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Statistical Analysis of Modern Reliability Data

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Springer Handbook of Engineering Statistics

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Abstract

Reliability analysis has been using time-to-event data, degradation data, and recurrent event data, while the associated covariates tend to be simple and constant over time. Over the past years, we have witnessed rapid development of sensor and wireless technology, which enables us to track the product usage and use environment. Nowadays, we are able to collect richer information on covariates which provides opportunities for better reliability predictions. In this chapter, we first review recent development on statistical methods for reliability analysis. We then focus on introducing several specific methods that were developed for different types of reliability data by utilizing the covariate information. Illustrations of those methods are also provided using examples from industry. We also provide a brief review on recent developments of test planning and then focus on illustrating the sequential Bayesian designs with examples of fatigue testing for polymer composites. The chapter is concluded with some discussions and remarks.

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References

  1. Meeker, W.Q., Escobar, L.A.: Statistical Methods for Reliability Data. Wiley, New York (1998)

    MATH  Google Scholar 

  2. Meeker, W.Q., Hong, Y.: Reliability meets big data: opportunities and challenges, with discussion. Qual. Eng. 26, 102–116 (2014)

    Google Scholar 

  3. Hong, Y., Zhang, M., Meeker, W.Q.: Big data and reliability applications: The complexity dimension. J. Qual. Technol. 50(2), 135–149 (2018)

    Google Scholar 

  4. Lawless, J.F., Crowder, M.J., Lee, K.A.: Analysis of reliability and warranty claims in products with age and usage scales. Technometrics 51, 14–24 (2009)

    MathSciNet  Google Scholar 

  5. Guo, H., Monteforte, A., Mettas, A., Ogden, D.: Warranty prediction for products with random stresses and usages. In: IEEE Proceedings Annual Reliability and Maintainability Symposium, pp. 72–77. IEEE, Fort Worth, TX (2009)

    Google Scholar 

  6. Lu, L., Anderson-Cook, C.M.: Using age and usage for prediction of reliability of an arbitrary system from a finite population. Qual. Reliab. Eng. Int. 27, 179–190 (2011)

    Google Scholar 

  7. Hong, Y., Meeker, W.Q.: Field-failure and warranty prediction based on auxiliary use-rate information. Technometrics 52, 148–159 (2010)

    MathSciNet  Google Scholar 

  8. Nelson, W.: Prediction of field reliability of units, each under differing dynamic stresses, from accelerated test data. In: Balakrishnan, N., Rao, C.R. (eds.) Handbook of Statistics 20: Advances in Reliability. North-Holland, Amsterdam (2001). Chap. IX

    Google Scholar 

  9. Voiculescu, S., Guérin, F., Barreau, M., Charki, A.: Reliability estimation in random environment: different approaches. In: IEEE Proceedings Annual Reliability and Maintainability Symposium, pp. 202–307. IEEE, Orlando, FL (2007)

    Google Scholar 

  10. Hong, Y., Meeker, W.Q.: Field-failure predictions based on failure-time data with dynamic covariate information. Technometrics 55, 135–149 (2013)

    MathSciNet  Google Scholar 

  11. Whitmore, G.A.: Estimation degradation by a Wiener diffusion process subject to measurement error. Lifetime Data Anal. 1, 307–319 (1995)

    MATH  Google Scholar 

  12. Doksum, K.A., Hóyland, A.: Models for variable-stress accelerated life testing experiments based on Wiener processes and the inverse Gaussian distribution. Technometrics 34, 74–82 (1992)

    MATH  Google Scholar 

  13. Wang, X.: Wiener processes with random effects for degradation data. J. Multivar. Anal. 101, 340–351 (2010)

    MathSciNet  MATH  Google Scholar 

  14. Lawless, J.F., Crowder, M.: Covariates and random effects in a gamma process model with application to degradation and failure. Lifetime Data Anal. 10, 213–227 (2004)

    MathSciNet  MATH  Google Scholar 

  15. Wang, X., Xu, D.: An inverse Gaussian process model for degradation data, Technometrics 52, 188–197 (2010)

    MathSciNet  Google Scholar 

  16. Ye, Z.-S., Chen, N.: The inverse Gaussian process as a degradation model. Technometrics 56, 302–311 (2014)

    MathSciNet  Google Scholar 

  17. Lu, C.J., Meeker, W.Q.: Using degradation measures to estimate a time-to-failure distribution. Technometrics 34, 161–174 (1993)

    MathSciNet  MATH  Google Scholar 

  18. Meeker, W.Q., Escobar, L.A., Lu, C.J.: Accelerated degradation tests: modeling and analysis. Technometrics 40, 89–99 (1998)

    Google Scholar 

  19. Bagdonavičius, V., Nikulin, M.S.: Estimation in degradation models with explanatory variables. Lifetime Data Anal. 7, 85–103 (2001)

