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On analysis of incomplete field failure data. (English) Zbl 1304.62150

Summary: Many commercial products are sold with warranties and indirectly through dealers. The manufacturer-retailer distribution mechanism results in serious missing data problems in field return data, as the sales date for an unreturned unit is generally unknown to the manufacturer. This study considers a general setting for field failure data with unknown sales dates and a warranty limit. A stochastic expectation–maximization (SEM) algorithm is developed to estimate the distributions of the sales lag (time between shipment to a retailer and sale to a customer) and the lifetime of the product under study. Extensive simulations are used to evaluate the performance of the SEM algorithm and to compare with the imputation method proposed by S. Ghosh [Ann. Appl. Stat. 4, No. 4, 1976–1999 (2010; Zbl 1220.62123)]. Three real examples illustrate the methodology proposed in this paper.

MSC:

62P30 Applications of statistics in engineering and industry; control charts
62N05 Reliability and life testing

Citations:

Zbl 1220.62123
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References:

[1] Akbarov, A. and Wu, S. (2013). Warranty claims data analysis considering sales delay. Qual. Reliab. Eng. Int. 29 113-123.
[2] Blischke, W., Karim, M. and Murthy, D. (2011). Warranty Data Collection and Analysis . Springer, Berlin. · Zbl 1226.90002
[3] Bordes, L., Chauveau, D. and Vandekerkhove, P. (2007). A stochastic EM algorithm for a semiparametric mixture model. Comput. Statist. Data Anal. 51 5429-5443. · Zbl 1445.62056
[4] Cariou, C. and Chehdi, K. (2008). Unsupervised texture segmentation/classification using 2-d autoregressive modeling and the stochastic expectation-maximization algorithm. Pattern Recogn. Lett. 29 905-917.
[5] Celeux, G. and Diebolt, J. (1985). The SEM algorithm: A probabilistic teacher algorithm derived from the EM algorithm for the mixture problem. Computational Statistics Quarterly 2 73-82.
[6] Chauveau, D. (1995). A stochastic EM algorithm for mixtures with censored data. J. Statist. Plann. Inference 46 1-25. · Zbl 0821.62013
[7] Coit, D. W. and Jin, T. (2000). Gamma distribution parameter estimation for field reliability data with missing failure times. IIE Trans. 32 1161-1166.
[8] Diebolt, J. and Celeux, G. (1993). Asymptotic properties of a stochastic EM algorithm for estimating mixing proportions. Comm. Statist. Stochastic Models 9 599-613. · Zbl 0783.62021
[9] Ghosh, S. (2010). An imputation-based approach for parameter estimation in the presence of ambiguous censoring with application in industrial supply chain. Ann. Appl. Stat. 4 1976-1999. · Zbl 1220.62123
[10] Hu, X. J. and Lawless, J. F. (1996). Estimation of rate and mean functions from truncated recurrent event data. J. Amer. Statist. Assoc. 91 300-310. · Zbl 0871.62032
[11] Ion, R. A., Petkova, V. T., Peeters, B. H. and Sander, P. C. (2007). Field reliability prediction in consumer electronics using warranty data. Qual. Reliab. Eng. Int. 23 401-414.
[12] Kalbfleisch, J. D., Lawless, J. F. and Robinson, J. A. (1991). Methods for the analysis and prediction of warranty claims. Technometrics 33 273-285. · Zbl 0761.62137
[13] Karim, M. R. (2008). Modelling sales lag and reliability of an automobile component from warranty database. Int. J. Reliab. Qual. Saf. Eng. 2 234-247.
[14] Lawless, J. F. (1998). Statistical analysis of product warranty data. Int. Stat. Rev. 66 41-60. · Zbl 0893.62099
[15] Louis, T. A. (1982). Finding the observed information matrix when using the EM algorithm. J. Roy. Statist. Soc. Ser. B 44 226-233. · Zbl 0488.62018
[16] Marschner, I. C. (2001). On stochastic versions of the EM algorithm. Biometrika 88 281-286. · Zbl 1028.62011
[17] McLachlan, G. J. and Krishnan, T. (2008). The EM Algorithm and Extensions , 2nd ed. Wiley, Hoboken, NJ. · Zbl 1165.62019
[18] Nielsen, S. F. (2000). The stochastic EM algorithm: Estimation and asymptotic results. Bernoulli 6 457-489. · Zbl 0981.62022
[19] Rai, B. and Singh, N. (2006). Customer-rush near warranty expiration limit, and nonparametric hazard rate estimation from known mileage accumulation rates. IEEE Trans. Reliab. 55 480-489.
[20] Svensson, I. and Sj√∂stedt-de Luna, S. (2010). Asymptotic properties of a stochastic EM algorithm for mixtures with censored data. J. Statist. Plann. Inference 140 111-127. · Zbl 1178.62020
[21] Wei, G. C. G. and Tanner, M. A. (1990). A Monte Carlo implementation of the EM algorithm and the poor man’s data augmentation algorithms. J. Amer. Statist. Assoc. 85 699-704.
[22] Wilson, S., Joyce, T. and Lisay, E. (2009). Reliability estimation from field return data. Lifetime Data Anal. 15 397-410. · Zbl 1282.62226
[23] Wu, S. (2012). Warranty data analysis: A review. Qual. Reliab. Eng. Int. 28 795-805.
[24] Wu, H. and Meeker, W. Q. (2002). Early detection of reliability problems using information from warranty databases. Technometrics 44 120-133.
[25] Xie, W. and Liao, H. (2013). Some aspects in estimating warranty and post-warranty repair demands. Naval Res. Logist. 60 499-511.
[26] Ye, Z.-S., Hong, Y. and Xie, Y. (2013). How do heterogeneities in operating environments affect field failure predictions and test planning? Ann. Appl. Stat. 7 2249-2271. · Zbl 1283.62210
[27] Ye, Z.-S. and Ng, H. K. T. (2014). Supplement to “On analysis of incomplete field failure data.” . · Zbl 1304.62150
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