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

Data analysis and simulation for warranties and golf handicaps

In this dissertation, we discuss the application of data analysis and numerical simulation in order to gain insight into problems related to warranty cost management and the effectiveness of the golf handicap system. Despite the commonalities of the approaches, we will discuss these problems in turn. For many moderately high value items with a substantial sales volume (such as automobiles), a warranty is used as an important element of marketing products as a better warranty typically signals higher product quality to customers. Much recent research on modeling and optimization of servicing costs for Non-Renewing Free Replacement Warranties (NR-FRW) assumes that the consumers’ usage profile is known. Such an assumption is unrealistic for many consumer durables. In such cases, it would be pragmatic to assume that the usage rate should be modeled by a probability distribution. This research seeks to model and minimize the expected costs of servicing strategies for NR-FRW; this is accomplished using a numerical technique known as simulated annealing while considering a variety of usage rate distributions. The relationship between the usage rate distribution and product life-length is modeled using the Accelerated Failure Time (AFT) formulation. We use a copula based approach to capture the adverse impact of increasing product usage rate on its time-to-failure. We obtain a unique copula based on the marginal distributions of both the usage rate and the product life-length, which we call the AFT Copula. The underlying dependency of our copula is evaluated using non-parametric measures of association. The Mean Time to First Failure (MTTF) indicates which usage rate distributions most likely correspond to highly reliable products. We found that certain warranty servicing strategies were more cost efficient than other commonly used approaches. We use data analysis techniques on a traction motor data set to study the practicality of our approach. The results obtained from this data are in qualitative agreement with our previous results. The ability of a golfer is measured by a player’s handicap which is an estimate of his/her potential based on previously played games. The handicap system is administered by the United States Golf Association (USGA); it is designed to enable players of differing abilities to compete against each other on an equitable basis. Most previous studies in golf have focused on analyzing golf scores. The goal of this research is to study the effectiveness of the current handicapping system. We use the AT&T Golf Tournament League data set for our study; this data set contains scores and handicaps of golfers from almost 100 different tournaments. In this study, we use data analysis methods including filtering to remove outliers and goodness of fit tests to determine the most appropriate distribution for the golf scores. Because each handicap requires a separate fit, we develop a technique of minimizing the average ranks of the candidate distributions in order to obtain the single best distribution for all handicaps. For this data set, the generalized extreme value distribution is the most appropriate. In order to investigate the effectiveness of the handicap system, we conduct simulations of competitions between golfers with varying handicaps based on the empirical and fitted data for golf scores. These simulations indicate that a player with a lower handicap has an advantage over a player with a higher handicap

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

A unified methodology of maintenance management for repairable systems based on optimal stopping theory

This dissertation focuses on the study of maintenance management for repairable systems based on optimal stopping theory. From reliability engineering’s point of view, all systems are subject to deterioration with age and usage. System deterioration can take various forms, including wear, fatigue, fracture, cracking, breaking, corrosion, erosion and instability, any of which may ultimately cause the system to fail to perform its required function. Consequently, controlling system deterioration through maintenance and thus controlling the risk of system failure becomes beneficial or even necessary. Decision makers constantly face two fundamental problems with respect to system maintenance. One is whether or when preventive maintenance should be performed in order to avoid costly failures. The other problem is how to make the choice among different maintenance actions in response to a system failure. The whole purpose of maintenance management is to keep the system in good working condition at a reasonably low cost, thus the tradeoff between cost and condition plays a central role in the study of maintenance management, which demands rigorous optimization. The agenda of this research is to develop a unified methodology for modeling and optimization of maintenance systems. A general modeling framework with six classifying criteria is to be developed to formulate and analyze a wide range of maintenance systems which include many existing models in the literature. A unified optimization procedure is developed based on optimal stopping, semi-martingale, and lambda-maximization techniques to solve these models contained in the framework. A comprehensive model is proposed and solved in this general framework using the developed procedure which incorporates many other models as special cases. Policy comparison and policy optimality are studied to offer further insights. Along the theoretical development, numerical examples are provided to illustrate the applicability of the methodology. The main contribution of this research is that the unified modeling framework and systematic optimization procedure structurize the pool of models and policies, weed out non-optimal policies, and establish a theoretical foundation for further development

