Elsevier

Computers & Industrial Engineering

Volume 135, September 2019, Pages 1047-1062
Computers & Industrial Engineering

Cost analysis of a piece-wise renewing free replacement warranty policy

https://doi.org/10.1016/j.cie.2019.07.015Get rights and content

Highlights

  • Study a new piece-wise renewing free replacement warranty.

  • Derive the expected warranty cost, warranty cycle, and cost rate.

  • The piece-wise renewing policy has lower warranty cost than a fully renewing policy.

  • Propose a modified policy with a threshold on the number of failures.

  • A real-life case study is conducted with warranty claim data of battery packs.

Abstract

Nowadays, fierce competition and increasing customer requirements force manufacturers to continuously provide better after-sales services and supports. One such kind of after-sales services is product warranty which has been offered for almost all products in today’s market. In this paper, we study a new warranty policy, called piece-wise renewing free replacement warranty. Under this policy, the whole warranty period is divided into two sub-periods and once an item fails in a specific sub-period, it will be replaced by a new identical one and the warranty period is fully or partially renewed. The expected warranty cost and warranty cycle of this policy are derived from the manufacturer’s perspective. The proposed model is then modified by involving three sub-periods and a failure limit, respectively. In the latter scenario, when the number of item failures over a warranty cycle exceeds a pre-specified threshold, the manufacturer has to refund the item’s purchase price, and consequently the warranty ceases. A real-world case study is presented using warranty data of a battery manufacturer. It is found that for a given warranty period, the piece-wise renewing free replacement policy has a better performance than traditional fully renewing policy, in terms of expected warranty cost, warranty cycle, and cost rate.

Introduction

Warranty is a contractual agreement attached to an item that requires the manufacturer to offer compensation to the consumer according to pre-specified terms when the warranted item fails to perform its intended functions within the warranty period (Blischke & Murthy, 1992). The past decades witnessed significant growth of employing product warranties as a strategic marketing tool to attract potential consumers. Meanwhile, warranty management has gained an extensive interest from different perspectives and disciplines, as summarized and reviewed in Murthy and Djamaludin, 2002, Murthy et al., 2004, Shafiee and Chukova, 2013, Wang and Xie, 2018, Wu, 2013, for example.

Generally speaking, warranty policies can be classified into various categories according to different criteria. Based on whether the policy is renewing or non-renewing, warranties can be categorized into renewing and non-renewing warranty policies (Blischke & Murthy, 1992). Under a renewing policy, whenever an item fails within the warranty period, it is replaced by a new identical one, and the new replacement is attached with a new warranty; while the repair or replacement of a failed item protected by a non-renewing warranty does not alter the original warranty. Both of renewing and non-renewing policies can be further divided into two groups—simple and combination policies. Free replacement warranty and pro-rata warranty are two typical simple policies. Under the former policy, all failures within the warranty period will be replaced by the manufacturer at no cost to consumers, while under the latter policy, the manufacturer only agrees to cover a fraction of replacement cost or to refund a fraction of original purchase price. A combination policy (also called hybrid policy), however, either applies different simple policies during different stages of the warranty period or combines a simple policy with additional features (Blischke & Murthy, 1992). In this paper, we propose and study a new type of renewing free replacement warranty policy.

However, offering warranty is by no means free for manufacturers, given that warranty is a kind of post-sales service. The warranty cost—resulting from the servicing of warranty claims in the field—is a huge financial burden to manufacturers, and can account for as much as 15% of net sales (Murthy & Djamaludin, 2002). As a result, accurate warranty cost evaluation is indispensable to manufacturers, particularly for designing a new warranty policy. Either underestimating or overestimating warranty servicing costs would result in economic losses for manufacturers. Specifically, overestimation may lead to high product price and thus low sales, while underestimation increases liquidity risks. It is therefore not surprising that warranty cost modeling and analysis have long been an important research topic; see Eliashberg et al., 1997, Frees and Nam, 1988, Mi, 1999, Murthy et al., 1995, Thomas and Rao, 1999 for some early references. In particular, the monograph (Blischke & Murthy, 1993) presents and summarizes detailed cost models for various warranty policies.

