: 2, 410 - 418, 20.08.2021

Arzu Altin Yavuz

https://doi.org/10.19113/sdufenbed.882152

Abstract

Parameter estimation is a very important issue in lifetime models. The data type encountered in practice is usually in the form of progressive censored data. Parameter estimation based on progressive censored samples is different from the classical full sample case. The aim of this study is to estimate the shape parameter of the Weibull distribution based on the progressive censored sample. For this purpose, the shape parameter of the Weibull distribution was estimated using a simple linear regression model. Least Squares (OLS) and robust estimation method M (Huber, Tukey and Hampel) estimators are used as estimation method. The efficiencies of these estimation methods were compared with the Monte-Carlo simulation study according to whether the data set contains outliers or not. As a result, M estimators was determined as the most effective estimators for the estimation of the shape parameter of the Weibull distribution based on the progressive censored sample.

Keywords

Statistics Reliability analysis Weibull distribution Prograssive censored sample Robust estimator

Project Number

2018-1935 kodlu

References

  • [1] Amstedter, B. L. 1971. Reliability Mathematics. McGraw-Hill, New York.
  • [2] Lewis, E. E. 1987. Introduction to Reliability Engineering. John Wiley & Sons, Canada.
  • [3] Shafer, S. M., Meredith, J. R. 1998. Operations Management. John Wiley & Sons, New York.
  • [4] Bentley, J. P. 1993. An introduction to Reliability and Quality Engineering. Logman Scientific and Technical. John Wiley & Sons, Inc, New York.
  • [5] Andrews, J. D., Moss, T. R. 2002. Reliability and Risk Assessment. Second Edition. Professional Engineering Publishing Limited: London and Bury St. Edmunds, UK, 540s.
  • [6] Hahn, G. J., Shapiro, S. S. 1967. Statistical Models in Engineering. John Wiley & Sons, Inc. New York, Chichester, Brisbane, Toronto.
  • [7] Moss, T. R. 2005. The Reliability Data Handbook. Professional Engineering Publishing Limited: London and Bury St Edmunds, UK, 287s.
  • [8] Klein, J. 2003. Survival analysis: techniques for censored and truncated data. 2nd ed. New York, London: Springer.
  • [9] Li, W. 2004. Evaluating Mean Life of Power System Equipment with Limited End-of-Life Failure Data. IEEE Transactions on Power Systems, (18), 236-242.
  • [10] Maciejewski, H., Anders, G., Endrenyi, J. 2011. On the use of statistical methods and models for predicting the end of life of electric power equipment. International Conference on Power Engineering, Energy and Electrical Drives (POWERENG).
  • [11] Abernethy, R. 2006. The New Weibull Handbook. 5th ed. Florida.
  • [12] Genschel, U., Meeker, W. 2010. A Comparison of Maximum Likelihood and Median-Rank Regression for Weibull Estimation. Quality Engineering, (22), 236-255.
  • [13] Olteanu, D., Freeman, L. 2010. The Evaluation of Median-Rank Regression and Maximum Likelihood Estimation Techniques for a Two- Parameter Weibull Distribution. Quality Engineering, (22), 256-272.
  • [14] Abernethy, R. 2010. Discussion of the Papers by Olteanu and Freeman and Grenshel and Meeker. Quality Engineering, (22), 281-283.
  • [15] Zhou, D. 2013. Comparison of Two Popular Methods for Transformer Weibull Lifetime Modelling. International Journal of Advanced Research in electrical, Electronics and Instrumentation Engineering, 2(4), 2320-3765.
  • [16] Cacciari, M., Montanari, G. C. 1987. A method to Estimate the Weibull Parameters for Progressively Censored Tests. IEEE Transaction on Reliability, (36), 87-93.
  • [17] Montanari, G. C., Mazzanti, G., Cacciari, M., Forhergill, J. C. 1997. Optimum Estimators for the Weibull Distribution of Censored Data. IEEE Transactions on Dielectrics and Electrical Insulation, (4), 462-469.
  • [18] Ng, H. K. T., Chan, P. S., Balakrishnan, N. 2004. Optimal Progressive Censoring Plans for the Weibull Distribution. Technometrics, (46), 470-481.
  • [19] Zhang, L. F., Xie, M., Tang, L. C. 2006. Robust Regression using Probability Plots for Estimating the Weibull Shape Parameter. Quality and Reliability International, (22), 905-917.
  • [20] Boudt, K., Caliskan, D., Croux, C. 2011. Robust Explicit Estimators of Weibull Parameters. Metrika, (73), 187-209.
  • [21] Olteanu, D., Freeman, L. 2010. The Evaluation of Median-Rank Regression and Maximum Likelihood Estimation Techniques for a Two-Parameter Weibull Distribution. Quality Engineering, (22), 256-272.
  • [22] Genschel, U., Meeker, W. Q. 2010. A Comparison of Maximum Likelihood and Median-Rank Regression for Weibull Estimation. Quality Engineering, (22), 236-255.
  • [23] Asgharzadeh, A., Valiollahi, R., Raqab, M. Z. 2011. Stress-strength Reliability of Weibull Distribution based on Progressively Censored Samples. SORT, (35), 103-124.
  • [24] Mohan, C. R., Rao, A. V., Anjaneyulu, G. V. S. R. 2013. Comparison of Least Square Estimators with Rank Regression Estimators of Weibull Distribution-A Simulation Study. Journal of Statistics, (20), 1-10.
  • [25] Lawson, C., Keats, J. B., Montgomery, D. C. 1997. Comparison of Robust and Least Squares Regression in Computer-Generated Probability Plots. IEEE Transactions on Reliability, 46(1), 108-121.
  • [26] Huber, P. J. 1981. Robust Statistics. John Wiley: New York.
  • [27] Hoaglin, D., Mosteller, F., Tukey, J. W. 1983. Understanding Robust and Exploratory Data Analysis. John Wiley & Sons, Inc.: New York.
  • [28] Tobias, P. A., Trindade, D. C. 1995. Applied Reliability (Second Edition), Van Nostrand Reinhold.:New York.
There are 28 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Arzu Altin Yavuz 0000-0002-3277-740X

