The Estimation Of Automobile Failure Rate Distribution And Cost Analysis During Two Dimensional Warranty

With the maturing of product’s aftermarket, product assurance has not only beenconsidered as an additional service, but has become a stand-alone paid products, notonly for the benefit of product assurance provider, but also for providing a guaranteefor consumers. Currently, product warranties are divided into one-dimensionalwarranty and two-dimensional warranty. One-dimensional warranty is usuallyprovided for household appliances, that is the manufacturer will provide guarantee forproduct quality or performance and other aspects only within a certain time limit.However, two-dimensional warranty is usually used in automotive industry, that is themanufacturer will provide guarantee with the coverage of both time and mileage.Such as the description of “three years or one hundred thousand kilometers”, whentime or mileage exceeds the guarantee conditions, then the two-dimensional warrantyexpires. Because the research of two-dimensional warranty is relatively more complexthan one-dimensional warranty, in recent years the majority of scholars have maderesearches on failure rate function and cost of automobile one-dimensional warrantyfrom different perspectives. Only a few scholars have made estimations of failure ratedistribution and cost of automobile two-dimensional automobile warranty, but theresults can not be easily applied in practice for the lack of real data as support.This paper is based on automobile two-dimensional warranty, using the realfailure service data from after-sales service shop of a certain automobile, andconsidering the first time to failure and consumer usage rate as the study variables. Bythe select and analysis of large data, using accelerated failure time model, firstly, wemake estimations of failure rate function during the basic warranty, then we propose amathematical model of warranty cost by renewal theory. Secondly, we makesensitivity analyses for automobile age and mileage separately, that is to say, we makeestimations of failure rate function and cost model again when automobile age ormileage changes. With the AFT model, we consider consumer usage rate as a parameter of the first time to failure distribution function, and then solving the modelwith a accelerated failure factor. Using the AFT model, we have achieved theconversion from two-dimensional model down to one-dimensional model effectively,making the solving process of the failure rate function and cost model more simplified.According to the failure rate function and cost model in the above, failure rate andwarrant cost depend on the distribution functions that the first time to failure andusage rate are subject to. Finding that under three different warranty coverages,Weibull distribution has the best goodness of fit for the first time to failure sampledata. However, for the usage rate sample data, when the time limit is three years,Weibull-distribution has the best goodness of fit, but when the time limit is extendedto five years, Exponential distribution takes the place of Weibull-distribution.Through the estimations of failure rate function and cost analysis, and thesensitivity analyses for automobile age and mileage, the results can not only provideto the manufacturer some quantitative and qualitative support for designing diverseautomobile two-dimensional warranty strategies and making the price of warranty, butalso provide some reference for consumers to choose warranty. As the basic researchfor automobile two-dimensional warranty, this paper has maken the foundation oftheory and method for automobile two-dimensional extended warranty longitudinally,and it also provides reference for other industries’ two-dimensional product warrantyanalysis laterally.