    MathSciNet  MATH  Google Scholar 

  20. Bae, S.J., Kuo, W., Kvam, P.H.: Degradation models and implied lifetime distributions. Reliab. Eng. Syst. Saf. 92, 601–608 (2007)

    Google Scholar 

  21. Duan, Y., Hong, Y., Meeker, W., Stanley, D., Gu, X.: Photodegradation modeling based on laboratory accelerated test data and predictions under outdoor weathering for polymeric materials. Ann. Appl. Stat. 11, 2052–2079 (2017)

    MathSciNet  MATH  Google Scholar 

  22. Escobar, L.A., Meeker, W.Q., Kugler, D.L., Kramer, L.L.: Accelerated destructive degradation tests: data, models, and analysis. In: Lindqvist, B.H., Doksum, K.A. (eds.) Mathematical and Statistical Methods in Reliability. World Scientific Publishing Company, Singapore (2003)

    Google Scholar 

  23. Xie, Y., King, C.B., Hong, Y., Yang, Q.: Semi-parametric models for accelerated destructive degradation test data analysis. Technometrics 60, 222–234 (2018)

    MathSciNet  Google Scholar 

  24. Ding, Y., Yang, Q., King, C.B., Hong, Y.: A general accelerated destructive degradation testing model for reliability analysis. IEEE Trans. Reliab. 68(4), 1272–1282 (2019). DOI: 10.1109/TR.2018.2883983

    Google Scholar 

  25. Hong, Y., Duan, Y., Meeker, W.Q., Stanley, D.L., Gu, X.: Statistical methods for degradation data with dynamic covariates information and an application to outdoor weathering data. Technometrics 57, 180–193 (2015)

    MathSciNet  Google Scholar 

  26. Xu, Z., Hong, Y., Jin, R.: Nonlinear general path models for degradation data with dynamic covariates. Appl. Stoch. Model. Bus. Ind. 32, 153–167 (2016)

    MathSciNet  MATH  Google Scholar 

  27. Zhao, R., Liu, B.: Renewal process with fuzzy interarrival times and rewards. Int. J. Uncertainty Fuzziness Knowledge Based Syst. 11, 573–586 (2003)

    MathSciNet  MATH  Google Scholar 

  28. Hong, Y., Li, M., Osborn, B.: System unavailability analysis based on window-observed recurrent event data. Appl. Stoch. Model. Bus. Ind. 31, 122–136 (2015)

    MathSciNet  Google Scholar 

  29. Kijima, M.: Some results for repairable systems with general repair. J. Appl. Probab. 26, 89–102 (1989)

    MathSciNet  MATH  Google Scholar 

  30. Wang, H., Pham, H.: A quasi renewal process and its applications in imperfect maintenance. Int. J. Syst. Sci. 27, 1055–1062 (1996)

    MATH  Google Scholar 

  31. Doyen, L., Gaudoin, O.: Classes of imperfect repair models based on reduction of failure intensity or virtual age. Reliab. Eng. Syst. Saf. 84, 45–56 (2004)

    Google Scholar 

  32. Lindqvist, B., Elvebakk, G., Heggland, K.: The trend-renewal process for statistical analysis of repairable systems. Technometrics 45, 31–44 (2003)

    MathSciNet  Google Scholar 

  33. Yang, Q., Hong, Y., Chen, Y., Shi, J.: Failure profile analysis of complex repairable systems with multiple failure modes. IEEE Trans. Reliab. 61, 180–191 (2012)

    Google Scholar 

  34. Pietzner, D., Wienke, A.: The trend-renewal process: a useful model for medical recurrence data. Stat. Med. 32, 142–152 (2013)

    MathSciNet  Google Scholar 

  35. Yang, Q., Hong, Y., Zhang, N., Li, J.: A copula-based trend-renewal process model for analysis of repairable systems with multitype failures. IEEE Trans. Reliab. 66(3), 590–602 (2017)

    Google Scholar 

  36. Xu, Z., Hong, Y., Meeker, W.Q., Osborn, B.E., Illouz, K.: A multi-level trend-renewal process for modeling systems with recurrence data. Technometrics 59, 225–236 (2017)

    MathSciNet  Google Scholar 

  37. Meeker, W.Q.: A comparison of accelerated life test plans for Weibull and lognormal distributions and type I censoring. Technometrics 26(2), 157–171 (1984)

    MATH  Google Scholar 

  38. Nelson, W.: Accelerated Testing: Statistical Models, Test Plans, and Data Analyses, (Republished in a paperback in Wiley Series in Probability and Statistics, 2004). Wiley, New York (1990)

