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Two-dimensional warranty policies exist for certain consumer products, such as automobiles. Here, warranty is specified in terms of the time since the sale of the product as well as mileage incurred during that period. Thus, at the time of purchasing the product, the manufacturer may offer a warranty of three years or 30,000 miles, whichever occurs first. Failures in the product within this specified period of time or mileage will be covered by the manufacturer.

In this chapter, we consider the scenario of enterprise warranty programs, where customers are given the option of extending the original warranty. Thus, the buyer could be given an option to purchase a five year—50,000 mile warranty, whichever occurs first. Of course, the buyer will be expected to pay a premium to purchase this extended warranty. Such enterprise warranty programs are also found in other consumer durables, such as refrigerators, washers, dryers, and cooking ranges.

This chapter explores determination of the decision variables, such as product price, warranty time, and usage limit under the original conditions and further, for the enterprise warranty, that is, the extended warranty time and extended usage limit, as well as the premium to be charged to the buyer who selects the extended warranty. Mathematical models are developed based on maximizing the expected unit profit by selecting an enterprise warranty program. Additionally, some other objectives are also considered based on the proportional increase in the expected unit profit due to the increased market share attained through the offering of an enterprise warranty program. Some results are obtained through consideration of various goal values of the chosen objectives.

Various types of warranty programs are offered for consumer products. The two most common are a linear pro-rata warranty or a lump-sum warranty, if product failure occurs prior to the specified warranty time. In this chapter we consider additional types of warranty programs that allow the consumer to purchase a one-time extended warranty in the event of no failure within the initial warranty period. For the extended period, warranty may be linearly pro-rated, starting at an amount that is lower than the initial purchase price. Alternatively, for the extended period, warranty may be a lump-sum amount, that is less than the initial warranty amount. Expressions for the expected costs under each of the programs are derived. Guidelines are provided for determining the parameters of each warranty program under relevant constraints. Sensitivity analysis is also conducted to determine the effect of the problem parameters on the expected warranty costs.

This chapter considers warranty policies involving two attributes, such as the time elapsed since sale of the product and product usage at a given point in time. Examples of such policies are found for automobiles, where warranty may be invoked by the consumer if both time and usage are within specified warranty parameters when a product failure occurs. Here, we assume that usage and product age are related through a random variable, the usage rate, which may have a certain probabilistic distribution as influenced by consumer behavior patterns. Furthermore, product failure rate is influenced by the usage rate and product age as well as research and development expenditures per unit. It is assumed that, in production, there is a learning effect with time. The attained market share of a product will be influenced by the warranty policy parameters of warranty time and usage limit and also by the product price and product quality. An integrated model is developed to address multiobjective goals such as attainment of a specified level of market share and net profit per unit when manufacturing and warranty costs are taken into account. The impact of the goal priorities are investigated on the attained warranty policy parameters.

The purpose of this paper is to develop a model that determines whether how much effort of preventive maintenance action is worthwhile for the consumer over the post-sale product life cycle of a repairable complex product where the product is under warranty and subject to stochastic multimode failure process, that is, damaging failure and light failure with different probabilities.

The expected life cycle cost is designed for a warranted product from the consumer perspective. The product failure is quantified with failure rate function, which is the number of failures incurred over the product life cycle. The authors consider the failure rate function reduction method in their model where the scale parameter of a failure rate function is maximized by applying the optimal preventive maintenance level. The scale parameter of any failure distribution refers to the meantime to failure (MTTF). The first-order condition is applied with respect to the maintenance level in order to achieve the convexity of the nonlinear function of the expected life cycle cost function.

The authors have found analytically the close form of the preventive maintenance level, which can be used to find the optimal reduced form of the failure rate function of the product and the minimum product expected life cycle cost under the given condition of multimode stochastic failure process. The authors have suggested different maintenance policies to consumers in order to implement the proposed preventive maintenance model under different conditions. A numerical example further illustrated the analytical model by considering the Weibull distribution.

The consumer may use this study in the accurate modeling of the life cycle cost of a product that is under warranty and fails with a multimode failure process. Also, the suggested preventive maintenance approach of this study helps the consumer in making appropriate maintenance decisions such as to minimize the expected life cycle cost of a product.

This study proposes an accurate estimation of a life cycle cost for a product that is under the support of warranty and fails with multimode. Furthermore, for such a kind of product, which is under warranty and fails with multimode, this study suggests a new preventive maintenance approach that assures the minimum expected life cycle cost.

Two-attribute warranty policies are considered that incorporate, for example, the time elapsed since sale of the product and product usage at a given point in time. Such policies occur in consumer products, such as automobiles, where warranty may be exercised if both time and usage are within specified warranty parameters when a product failure occurs. In this chapter, it is assumed that usage and product age are related through a random variable, the usage rate, which may have a certain probabilistic distribution as influenced by consumer behavior patterns. Product quality is modeled through the product failure rate, which is influenced by unit research and development expenditures as well as the usage rate and product age. The attained market share of the product is modeled as a function of the warranty policy parameters of price, warranty time, and usage limit, with product quality also having an influence. Attainment of single and multiple objectives are explored. Such objectives encompass expected total unit costs as a proportion of unit product price and market share.

