Warranty Cost Modeling And Analysis - IJSER

International Journal of Scientific & Engineering Research, Volume 5, Issue 12, December-2014ISSN 2229-5518Warranty Cost Modeling and Analysis Mr. Saurabh Ambekar1, Mr. Madan M. Jagtap21Saraswati College of com2Saraswati College of Engineering, Kharghar,India,jagtap.aero@gmail.comABSTRACT:For products sold with warranty, themanufacturer incurs costs resulting from theservicing of failures occurring under warranty.These costs depend on several factors, the mostimportant being the reliability of the product. Forplanning purposes, the manufacturer must estimatethe expected cost of warranty per unit sold and theexpected cost per unit time over the product lifecycle. This must be done in the productdevelopment stage. This article deals with modelsthat may be used to obtain these cost estimates forproducts sold with free-replacement and prorata warranties.product performance, buyer responsibilities andwhat the warranty will do if an item purchased failsto meet the stated performance.”A. Types of Warranty –There is generally two typesa. 1 dimensionalb. 2 dimensional.1) 1-d warranty (different policies)a)IJSERKey words: warranty; reliability; cost analysis; cost modelsINTRODUCTIONPolicy 1Non renewing free replacement policy – inwarranty period seller repairs or replacesthe failed item in free of cost. Let thewarranty period is W. After completing Wperiod warranty gets finished.It is non renewing means if object fails inW and then it get repair/replaced. Afterrepair/replace it doesn’t get another extraW1 period of warranty. Warranty expireson its initial W period only.In present market, customers want that whatever heis purchasing; that product should give satisfactionduring its useful life. So the manufacturer has toprovide that assurance to customer. Otherwisemanufacturer can’t survive in this race.Here the warranty introduces. It helpsmanufacturer to stay in market. Warranty gives – protection to manufacturer and buyer indication of product quality assurance of good performance of product right to buyer to compensate when apurchased object can’t work satisfactorilyas manufacturer saidb)Policy 2Basic rebate warranty policy – in this, sellerrefunded an amount which is equal to αC.Where 0 α 1. But for refunding itemshould be in warranty period.Here α scale parameterC cost to buyerc)Policy 3Renewing pro-rata policy – in this, if itemfails in W then for repairing manufacturertakes some cost from buyer to repair it. Thiscost is equal to (1 . After repairing/replacing an item he also provides anotherwarranty on replaced item i.e. renewingpolicy.Here, X time to failure of an itemWhat is warranty?“It is a written and/or oral manufacturer’sassurance to a buyer that a product or service is orshall be as represented. It may be considered to be acontractual agreement between buyer andmanufacturer that is entered into upon sale of theproduct or service. The contract specifies theIJSER 2014http://www.ijser.org40

International Journal of Scientific & Engineering Research, Volume 5, Issue 12, December-2014ISSN 2229-5518d)Policy 4Pro-rata rebate policy – in this, if item failsin W then manufacturer refund fraction ofC. the amount of refund is calculated on thebasis of at which age item is failed. Refundis linear or non linear function of W – X,remaining warranty period.α (1 is the refund for linear pro-ratapolicy. When α 1; then we get fullpro-rated refund and less if α 1.reliability and quality were not good enough tosupport the longer warranty.In late ‘60s manufacturers reversed their strategyand began decreasing warranty coverage,resulting in ill feelings among consumers.I BASIS FOR WARRANTY COSTANALYSIS:When in warranty period, item returned tomanufacturers; both buyers and manufacturerencountered with following important costs –1. warranty cost per unit sale2. life cycle cost per unit saleC. WARRANTY COST PER UNIT SALE:Basic warranty cost is total amount required to doservicing on item. Warranty periods (WP) totallydepends on warranty type. For 1-d non renewingwarranty WP is W. One can get benefit of warrantyonly if the item fails in W.But in renewing policythe picture is different. It is shown in following fig.IJSERFigure 1: Rebate function for FRW policiesB. 2 dimensional warranty:In this case warranty has two space dimensions. Onone axis time or age is placed and on other itemusage.As we can see the importance of warranty, there isanother important parameter related with warranty.It is cost analysis of warranty.Providing warranty, there requires extra cost otherthan the actual price of product. Manufacturer sellsit at C which includes that extra cost. This extraamount is called warranty cost.This cost depends on- reliability of product- warranty type- period length of warranty- product type(electronics, mechanical, etc)We can find out the importance of warranty costfrom following example,Warranty servicing cost ( 300 million for Ford, 580 million for GM, 200 for Chrysler in 1969)had increased significantly because productFigure 2: 1-D renewing warranty policyFor 2-d non renewing warranty there are two WP.One is decided on the usage of item (U) and otheris on the warranty time (W). It is shown infollowing fig.Figure 3: 2-D non renewing warranty policyThe warranty cost (i.e., the cost of servicing allwarranty claims for an item over the total warrantyperiod) is a sum of a random number of suchindividual costs, since the number of claims overthe warranty period is also random.IJSER 2014http://www.ijser.org41

