Imperfect Repair Strategies for Two-Dimensional Warranty

When a repairable product under warranty fails, the manufacturer (warrantor) has the choice to either repair or replace the failed product. When repairing a failed product, the degree of repair which affects the working condition of the product can vary, and this is assumed to have an impact on the cost of the repair. The main motivation of this study is to develop a warranty repair strategy that minimizes the costs associated with servicing the warranty. In this research, the product coverage is represented by a two-dimensional rectangular region with a free-replacement warranty. We propose an imperfect repair strategy that suggests employing imperfect repairs of a predefined degree, in prespecified subregions of the warranty region. The aim is to then minimize the expected warranty servicing cost to the manufacturer by determining the optimal partitioning of the warranty region for the chosen degrees of repair. Two imperfect repair models are considered, and for both, the expressions for the distribution of the times to imperfect repair and the expected warranty servicing cost per product sold are derived. We numerically illustrate our findings and compare the expected costs of the proposed imperfect repair strategy with those of previously developed repair-replacement warranty strategies

Imperfect Repair Strategies for Two-Dimensional Warranty

When a repairable product under warranty fails, the manufacturer (warrantor) has the choice to either repair or replace the failed product. When repairing a failed product, the degree of repair which affects the working condition of the product can vary, and this is assumed to have an impact on the cost of the repair. The main motivation of this study is to develop a warranty repair strategy that minimizes the costs associated with servicing the warranty. In this research, the product coverage is represented by a two-dimensional rectangular region with a free-replacement warranty. We propose an imperfect repair strategy that suggests employing imperfect repairs of a predefined degree, in prespecified subregions of the warranty region. The aim is to then minimize the expected warranty servicing cost to the manufacturer by determining the optimal partitioning of the warranty region for the chosen degrees of repair. Two imperfect repair models are considered, and for both, the expressions for the distribution of the times to imperfect repair and the expected warranty servicing cost per product sold are derived. We numerically illustrate our findings and compare the expected costs of the proposed imperfect repair strategy with those of previously developed repair-replacement warranty strategies

Optimising Age-Replacement and Extended Non-Renewing Warranty Policies in Lifecycle Costing

This paper analyses the life cycle cost of equipment protected by both base and extended warranty policies from a consumer's perspective. We assume that the equipment has two types of failure: minor and catastrophic. A minor failure can be corrected with minimal repair whereas a catastrophic failure can only be removed by a replacement. It is assumed that equipment is maintained at no charge to the consumer during the warranty period, whereas the consumer is fully charged for any maintenance on failures after the extended warranty expires. We formulate the expected life cycle cost of the equipment under a general failure time distribution, and then for special cases we prove that the optimal replacement and extended warranty policies exists where the expected life cycle cost per unit time is minimised. This is examined with numerical examples. © 2011 Elsevier B.V. All rights reserved

Some contributions to modeling usage sensitive warranty servicing strategies and their analyses

Providing a warranty as a part of a product\u27s sale is a common practice in industry. Parameters of such warranties (e.g., its duration limits, intensity of use) must be carefully specified to ensure their financial viability. A great deal of effort has been accordingly devoted in attempts to reduce the costs of warranties via appropriately designed strategies to service them. many such strategies, that aim to reduce the total expected costs of the warrantor or / and are appealing in other ways such as being more pragmatic to implement - have been suggested in the literature. Design, analysis and optimization of such servicing strategies is thus a topic of great research interest in many fields. In this dissertation, several warranty servicing strategies in two-dimensional warranty regimes, typically defined by a rectangle in the age-usage plane, have been proposed, analyzed and numerically illustrated. Two different approaches of modeling such usage sensitive warranty strategies are considered in the spirit of Jack, Iskandar and Murthy (2009) and Iskandar (2005). An `Accelerated Failure Time\u27 (AFT) formulation is employed to model product degradation resulting due to excessive usage rate of consumers. The focus of this research is on the analysis of warranty costs borne by the manufacturer (or seller or third party warranty providers) subject to various factors such as product\u27s sale price, consumer\u27s usage rate, types and costs of repair actions. By taking into account the impact of the rate of use of an item on its lifetime, a central focus of our research is on warranty cost models that are sensitive to the usage rate. Specifically, except the model in Chapter 4 where the rate at which an item is used is considered to be a random variable; all other warranty servicing policies that we consider, have usage rate as a fixed parameter, and hence are policies conditional on the rate of use. Such an approach allows us to examine the impact of a consumer\u27s usage rate on the expected warranty costs. For the purpose of designing warranties, exploring such sensitivity analysis may in fact suggest putting an upper limit on the rate of use within the warranty contract, as for example in case of new or leased vehicle warranties. A Bayesian approach of modeling 2-D Pro-rated warranty (PRW) with preventive maintenance is considered and explored in the spirit of Huang and Fang (2008). A decision regarding the optimal PRW proportion (paid by the manufacturer to repair failed item) and optimal warranty period that maximizes the expected profit of the rm under different usage rates of the consumers is explored in this research. A Bayesian updating process used in this context combines expert opinions with market data to improve the accuracy of the parameter estimates. The expected profit model investigated here captures the impact of juggling decision variables of 2-D pro-rated warranty and investigates the sensitivity of the total expected profit to the extent of mis-specification in prior information

