This paper deals with a post-warranty maintenance model for the second-hand product as follows. The second-hand product of age , which is assumed to be positive, is purchased with a fixed length of non-renewing warranty, during which the product is given a fixed number of preventive maintenances periodically by the dealer. At each preventive maintenance, the failure rate of the product is adjusted to some extent for the purpose of reducing the likelihood of product failure. At the expiration of warranty, the user starts to self-maintain the product until a pre-determined number of failures occur, at which time the product is replaced by another one. For each post-warranty failure, only a minimal repair is taken to restore the failed product to its previous functioning state. This paper aims to determine an optimal number of post-warranty product failures that minimizes the expected cost rate during the second-hand product’s life cycle. To this end, we derive a formula to evaluate the expected cost rate during the second-hand product’s life cycle by assuming a certain cost structure for maintaining the product during the life-span of the product and determine an optimal number of post-warranty product failures from the user’s perspective. And we provide a numerical example to illustrate our proposed optimal maintenance model by assuming a Weibull failure distribution. The main contribution of this work is to use the number of post-warranty failures to propose a maintenance model for the second-hand product, where the number of failures is in general easier to observe than the failure times.
LimJHKimDKParkDH. Maintenance optimization for second-hand products following periodic imperfect preventive maintenance warranty period. Appl Stoch Model Bus Ind2019; 35: 1077–1089.
ParkMPhamH. Maintenance and warranty concepts. In: HPham (ed.) Safety and risk modeling and its applications. London: Springer, 2011, pp.101–122.
6.
WangXXieW. Two-dimensional warranty: a literature review. Proc IMechE, Part O: J Risk and Reliability2018; 232(3): 284–307.
7.
ShrivastavaAKSharmaRPhamH. Software reliability and cost models with warranty and life cycle. Proc IMechE, Part O: J Risk and Reliability2023; 237(1): 166–179.
8.
ShafieeMChukovaS. Optimal upgrade strategy, warranty policy and sale price for second-hand products. Appl Stoch Model Bus Ind2013; 29: 157–169.
9.
ShafieeMFinkelsteinMChukovaS. On optimal upgrade level for used products under given cost structures. Reliab Eng Syst Saf2011; 96: 286–291.
10.
DarghouthMNChelbiAAit-kadiD. On reliability improvement of second-hand products. In: 15th IFAC Symposium on Information Control Problems in Manufacturing — INCOM2015, Ottawa, Canada, vol. 48, pp. 2158–2163.
11.
LinDZuoMJYamRCM. General sequential imperfect preventive maintenance models. Int J Reliab Qual Saf Eng2000; 7(3): 253–266.
12.
ChattophadayaGMurthyDNP. Warranty cost analysis for second hand products. Math Comput Model2000; 30: 81–88.
13.
ChattophadayaGMurthyDNP. Optimal reliability improvement for used items sold with warranty. Int J Reliab2004; 5(2): 47–57.
14.
SuCWangX. Optimizing upgrade level and preventive maintenance policy for second-hand products sold with warranty. Proc IMechE, Part O: J Risk and Reliability2014; 228: 518–528.
15.
YehRHLoHCYuRY. A study of maintenances policies for second-hand products. Comput Ind Eng2011; 60: 438–444.
16.
KimDKLimJHParkDH. Optimal maintenance level for second-hand product with periodic inspection schedule. Appl Stoch Model Bus Ind2015; 31(3): 349–359.
17.
DaiAWeiGWangD, et al. The opportunity study of PM strategy for second-hand products sold with a two-dimensional warranty. Reliab Eng Syst Saf2021; 214: 107699.
18.
WangYLiuYZhangA. Preventive maintenance optimization for repairable products considering two-dimensional warranty and customer satisfaction. Proc IMechE, Part O: J Risk and Reliability2019; 233(4): 553–566.
19.
ZhengRSuCZhengY. Two-stage flexible warranty decision-making considering downtime loss. Proc IMechE, Part O: J Risk and Reliability2020; 234(3): 527–535.
20.
DehghanbaghiMDabbaghiA. Stochastic cost modeling for second-hand products’ optimum warranty period and upgrade level. J Appl Res Ind Eng2021; 8(2): 116–128.
21.
HeydariM. Optimal inspection policy for a second-hand product with a two-dimensional warranty. IMA J Manag Math2022; 33(3): 395–416.
22.
SahinIPolatogluH. Maintenance strategies following the expiration of warranty. IEEE Trans Reliab1996; 45: 220–228.
23.
ShangLSiSSunS, et al. Optimal warranty design and post-warranty maintenance for products subject to stochastic degradation. IISE Trans2018; 50: 913–927.
24.
ShangLCaiZChenH, et al. Post-warranty maintenance optimization for products with deterioration depending on aging and shock. Qual Technol Quant Manag2019; 16: 651–671.
25.
KimDKLimJHParkDH. Optimization of post-warranty sequential inspection for second-hand product. J Syst Eng Electron2017; 28: 793–800.
26.
ParkKS. Optimal number of minimal repairs before replacement. IEEE Trans Reliab1979; 28(2): 137–140.
27.
NakagawaT. Generalized models for determining optimal number of minimal repairs before replacement. J Oper Res Soc Jpn1981: 24(4): 325–337.
28.
ChienYH. Optimal number of minimal repairs before ordering spare for preventive replacement. Appl Math Model2010; 34: 3439–3450.
29.
LaiMT. Optimal number of minimal repairs under a cumulative damage model with cumulative repair cost limit. Eksploat Niezawod2014; 16(3): 464–471.
30.
ChangCCSheuSHChenYL. Optimal number of minimal repairs before replacement based on a cumulative repair-cost limit policy. Comput Ind Eng2010; 59: 603–610.
31.
LimJHKimDKParkDH. Determination of optimal post-warranty variable maintenance period for repairable second-hand product based on mean residual life. Proc IMechE, Part O: J Risk and Reliability2022; 236(6): 981–993.
32.
KijimaM. Some results for repairable systems with general repair. J Appl Probab1989; 1: 89–102.