For certain consumer durables, such as automobiles, warranty policies involve two attributes. These could be the time elapsed since sale of the product and usage of the product at a given point in time. Warranty may be invoked by the consumer if both time and usage are within specified warranty parameters when a product failure occurs. In this chapter, we assume that usage and product age are related through a random variable, the usage rate, which may have a certain probabilistic distribution as influenced by consumer behavior patterns. Additionally, product failure rate is influenced by the usage rate and product age. The integrated model includes expected unit warranty costs, expected unit research and development costs, and expected unit production costs. It is assumed that in production, there is a learning effect with time. A multiobjective model is incorporated with the objectives being market share and proportion of expected warranty costs relative to total manufacturing expenditures per unit. The goals could be conflicting in nature. The problem then is to determine the warranty policy parameters while attaining certain desirable values of the two objectives.

Some consumer durables, such as automobiles, involve warranties involving two attributes. These are time elapsed since the sale of the product and the usage of the product at a given point in time. Warranty may be invoked by the customer if both time and usage are within the specified warranty parameters and product failure occurs. In this chapter, we assume that usage and product age are related through a random variable, the usage rate, which may have a certain probabilistic distribution as influenced by consumer behavior pattern. Further, product failure rate is influenced by the usage rate and product age. Of importance to the organization is to contain expected warranty costs and select appropriate values of the warranty parameters accordingly. An avenue to impact warranty costs is through research on product development. This has the potential to reduce the failure rate of the product. The objective then becomes to determine warranty parameters, while constraining the sum of the expected unit warranty costs and research and development (R&D) costs per unit sales, under a limited R&D budget.

The purpose of this paper is to identify and quantify the key components of the overall cost of software development when warranty coverage is given by a developer. Also, the authors have studied the impact of imperfect debugging on the optimal release time, warranty policy and development cost which signifies that it is important for the developers to control the parameters that cause a sharp increase in cost.

An optimization problem is formulated to minimize software development cost by considering imperfect fault removal process, faults generation at a constant rate and an environmental factor to differentiate the operational phase from the testing phase. Another optimization problem under perfect debugging conditions, i.e. without error generation is constructed for comparison. These optimization models are solved in MATLAB, and their solutions provide insights to the degree of impact of imperfect debugging on the optimal policies with respect to software release time and warranty time.

A real-life fault data set of Radar System is used to study the impact of various cost factors via sensitivity analysis on release and warranty policy. If firms tend to provide warranty for a longer period of time, then they may have to bear losses due to increased debugging cost with more number of failures occurring during the warrantied time but if the warranty is not provided for sufficient time it may not act as sufficient hedge during field failures.

Every firm is fighting to remain in the competition and expand market share by offering the latest technology-based products, using innovative marketing strategies. Warranty is one such strategic tool to promote the product among masses and develop a sense of quality in the user’s mind. In this paper, the failures encountered during development and after software release are considered to model the failure process.

The main contribution of this manuscript is to suggest new approaches in order to deal with dynamic lot-sizing and maintenance problem under aspect energetic and risk analysis. The authors introduce a new maintenance strategy based on the centroid approach to determine a common preventive maintenance plan for all machines to minimize the total maintenance cost. Thereafter, the authors suggest a risk analysis study further to unforeseen disruption of availability machines with the aim of helping the production stakeholders to achieve the obtained forecasting lot-size plan.

The authors tackle the dynamic lot-sizing problem using an efficient hybrid approach based on random exploration and branch and bound method to generate possible solutions. Indeed, the feasible solutions of random exploration method are used as input for branch and bound to determine the near-optimal solution of lot-size plan. In addition, our contribution to the maintenance part is to determine the optimal common maintenance plan for M machines based on a new algorithm called preventive maintenance (PM) periods means.

First, the authors have funded the optimal lot-size plan that should satisfy the random demand under service level requirement and energy constraint while minimizing the costs of production and inventory. Indeed, establishing a best lot-size plan is to determine the appropriate number of available machines and manufactured units per period. Second, for risk analysis study, the solution of subcontracting is proposed by specifying a maximum cost of subcontractor in the context of a calling of tenders.

For maintenance problem, the originality consists in regrouping the maintenance plans of M machines into only one plan. This approach lets us to minimize the total maintenance cost and reduces the frequent breaks of production. As a second part, this paper contributed to the development of a new risk analysis study further to unforeseen disruption of availability machines. This risk analysis developed a decision-making system, for production stakeholders, in order to achieve the forecasting lot-size plan and keeps its profitability, by specifying the unit cost threshold of subcontractor in the context of a calling of tender.

To provide a brief survey of the literature directed towards the analysis of warranty claim data.

For convenience, this survey of the analysis of warranty claims data is somewhat arbitrarily be classified by topics as follows: age‐based claims analysis, aggregated warranty claims analysis, marginal counts of claims analysis, warranty claims analysis by using covariates, estimation of lifetime distribution using supplementary data, two‐dimensional warranty, warranty costs analysis, sales lag and reporting lag analysis, and forecasts of warranty claims.

Emphasis is placed on a discussion of different kinds of warranty claims data selected from reviews and on a comparison of the statistical models and methods used to analyze such data.

Since the literature on product warranty data is vast, more work on this problem is needed.

This review points out why warranty claims data is important and gives a survey of the literature pertaining to the analysis of such data. The emphasis is on the analysis of minimal databases of real warranty data, constructed by combining information from different sources, which can be collected economically and efficiently through service networks. The research is applicable for those responsible for product reliability, product design decisions and warranty management in manufacturing industries.

The paper reviews different statistical models and methods used to analyze warranty claims data. The statistical models and methods presented are be valuable and meaningful tools for product reliability and warranty management and analysis.