International Journal of Scientific & Engineering Research, Volume 5, Issue 12, December-2014ISSN 2229-5518Now, warranty cost for –A. manufacturer :Warranty cost for manufacturer is the costat which item is sold plus the servicing cost.In the analysis and examples presented, wegive the expected (or average) value of thiscost. This cost is important in the context ofpricing the product. To stay in profitmanufacturer should sale an item at costexceeding this cost.B. Customer :Cost to them is only initial purchasingprice.II. METHODOLOGY FOR WARRANTYCOST ANALYSISFollowing fig. shows the flow chart for warrantycost analysis. From that one can predict, decide thewarranty cost.D. LIFE CYCLE COST PER UNIT SALEProducts like aircraft, automobile, locomotive areused for long periods. Product life (L) for suchitems ranges from 40 - 10 years. But the productlife of component used in these items has short lifethan that of item. So we have to replace it aftersuccessive interval of time over period L. sometime replacement has to be done after expiry of itsoriginal warranty (W). This replacement is coveredby another warranty. Purchasing history is shownin following fig.IJSERFigure 5: warranty cost estimation flow chartA. SYSTEM CHARACTERIZATION –Characterization is required to formulate workingcost model. There are two systemcharacterizations; Simple system characterization :Figure 4: history of repeat purchase over LHere, warranty cost for –A. Manufacturer :Sum of production cost of item and servicingcost of item if it fails in original warrantyperiod (W).Figure 6: simple characterizationB. Customer :Purchase prize and cost related to warrantyclaims. IJSER 2014http://www.ijser.orgThis model is useful to estimate thewarranty cost per unit sale from both thepoint of view i.e. manufacturer andcustomer.Detailed system characterization :42

International Journal of Scientific & Engineering Research, Volume 5, Issue 12, December-2014ISSN 2229-5518 This chart is useful in estimating the lifecycle costs.IJSERFigure 7: detailed system characterizationB. MODELING –Cost models (considering manufacturer’s view) ofwarranty analysis depends on following factors –1. Type of warranty given on sold item2. Failure distribution of that item in warrantyperiodTo model this failure distribution of items differentprobability distributions are used. Standarddistribution is used to plot failure distribution ofpractically simple items.Figure 8: standard distribution (shown in red line)To model failure pattern of complex item becomesvery difficult. For that calculation we requiredcomputers.Results:i.1-D warranties :Univariate distribution is used to plotfailure models of 1-d warranties. To selectproper distribution we have to see whetherthere is failure data available or not. If yesthen we use different distribution, if not weuse another distribution.Two parameter Weibull distribution isextensively used in reliability application.F(x; θ) 1 – exp {-(x/α) β}Here, θ set {α, β}Two parameters are α, β. α is nondimensional shape parameter. Distributionshape and failure rate function aredetermined by it. When α 1; it means thefailure rate is constant over period. α 1; itmeans failure rate is decreasing overperiod. α 1; it means failure rate isincreasing over period.β gives idea of usage time.ii.2-D warranties :-IJSER 2014http://www.ijser.org43