Accelerated Life Testing and Its Application in the Field of Warranty Policy under Type-I Censoring Scheme
Keywords:
Accelerated life test, constant stress, Fréchet distribution, warranty policy, age-replacement, Type-I censoring, Fisher information matrix, simulationAbstract
In this paper, we describe how to propose and analyze the accelerated life testing plans to develop the excellence and reliability of the item for consumption. We also focus on finding the expected cost rate and the expected total cost for age replacement under pro rate rebate warranty policy. The problem is studied using constant stress, under the assumption that the lifetimes of the units follow the Fréchet failure model for predicting the cost of age replacement under the warranty policy. Asymptotic variance and covariance matrix of the estimators are obtained by using the Fisher information matrix. Confidence intervals for parameters and respective errors are also obtained. A simulation study is performed to illustrate the statistical properties.
References
Abdel-Ghaly AA, Attia AF, Aly HM. Estimation of the parameters of Pareto distribution and the reliability function using accelerated life testing with censoring. Commun Stat - Simul Comput. 1998; 27(2): 469-484.
Alam I, Intezar MA, Ahmed A. Costs of maintenance service policy: a new approach on constant stress partially accelerated life test for generalized inverted exponential distribution. Reliab: Theory Appl. 2021; 16(2): 45-57.
Alam I, Islam A, Ahmed A. Parametric estimation on constant stress partially accelerated life tests for the exponentiated exponential distribution using multiple censoring. Reliab: Theory Appl. 2019a; 14(4): 20-31.
Alam I, Islam A, Ahmed A. Parametric estimation under step-stress partially accelerated life tests for inverse Rayleigh distribution based on adaptive Type-I progressively hybrid censoring. Int J Emerg Technol Innov Res. 2019b; 6(6): 96-106.
Alam I, Islam AU, Ahmed A. Accelerated life test plans and age-replacement policy under warranty on burr Type-X distribution with Type-II censoring. J Stat Appl Prob. 2020; 9(3): 1-10.
Attia AF, Aly HM, Bleed SO. Estimating and planning accelerated life test using constant stress for generalized logistic distribution under Type-I censoring. Int Sch Res Notices. 2011; 11: 1-15.
Attia, AF, Shaban AS, Abd El Sattar MH. Estimation in constant-stress accelerated life testing for Birnbaum-Saunders distribution under censoring. Int J Contemp Math Sci. 2013; 8(4): 173-188.
Borgia O, DeCarlo F, Fanciullacci N, Tucci M. Accelerated life tests for new product qualification: a case study in the household appliance. In: Proceedings of the 11th IFAC Workshop on Intelligent Manufacturing Systems. International Federation of Automatic Control; 2013. p. 269-274.
Calabria R, Pulcini G. Confidence limits for reliability and tolerance limits in the inverse Weibull distribution. Reliab Eng Syst Saf. 1989; 24(1): 77-85.
Chaudhary S, Kumar J, Tomer SK. Estimation of P[Y< X] for Maxwell distribution. Int J Stat Manag Syst. 2017; 20(3): 467-481.
Chaudhary S, Tomer SK. Estimation of stress–strength reliability for Maxwell distribution under progressive Type-II censoring scheme. Int J Syst Assur. 2018; 9(5): 1107-1119
Chi-chao L. A comparison between the Weibull and lognormal models used to analyze reliability data. PhD [dissertation]. Nottingham: University of Nottingham; 1997.
Chien YH. The effect of a Pro-Rata rebate warranty on the age replacement policy with salvage value consideration. IEEE Trans Reliab. 2010; 59(2): 383-392.
Chien YH, Chang FM, Liu TH. The Effects of salvage value on the age-replacement policy under renewing warranty. In Proceedings of the International Conference on Industrial Engineering and Operations Management (ICIEOM), Bali, Indonesia. 2014: 1840-1848.
El-Dessouky EA. Accelerated life testing and age-replacement policy under warranty on exponentiated Pareto distribution. Appl Math Sci. 2015; 9(36): 1757-1770.
El-Dessouky EA. Estimating costs of maintenance service policy using step stress partially accelerated life testing for the extension of exponential distribution under type-II censoring. Int J Contemp Math Sci. 2017; 12(5): 225-242.
Erto P. Genesis, properties and identification of the inverse Weibull lifetime model. Stat e Appl. 1989; 1: 117-128.
Gupta SK, De S, Chatterjee A. Warranty forecasting from incomplete two-dimensional warranty data. Reliab Eng Syst Saf. 2014; 126: 1-13.
Huang HZ, Liu Z J, Li Y, Liu Y, He L. A warranty cost model with intermittent and heterogeneous usage. Mainte Relia. 2008; 4: 9-15.
Huang HZ, Liu ZJ, Murthy DNP. Optimal reliability, warranty, and price for new products. IIE Trans. 2007; 39(8): 819-827.
Huang YS, Huang CD, Ho JW. A customized two-dimensional extended warranty with preventive maintenance. Eur J Oper Res. 2017; 257(3): 971-978.
Jack N, Iskandar BP, Murthy DP. A repair-replace strategy based on usage rate for items sold with a two-dimensional warranty. Reliab Eng Syst Saf. 2009; 94(2): 611-617.
Jung KM, Park M, Park DH. Cost optimization model following extended renewing two-phase warranty. Comput Ind Eng. 2015; 79: 188-194.
Mamer JW. Cost analysis of pro rata and free‐replacement warranties. Nav Res Logist. 1982; 29(2): 345-356.
Matis TI, Jayaraman R, Rangan A. Optimal price and pro rata decisions for combined warranty policies with different repair options. IIE Trans. 2008; 40(10): 984-991.
Meeker WQ, Escobar LA. A review of recent research and current issues in accelerated testing. Int Stat Rev. 1993; 63(1): 147-168.
Murthy DNP, Djamaludin I. New product warranty: a literature review. Int J Prod Econ. 2002; 79(3): 231-260.
Ramos PL, Louzada F, Ramos E, Dey S. The Fréchet distribution: estimation and application-an overview. Int J Stat Manag Syst. 2019; 23(3): 1-30.
Xie W, Ye ZS. Aggregate discounted warranty cost forecast for a new product considering stochastic sales. IEEE Trans Reliab. 2016; 65(1): 486-497.
Yang G. Accelerated life test plans for predicting warranty cost. IEEE Trans Reliab. 2010; 59(4): 628-634.
Ye ZS, Murthy DP. Warranty menu design for a two-dimensional warranty. Reliab Eng Syst Saf. 2016; 155: 21-29.
Zhao X, Xie M. Using accelerated life tests data to predict warranty cost under imperfect repair. Comput Ind Eng. 2017; 107: 223-234.
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