    Google Scholar 

  39. Zhang, Y., Meeker, W.Q.: Bayesian life test planning for the Weibull distribution with given shape parameter. Metrika 61(3), 237–249 (2005)

    MathSciNet  MATH  Google Scholar 

  40. Zhang, Y., Meeker, W.Q.: Bayesian methods for planning accelerated life tests. Technometrics 48(1), 49–60 (2006)

    MathSciNet  Google Scholar 

  41. Hong, Y., King, C.B., Zhang, Y., Meeker, W.Q.: Bayesian life test planning for log-location-scale family of distributions. J. Qual. Technol. 47, 336–350 (2015)

    Google Scholar 

  42. King, C., Hong, Y., Dehart, S.P., Defeo, P.A., Pan, R.: Planning Fatigue Tests for Polymer Composites. J. Qual. Technol. 48, 227–245 (2016)

    Google Scholar 

  43. Lee, I.-C., Hong, Y., Tseng, S.-T., Dasgupta, T.: Sequential Bayesian design for accelerated life tests. Technometrics 60(4), 472–483 (2018)

    MathSciNet  Google Scholar 

  44. Lu, L., Lee, I., Hong, Y.: Bayesian Sequential design based on dual objectives for accelerated life tests. In: Lio, Y., Ng, H., Tsai, T., Chen, D. (eds.) Statistical Quality Technologies, pp. 257–277. Springer, Berlin (2019)

    Google Scholar 

  45. Meeker, W.Q., Hong, Y., Escobar, L.A.: Degradation Models and Analyses. In: Handbook of Engineering, Quality Control, and Physical Sciences. Wiley, New York (2010). DOI: 10.1002/0471667196.ess7148

    Google Scholar 

  46. Hong, Y., Meeker, W.Q., McCalley, J.D.: Prediction of remaining life of power transformers based on left truncated and right censored lifetime data. Ann. Appl. Stat. 3, 857–879 (2009)

    MathSciNet  MATH  Google Scholar 

  47. Bagdonavičius, V., Nikulin, M.S.: Accelerated Life Models: Modeling and Statistical Analysis. Chapman & Hall/CRC, Boca Raton (2001)

    MATH  Google Scholar 

  48. Lawless, J.F., Fredette, M.: Frequentist prediction intervals and predictive distributions. Biometrika 92, 529–542 (2005)

    MathSciNet  MATH  Google Scholar 

  49. Hong, Y.: On Computing the distribution function for the Poisson Binomial Distribution. Comput. Stat. Data Anal. 59, 41–51 (2013)

    MathSciNet  MATH  Google Scholar 

  50. Meyer, M.C.: Inference using shape-restricted regression splines. Ann. Appl. Stat. 2, 1013–1033 (2008)

    MathSciNet  MATH  Google Scholar 

  51. Fraser, D., Massam, A.S.H.: A mixed primal-dual bases algorithm for regression under inequality constraints. Application to concave regression. Scand. J. Stat. 16, 65–74 (1989)

    MATH  Google Scholar 

  52. Carpenter, J.R., Goldstein, H., Rasbash, J.: A novel bootstrap procedure for assessing the relationship between class size and achievement. Appl. Stat. 52, 431–443 (2003)

    MathSciNet  MATH  Google Scholar 

  53. Lütkepohl, H.: New Introduction to Multiple Time Series Analysis, 2nd edn. Springer, Berlin (2005)

    MATH  Google Scholar 

  54. Epaarachchi, J.A., Clausen, P.D.: An empirical model for fatigue behavior prediction of glass fibre-reinforced plastic composites for various stress ratios and test frequencies. Compos. A: Appl. Sci. Manuf. 34(4), 313–326 (2003)

    Google Scholar 

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Acknowledgements

The authors thank the editor for his valuable comments which greatly helped improve this chapter. The research by Wang and Hong was partially supported by National Science Foundation Grants CMMI-1904165 to Virginia Tech.

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Authors and Affiliations

  1. Department of Statistics, Virginia Tech, Blacksburg, VA, USA

    Yueyao Wang & Yili Hong

  2. Department of Statistics, National Cheng Kung University, Tainan, Taiwan

    I-Chen Lee

  3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, USA

    Lu Lu

Authors
  1. Yueyao Wang
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  2. I-Chen Lee
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  3. Lu Lu
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  4. Yili Hong
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Corresponding author

Correspondence to Yili Hong .

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Editors and Affiliations

  1. Department of Industrial & Systems Engineering, Rutgers University, Piscataway, NJ, USA

    Hoang Pham

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    Wang, Y., Lee, IC., Lu, L., Hong, Y. (2023). Statistical Analysis of Modern Reliability Data. In: Pham, H. (eds) Springer Handbook of Engineering Statistics. Springer Handbooks. Springer, London. https://doi.org/10.1007/978-1-4471-7503-2_6

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