Project Number 2018-1935 kodlu
Publication Date August 20, 2021
Published in Issue Year 2021 Volume: 25 Issue: 2

Cite

APA Altin Yavuz, A. (2021). İlerleyen Sansürlü Örneklemlere Dayalı Olarak Weibull Dağılımının Şekil Parametresinin Sağlam Tahmin Edicileri. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 25(2), 410-418. https://doi.org/10.19113/sdufenbed.882152
AMA Altin Yavuz A. İlerleyen Sansürlü Örneklemlere Dayalı Olarak Weibull Dağılımının Şekil Parametresinin Sağlam Tahmin Edicileri. SDÜ Fen Bil Enst Der. August 2021;25(2):410-418. doi:10.19113/sdufenbed.882152
Chicago Altin Yavuz, Arzu. “İlerleyen Sansürlü Örneklemlere Dayalı Olarak Weibull Dağılımının Şekil Parametresinin Sağlam Tahmin Edicileri”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 25, no. 2 (August 2021): 410-18. https://doi.org/10.19113/sdufenbed.882152.
EndNote Altin Yavuz A (August 1, 2021) İlerleyen Sansürlü Örneklemlere Dayalı Olarak Weibull Dağılımının Şekil Parametresinin Sağlam Tahmin Edicileri. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 25 2 410–418.
IEEE A. Altin Yavuz, “İlerleyen Sansürlü Örneklemlere Dayalı Olarak Weibull Dağılımının Şekil Parametresinin Sağlam Tahmin Edicileri”, SDÜ Fen Bil Enst Der, vol. 25, no. 2, pp. 410–418, 2021, doi: 10.19113/sdufenbed.882152.
ISNAD Altin Yavuz, Arzu. “İlerleyen Sansürlü Örneklemlere Dayalı Olarak Weibull Dağılımının Şekil Parametresinin Sağlam Tahmin Edicileri”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 25/2 (August 2021), 410-418. https://doi.org/10.19113/sdufenbed.882152.
JAMA Altin Yavuz A. İlerleyen Sansürlü Örneklemlere Dayalı Olarak Weibull Dağılımının Şekil Parametresinin Sağlam Tahmin Edicileri. SDÜ Fen Bil Enst Der. 2021;25:410–418.
MLA Altin Yavuz, Arzu. “İlerleyen Sansürlü Örneklemlere Dayalı Olarak Weibull Dağılımının Şekil Parametresinin Sağlam Tahmin Edicileri”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 25, no. 2, 2021, pp. 410-8, doi:10.19113/sdufenbed.882152.
Vancouver Altin Yavuz A. İlerleyen Sansürlü Örneklemlere Dayalı Olarak Weibull Dağılımının Şekil Parametresinin Sağlam Tahmin Edicileri. SDÜ Fen Bil Enst Der. 2021;25(2):410-8.
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