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Considers the estimation problem of the total warranty cost under two types of warranty. The product (e.g. car) is sold under two types of warranty (mileage and age). The failed product will be minimally repaired by the manufacturer during the preassigned warranty, the length of which is determined by mileage or age, whichever occurs first. Under general distributions, obtains the formula of the expected value and variance of total warranty cost. Analyses special cases of the failure and running behaviours. Includes a numerical example.

The purpose of this paper is to investigate preventive‐repair warranty policies for repairable deteriorating systems using Zhang's geometric process repair model.

The paper aims to establish the importance of preventive repair during warranty. Three cost models have been developed using the average cost rate for the system as the objective function, employing N‐policy for two models therein.

The models have practical applications in warranty cost analysis, as product warranty is an important factor in designing an optimal maintenance policy.

The paper observes that product warranty has not been considered in the study of maintenance policies for repairable deteriorating systems using monotone processes. The numerical example given illustrates that a preventive repair during warranty with N‐policy is preferable compared with a non‐warranted product or a warranted product without preventive repair.

In this article we present an application of Gumbel's bivariate exponential distribution model in the context of estimating warranty costs of motor cycles under a new warranty policy. The problem in question is as follows: Under the present two‐dimensional warranty policy, repair costs (termed as warranty costs) of a motorcycle during the age of first six months or within the usage of 8,000 kilometers are borne by the company. To enhance customer satisfaction, the company wanted to bear the repair costs up to an age of one year or a usage of 12,000 kilometers. The problem is to estimate the expected hike in warranty costs if the warranty policy were revised as mentioned above. Using the past data, the problem is solved by studying the underlying renewal process. Gumbel's bivariate exponential distribution function is found to be useful in approximating the renewal function. Some practical difficulties posed by the past data in the analysis are highlighted and tackled in an interesting way.

A warranty policy involving two attributes, for example time and usage, is considered. Usage is assumed to be related to time through the usage rate, which is considered to be a random variable satisfying a specified probability distribution. The paper analyzes a policy where warranty is not renewed on product failure, within the specified time period and amount of usage, but is minimally repaired. Unit cost of minimal repair, conditional on the usage rate, is assumed to be a non-linear function of the two warranty parameters. Expressions for the expected warranty costs per unit sales are derived. Applications of the results are presented through sample computations. The results demonstrate the use of warranty cost information in selecting the parameters of the warranty policy.

To investigate the optimal burn‐in time from the perspective of minimizing the expected total cost (i.e. manufacturing plus warranty costs) per unit of product sold under a failure‐free renewing warranty policy. The conditions indicating when burn‐in becomes beneficial were also derived.

An age‐dependent general repairable product sold under a failure‐free renewing warranty agreement was considered. In the case of such a general repairable model, there are two ways in which the product can fail: type I failure (minor) can be rectified through minimal repairs; while in type II failure (catastrophic), the product must be replaced. Then optimal burn‐in time is then examined in order to achieve a trade‐off between reducing the warranty cost and increasing the manufacturing cost.

The optimal burn‐in time depends on the failure/repair characteristics, length of warranty, cost parameters and the probability of failure type II (catastrophic). A burn‐in program is beneficial if the initial failure rate is high or product failures during the warranty period are costly. Moreover, the optimal burn‐in time is always less than the infant mortality period.

The product considered in this paper is an age‐dependent general repairable product: on which no such study has yet been conducted. This is also the first study to apply a failure‐free renewing warranty to a general repairable item. It can be seen that the present model is a generalization of the model considered by Chien and Sheu.

The purpose of this paper is to develop an attractiveness index-based warranty cost model considering decision variables as design alternatives, warranty duration and support level.

A warranty optimization approach is illustrated using a real life example of an automobile engine with Mean Time Between Failures and Warranty Attractiveness Index as constraints.

It will help to improve the customer satisfaction by giving a more attractive warranty compared to that being offered by the competitors.

Approaches that consider the effect of decision variables on attractiveness of a warranty policy in a quantitative manner have received relatively less attention. The paper attempts to capture the attractiveness of warranty from the manufacturer as well as customer point of view.

The proposed approach will help manufacturers to take appropriate decisions related to warranty parameters and component selection at the design stage.

The authors consider a system which is a part of a complex equipment (e.g. aircraft, automobile, medical equipment, production machine, etc.), and which consists of N independent series subsystems. The purpose of this paper is to determine simultaneously the system design (reliability) and its preventive maintenance (PM) replacements periodicity which minimize the total average cost per time unit over the equipment useful life, taking into account a minimum required reliability level between consecutive replacements.

The problem is tackled in the context of reliability-based design (RBD) considering at the same time the burn-in of components, the warranty commitment and the maintenance strategy to be adopted. A mathematical model is developed to express the total average cost per time unit to be minimized under a reliability constraint. The total average cost includes the cost of acquiring and assembling components, the burn-in of each component, preventive and corrective replacements performed during the warranty and post-warranty periods. A numerical procedure is proposed to solve the problem.

For any given set of input data including components reliability, their cost and the costs of their preventive and corrective replacements, the system design (reliability) and the periodicity of preventive replacement during the post-warranty period is obtained such as the system’s total average cost per time unit is minimized. The obtained results clearly indicate that a decrease in the number of PM actions to be performed during the post-warranty period increases the number of components to be added at each subsystem at the design stage.

Given that the objective function (cost rate function) to be minimized is non-linear and involves several integer variables, it has not been possible to derive the optimal solution. A numerical procedure based on a heuristic approach has been proposed to solve the problem finding a nearly optimal solution for a given set of input data.

This paper offers to manufacturers a comprehensive approach to look for the most economical combination of the reliability level to be given to their products at the design stage, on one hand, and the PM policy to be adopted, on the other hand, given the offered warranty and service for the products and reliability requirements during the life cycle.

While the RBD problem has been largely treated, most of the published works have focussed on the development or the improvement of solving techniques used to find the optimal configuration. In this paper the authors provide a more comprehensive approach that considers simultaneously RBD, the burn-in and warranty periods, along with the maintenance policy to be adopted. The authors also consider the context of products whose component failures cannot be rectified through repair actions. They can only be fixed by replacement.

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.

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.

Warranty policies for certain products, such as automobiles, often involve consideration of two attributes, for example, time and usage. Since consumers are not necessarily homogeneous in their use of the product, such policies provide protection to users of various categories. In this chapter, product usage at a certain time is linked to the product age through a variable defined as usage rate. This variable, usage rate, is assumed to be a random variable with a specified probability distribution, which permits modeling of a variety of customer categories. Another feature of the chapter is to model the propensity to execute the warranty, in the event of a failure within specified parameter values (say time or usage). In a competitive market, alternative product/warranty offerings may reduce the chances of exercising the warranty. This chapter investigates the impact of warranty policy parameters with the goal of maximizing market share, subject to certain constraints associated with expected warranty costs per unit not exceeding a desirable level.