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PRICING A MOTOR EXTENDED WARRANTY WITH LIMITED USAGE COVER

Published online by Cambridge University Press:  17 November 2014

Fidelis T. Musakwa*
Affiliation:
Wits Business School, University of Witwatersrand, 2 St David's Place, Parktown, Johannesburg, South Africa

Abstract

Providers of motor extended warranties with limited usage often face difficulty evaluating the impact of usage limits on warranty price because of incomplete usage data. To address this problem, this paper employs a non-parametric interval-censored survival model of time to accumulate a specific usage. This is used to develop an estimator of the probability that a provider is on risk at a specific time in service. The resulting pricing model is applied to a truck extended warranty case study. The case study demonstrates that interval-censored survival models are ideal for use in pricing motor extended warranties with limited usage cover. The results also suggest that employing a usage rate distribution to forecast the number of vehicles on risk can be misleading, especially on an extended warranty with a relatively high usage limit.

Type
Research Article
Copyright
Copyright © ASTIN Bulletin 2014 

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References

Adamic, P., Dixon, S. and Gillis, D. (2010) Multiple decrement modeling in the presence of interval censoring and masking. Scandinavian Actuarial Journal, 2010 (4), 312327.Google Scholar
Alam, M.M. and Suzuki, K. (2009) Lifetime estimation using only failure information from warranty database. IEEE Transactions on Reliability, 58 (4), 573582.CrossRefGoogle Scholar
Antonio, K., Frees, E.W. and Valdez, E.A. (2010) A multilevel analysis of intercompany claim counts. ASTIN Bulletin, 40 (1), 151177.Google Scholar
Cheng, J. (2002) Unearned premiums and deferred policy acquisition expenses in automobile extended warranty insurance. Journal of Actuarial Practice, 10, 6395.Google Scholar
Cheng, J.S. and Bruce, S.J. (1993) A pricing model for new vehicle extended warranties. Casualty Actuarial Society Forum, Special Edition, 124. Arlington, VA.Google Scholar
Dehghan, M. and Duchesne, T. (2011) A generalization of Turnbull's estimator for nonparametric estimation of the conditional survival function with interval-censored data. Lifetime Data Analysis, 17 (2), 234255.CrossRefGoogle ScholarPubMed
Dempster, A.P., Laird, N.M. and Rubin, D.B. (1977) Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B (Methodological), 39 (1), 138.Google Scholar
Fay, M.P. and Shaw, P.A. (2010) Exact and asymptotic weighted logrank tests for interval-censored data: The interval R package. Journal of Statistical Software, 36 (2), 134.CrossRefGoogle ScholarPubMed
Gentleman, R. and Geyer, C.J. (1994) Maximum likelihood for interval-censored data: Consistency and computation. Biometrika, 81 (3), 618623.CrossRefGoogle Scholar
Gentleman, R. and Vandal, A.C. (2001) Computational algorithms for censored-data problems using intersection graphs. Journal of Computational and Graphical Statistics, 10 (3), 403421.Google Scholar
Gómez, G., Calle, M.L., Oller, R. and Langohr, K. (2009) Tutorial on methods for interval-censored data and their implementation in R. Statistical Modelling, 9 (4), 259297.Google Scholar
Groeneboom, P., Jongbloed, G. and Wellner, J.A. (2008) The support reduction algorithm for computing non-parametric function estimates in mixture models. Scandinavian Journal of Statistics, 35 (3), 385399.Google Scholar
Groeneboom, P. and Wellner, J.A. (1992) Information Bounds and Non-Parametric Maximum Likelihood Estimation. Basel: Birkhäuser.Google Scholar
Hayne, R.M. (2007) Extended service contracts, an overview. Variance, 1 (1), 839.Google Scholar
Hsu, C.-H., Taylor, J.M.G., Murray, S. and Commenges, D. (2007) Multiple imputation for interval-censored data with auxiliary variables. Statistics in Medicine, 26 (4), 769781.Google Scholar
Jack, N., Iskandar, B.P. and Murthy, D.N.P. (2009) A repair — replace strategy based on usage rate for items sold with a two-dimensional warranty. Reliability Engineering and System Safety, 94 (2), 611617.Google Scholar
Jack, N. and Murthy, D.N.P. (2007) A flexible extended warranty and related optimal strategies. The Journal of the Operational Research Society, 58 (12), 16121620.Google Scholar