Optimal Two Dimensional Preventive Maintenance Policy Based on Asymmetric Copula Function

For some kinds of products, the consumers have strict requirements to the reliability of these products in the based warranty period. Then the manufacturer is inclined to provide the two-dimensional preventive maintenance policy to take the usage degree of the product into account. As a result, two-dimensional preventive maintenance policy in the warranty period has recently obtained increasing attention from manufacturers and consumers. In this paper, we focused on the optimization of based warranty cost and proposed a new expected based warranty cost model considering the two-dimensional imperfect preventive maintenance policy from the perspective of the manufacture. Asymmetric copula function was applied to modeling the failure function of the product. And the optimal two-dimensional preventive maintenance period was obtained by minimizing based warranty cost. At last, numerical examples are given to illustrate the proposed models, of which the results prove the model effective and validate

Optimal Burn-in Time and Imperfect Maintenance Strategy for a Warranted Product with Bathtub Shaped Failure Rate

‘Burn-in/preventive maintenance’ programme is an efficient approach used to minimise the warranty servicing cost of a product with bathtub shaped failure rate. Burn-in is a widely used method to improve the quality of product during its ‘infant mortality’ period and preventive maintenance is a scheduled necessary activity carried out during its ‘wear-out’ period. In this paper, an optimisation model is developed to determine the optimal burn-in time and optimal imperfect preventive maintenance strategy that minimises the total mean servicing cost of a warranted product with an age-dependent repair cost. We provide a numerical study to illustrate our results

Warranty and Sustainable Improvement of Used Products through Remanufacturing

Currently, a large number of used/second-hand products are being sold with remanufacturing. Remanufacturing is a process of bringing used products to a better functional state and can be applied as a way for (1) controlling the deterioration process, (2) reducing the likelihood of a failure over the warranty period and (3) making the used item effectively younger. Remanufacturing is relatively a new concept and has received very limited attention. In this paper, we develop an important sustainable improvement approach for used items sold with failure free warranty to determine the optimal improvement level. Our model makes a useful contribution to the reliability growth literature, as it captures the uncertainty and suggests improvement in the remanufacturing process. By using this model, the dealers can decide whether and how much to invest in remanufacturing projects

Joint Determination of Price and Upgrade Level for a Warranted Second-hand Product

An upgrade action is a pre-sale procedure that brings the second-hand item to an improved functional state and effectively reduces its age. This action is usually costly and adds directly to the sale price of the second-hand product, but it improves the product reliability and can reduce the warranty servicing cost. In the present paper, we propose a decision model to determine the optimal price and upgrade strategy of a warranted second-hand product to maximize the dealer's expected profit. The objective function includes both demand and cost functions, where purchase price from an end user, upgrade cost, and warranty cost are involved. We illustrate our finding using real data on second-hand electric device. Also, a sensitivity analysis is conducted to evaluate the effect of model parameters on the optimal solution

The Mean Value Theorem for Integrals Method for Estimating Two-Dimensional Renewal Functions

An important aspect in the provision of a two-dimensional warranty is the expected number of failures of a component during the two-dimensional warranty period. The purpose of this paper is to present a new method to obtain the expected number of failures of a nonrepairable compo­nent from the two-dimensional renewal functions as the so­lution of two-dimensional renewal integral equations through the Mean Value Theorem for Integrals (MeVTI) method. The two-dimensional renewal integral equation involves Lu-Bhattacharyya’s bivariate Weibull model as a two-dimensional failure model. It turns out that the estimation of the expected number of failures using the MeVTI method is close to that of the other method, Riemann-Stieljies method. The bivariate data behaviour of the failures of an automobile component is also studied in this paper