Two-dimensional Warranty Cost Analysis for Second-hand Products

In spite of the recent steady increase of the volume of the second-hand markets, often customers remain in doubt regarding the quality and durability of the secondhand products. Aiming to reduce and share this uncertainty, dealers offer warranty on their products. Offering warranty for second-hand products is a relatively new marketing strategy employed by dealers of used electronic equipment, furniture, automobiles, etc. Usually, for used products, the dealer’s expected warranty cost is a function of product reliability, past age and usage, servicing strategy and conditions and terms of the warranty policy/contract. Sometimes the offered policy is limited by two parameters, typically the product age and usage after the sale. This type of policies is referred to as two-dimensional warranty policies. In this article, we develop statistical models for estimating the dealer’s expected warranty cost for second-hand products sold with two-dimensional free repair/replacement warranty

A General Approach to Electrical Vehicle Battery Remanufacturing System Design

One of the major difficulties electrical vehicle (EV) industry facing today is the production and lifetime cost of battery packs. Studies show that using remanufactured batteries can dramatically lower the cost. The major difference between remanufacturing and traditional manufacturing is the supply and demand variabilities and uncertainties differences. The returned core for remanufacturing operations (supply side) can vary considerably in terms of the time of returns and the quality of returned products. On the other hand, because different contracts can be used to regulate suppliers, it is almost always assumed zero uncertainty and variability for traditional manufacturing systems. Similarly, customers demand traditional manufacturers to sell newly produced products in constant high quality. But, remanufacturers usually sell in aftermarket, and the quality of the products demanded can vary depends on the price range, usage, customer segment and many other factors. The key is to match supply and demand side variabilities so the overlapping between them can be maximized. Because of these differences, a new framework is needed for remanufacturing system design. This research aims at developing a new approach to use remanufactured battery packs to fulfill EV warranties and customer aftermarket demands and to match supply and demand side variabilities. First, a market lifetime EV battery return (supply side) forecasting method is develop, and it is validated using Monte Carlo simulation. Second, a discrete event simulation method is developed to estimate EV battery lifetime cost for both customer and manufacturer/remanufacturer. Third, a new remanufacturing business model and a simulation framework are developed so both the quality and quantity aspects of supply and demand can be altered and the lifetime cost for both customer and manufacturer/remanufacturer can be minimized. The business models and methodologies developed in this dissertation provide managerial insights to benefit both the manufacturer/remanufacturer and customers in EV industry. Many findings and methodologies can also be readily used in other remanufacturing settings. The effectiveness of the proposed models is illustrated and validated by case studies.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143955/1/xrliang_1.pd

Modeling and Analysis of Effective Ways for Improving the Reliability of Second-hand Products Sold with Warranty

Often, customers are uncertain about the performance and durability of the used/second-hand products. The warranties play an important role in reassuring the buyer. Offering the warranty implies that the dealer incurs additional costs to service any claims made by the customers. Reducing warranty costs is an issue of great interest to dealers. One way of improving the reliability and reducing the warranty servicing cost for second-hand items is through actions such as overhaul and upgrade which are carried out by the dealer or a third party. Improving actions allow the dealer to offer better warranty terms and to sell the item at a higher price. This paper deals with two effective approaches (virtual age approach and screening test approach) to decide on the reliability improvement strategies for second-hand products sold under various warranty policies (failure-free, rebate warranty, and a combination of free replacement and lump sum). A numerical example illustrates that from a dealer’s point of view, it is beneficial to carry out an improvement action only if the reduction in the warranty servicing cost is greater than the extra cost incurred due to this improvement action

Determination of optimal pricing and warranty policies

An important problem facing manufacturers in today\u27s competitive market is the determination of the selling price of a product and its warranty period. A longer warranty may serve as a signal of product reliability; however, it may also lead to an increase in cost and hence reduce the profit if the product reliability is low. A burn-in test may be used to improve the reliability of products prior to their shipment.;This research presented integrated models for maximizing the expected profit for products that are subjected to a burn-in test and sold with warranty. The burn-in time, warranty period, and price were chosen as three decision variables in these models. The price and warranty period were treated as marketing variables and a simple multiplicative form was used to model their effect on sales. Solution procedures were developed for several warranty policies. These procedures are applicable for any failure time distribution. Three failure time distributions were further investigated and formulas for optimal solutions were derived. Finally, two sets of data were used to illustrate the application of the models. Two computer programs were developed to solve the models both parametrically and nonparametically