The existing studies on warranty cost modeling and analysis focus predominately on renewing free replacement warranty, non-renewing free repair/replacement warranty, and hybrid or combination warranty, among others. Dimitrov, Chukova, and Khalil (2004) analyzed expected warranty servicing costs for repairable products sold with free replacement (non-renewing and renewing) and linear pro-rata warranties, with age-dependent failure/repair models. Bai and Pham (2006) tackled cost analysis on renewable full-service warranties for repairable multi-component systems. Liu, Wu, and Xie (2015) developed a warranty cost model for a renewing free replacement policy by considering failure interactions in multi-component systems. Marshall, Arnold, Chukova, and Hayakawa (2018) proposed two new cost analysis models for renewing and non-renewing free repair warranties with non-zero increasing repair times. Zhang, Fouladirad, and Barros (2018) evaluated warranty cost for a two-component series system with type I stochastic dependence between the components, under both non-renewing and renewing free replacement policies. For both repairable and non-repairable products, Manna, Pal, and Sinha (2008) discussed the discrepancy in two-dimensional warranty cost models based on univariate and bivariate approaches, respectively. Su and Shen (2012) analyzed expected costs and profits for extended warranties with three corrective repair options. By coupling stochastic sales process with product failure process, Xie, Shen, and Zhong (2017) presented a general aggregate repair demand forecasting model for a two-dimensional free repair warranty policy. Zhao and Xie, 2017, Zhao et al., 2018 developed warranty cost optimization frameworks, based on life/degradation testing data, for repairable products under imperfect repairs. Furthermore, Chien and Zhang (2015) studied a hybrid warranty policy with a renewable free replacement period and a rebate period for discrete-time operating products. Zhang and Wang (2019) introduced a geometric process repair model to derive the expected warranty cost for a non-renewing combination policy. In recent years, warranty cost analysis has attracted increasing attentions in terms of supporting, e.g., warranty contract design (Tong et al., 2014, Ye and Murthy, 2016, Zhang et al., 2019), warranty reserve management (Wang et al., 2017, Xie and Ye, 2016), and maintenance decision-making (Chien, 2019, Su and Wang, 2016, Wang et al., 2019), etc.

This paper deals with cost analysis of a new piece-wise renewing free replacement warranty policy, which has not been studied in the existing literature. Under this policy, the entire warranty period is divided into two sub-periods and different warranty renewing mechanisms, following failure replacements, are applied in these periods. The expected warranty cost and warranty cycle of this policy are derived from the manufacturer’s perspective. After that, the proposed model is modified by considering one more sub-period and a failure limit within the warranty cycle, respectively. In the latter scenario, the manufacturer has to return original purchase price to the consumer should the number of failures over a warranty cycle exceed a pre-specified threshold, and consequently the warranty is terminated. This failure-limit policy is in line with the spirit of “Lemon Law” for automobiles sold in the USA (Coffinberger & Samuels, 1985). It is worth mentioning that this study is motivated by the warranty policy adopted by a battery manufacturer, and a real-world case study is also presented using the warranty claim data collected by this company.

The remainder of this paper is organized as follows. Section 2 describes the piece-wise renewing free replacement warranty policy in detail, and derives its expected warranty cost and warranty cycle. This warranty policy is then extended in Section 3 by considering three sub-periods and a pre-specified threshold on the number of item failures, respectively. Section 4 presents a case study to demonstrate the implementation of warranty cost models using battery warranty claim data. Finally, Section 5 concludes this paper with some suggestions on future research topics.

Section snippets

Warranty policy description

Under the proposed piece-wise renewing free replacement warranty, the whole warranty period [0,W] is divided into two sub-periods—[0, W1] and W1,W, as illustrated in Fig. 1. Different warranty renewing mechanisms, following failure replacements, are applied in these periods. More specifically,

  • if an item fails in [0,W1], then it will be replaced by a new one, and the warranty period is totally renewed, i.e., a new identical warranty of length W is attached to the new replacement;

  • if an item fails

Model extensions

In this section, two extensions are presented to enhance the applicability of the piece-wise renewing free replacement warranty. The first extension specifies one more sub-period, i.e., there are totally three renewing periods during the warranty period; while the second one considers the Lemon Law—when the number of failures over a warranty cycle exceeds a pre-specified threshold, the manufacturer has to refund the item’s purchase price.

Case study

In this section, we demonstrate the proposed warranty cost models by applying them to a lead-acid battery pack model manufactured by a Chinese battery company. The battery pack is mainly used to drive two-wheel or three-wheel electric bikes, and it contains four 12 V lead-acid cells in series to produce 48 V nominal voltage. Good battery performance is essential because quality and reliability problems during the warranty period will damage customer satisfaction and result in economic losses

Concluding remarks

Warranty designers, such as product manufacturers, are constantly seeking novel ideas to promote their products due to more-than-ever fierce market competition and high consumer requirements. In this paper, we investigate the cost analysis of a new piece-wise renewing free replacement warranty as well as its two modifications with three sub-periods and a threshold point on the number of item failures, respectively. The expressions of expected total warranty costs, warranty cycles, and cost

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 71601166, 71532008) and also by the Research Grants Council of Hong Kong under Theme-based Research Fund (Grant No. T32-101/15-R) and General Research Fund (Grant Nos. CityU 11203815, CityU 11203519). The authors are grateful to the three anonymous reviewers for their helpful comments and suggestions on this paper.

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