Jung, M. and Bai, D.S. (2007) Analysis of field data under two-dimensional warranty. Reliability Engineering and System Safety, 92 (2), 135143.CrossRefGoogle Scholar
Kalbfleisch, J.D., Lawless, J.F. and Robinson, J.A. (1991) Methods for the analysis and prediction of warranty claims. Technometrics, 33 (3), 273285.Google Scholar
Karim, M.R. and Suzuki, K. (2005) Analysis of warranty claim data: A literature review. International Journal of Quality and Reliability Management, 22 (7), 667686.CrossRefGoogle Scholar
Kerper, J. and Bowron, L. (2007) An exposure based approach to automobile warranty ratemaking and reserving. Casualty Actuarial Society Forum, Spring, 2943. Arlington, VA.Google Scholar
Law, C.G. and Brookmeyer, R. (1992) Effects of mid-point imputation on the analysis of doubly censored data. Statistics in Medicine, 11 (12), 15691578.Google Scholar
Lawless, J.F. (1998) Statistical analysis of product warranty data. International Statistical Review, 66 (1), 4160.Google Scholar
Li, K., Mallik, S. and Chhajed, D. (2012) Design of extended warranties in supply chains under additive demand. Production and Operations Management, 21 (4), 730746.Google Scholar
Maathuis, M.H. and Hudgens, M.G. (2011) Nonparametric inference for competing risks current status data with continuous, discrete or grouped observation times. Biometrika, 98 (2), 325340.CrossRefGoogle ScholarPubMed
Majeske, K.D. (2007) A non-homogeneous Poisson process predictive model for automobile warranty claims. Reliability Engineering and System Safety, 92 (2), 243251.Google Scholar
Murthy, D.N.P. (1992) A usage dependent model for warranty costing. European Journal of Operational Research, 57 (1), 8999.CrossRefGoogle Scholar
Murthy, D.N.P. and Djamaludin, I. (2002) New product warranty: A literature review. International Journal of Productions Economics, 79 (3), 231260.Google Scholar
Musakwa, F.T. (2012) Valuing the unexpired risk of motor service plans. Conference Proceedings of the Actuarial Society of South Africa 2012 Convention, Cape Town International Convention Centre, Cape Town, 16–17 October 2012, pp. 147–166.Google Scholar
Rai, B. and Singh, N. (2004) Modeling and analysis of automobile warranty data in the presence of bias due to customer-rush near warranty expiration limit. Reliability Engineering and System Safety, 86 (1), 8394.Google Scholar
Rai, B. and Singh, N. (2005) A modeling framework for assessing the impact of new time/mileage warranty limits on the number and cost of automotive warranty claims. Reliability Engineering and System Safety, 88 (2), 157169.Google Scholar
Shafiee, M., Chukova, S., Saidia-Mehrabad, M. and Niaki, S.T.A. (2011) Two-dimensional warranty cost analysis for second-hand products. Communications in Statistics — Theory and Methods, 40 (4), 684701.CrossRefGoogle Scholar
Shahanaghi, K., Noorossana, R., Jalali-Naini, S.G. and Heydari, M. (2013) Failure modeling and optimizing preventive maintenance strategy during two-dimensional extended warranty contracts. Engineering Failure Analysis, 28, 90102.Google Scholar
Su, C. and Shen, J. (2012) Analysis of extended warranty policies with different repair options. Engineering Failure Analysis, 25, 4962.Google Scholar
Sun, J. (2001) Variance estimation of a survival function for interval-censored survival data. Statistics in Medicine, 20 (8), 12491257.Google Scholar
Turnbull, B.W. (1976) The empirical distribution function with arbitrarily grouped, censored and truncated data. Journal of the Royal Statistical Society, Series B (Methodological), 38 (3), 290295.Google Scholar
Wellner, J.A. and Zhan, Y. (1997) A hybrid algorithm for computation of the nonparametric maximum likelihood estimator from censored data. Journal of the American Statistical Association, 92 (439), 945959.Google Scholar
Weltmann, L.N. and Muhonen, D. (2002) Extended warranty ratemaking. Casualty Actuarial Society, Winter, 187216. Arlington, VA.Google Scholar
Wu, S. (2012) Warranty data analysis: A review. Quality and Reliability Engineering International, 28 (8), 795805.Google Scholar
Wu, S. and Akbarov, A. (2011) Support vector regression for warranty claim forecasting. European Journal of Operational Research, 213 (1), 196204.Google Scholar
Zhang, Z. and Sun, J. (2010) Interval censoring. Statistical Methods in Medical Research, 19 (1), 5370.Google Scholar