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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.

This article deals with the problem of cost estimation for increased warranty time of a multi‐module product. The warranty policy of interest is two‐dimensional involving warranty limits on both age and usage of the product. Failure of the product is caused due to malfunctioning of its module(s). Warranty service is rendered through repair or replacement of the respective module(s). From the past data, it is observed that age and usage are highly correlated. Based on life (age) data, the joint life distribution of the modules is well described by multivariate exponential distribution of Marshall and Olkin. The same is utilized to estimate cost for desired warranty times by the method of simulation.

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 product warranty has become an increasingly important factor contributing to the consumer's assessment of overall product value in recent years and, in consequence, can nowadays have a significant effect on demand levels for a particular product make or brand. The warranty is in effect an “added value” component by which the manufacturer commits himself to a given level of responsibility (usually over a specific time period) for the performance of the product he sells.

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.

The study aims to design the limited number of random working cycle as a warranty term and propose two types of warranties, which can help manufacturers to ensure the product reliability during the warranty period. By extending the proposed warranty to the consumer's post-warranty maintenance model, besides the authors investigate two kinds of random maintenance policies to sustain the post-warranty reliability, i.e. random replacement first and random replacement last. By integrating depreciation expense depending on working time, the cost rate is constructed for each random maintenance policy and some special cases are provided by discussing parameters in cost rates. Finally, sensitivities on both the proposed warranty and random maintenance policies are analyzed in numerical experiments.

The working cycle of products can be monitored by advanced sensors and measuring technologies. By monitoring the working cycle, manufacturers can design warranty policies to ensure product reliability performance and consumers can model the post-warranty maintenance to sustain the post-warranty reliability. In this article, the authors design a limited number of random working cycles as a warranty term and propose two types of warranties, which can help manufacturers to ensure the product reliability performance during the warranty period. By extending a proposed warranty to the consumer's post-warranty maintenance model, the authors investigate two kinds of random replacement policies to sustain the post-warranty reliability, i.e. random replacement first and random replacement last. By integrating a depreciation expense depending on working time, the cost rate is constructed for each random replacement and some special cases are provided by discussing parameters in the cost rate. Finally, sensitivities to both the proposed warranties and random replacements are analyzed in numerical experiments.

It is shown that the manufacturer can control the warranty cost by limiting number of random working cycle. For the consumer, when the number of random working cycle is designed as a greater warranty limit, the cost rate can be reduced while the post-warranty period can't be lengthened.

The contribution of this article can be highlighted in two key aspects: (1) the authors investigate early warranties to ensure reliability performance of the product which executes successively projects at random working cycles; (2) by integrating random working cycles into the post-warranty period, the authors is the first to investigate random maintenance policy to sustain the post-warranty reliability from the consumer's perspective, which seldom appears in the existing literature.

In this study, the focus was shifted from repairing durable goods to achieving healthier ecology, making durable goods more secure in turn. This study introduced preventive maintenance behavior to trace the ex-post control of “curling” back to the ex-post control of “self-healing.” This study tries to close the gap between the human repair of machines and their “self-curing.” Finally, the author makes the machines healthier.

The paper constructed a mathematical model of preventive maintenance behavior during a specific period for durable consumer goods. The author builds a simulation function of the two-stage preventative maintenance behavior relations. The study used simulations to analyze the influencing relationship and differences between three preventive maintenance behavior elements to basic warranty preventive maintenance (BWPM) behavior and extended warranty preventive maintenance (EWPM) behavior.

Both BWPM behavior and EWPM behavior were affected by the preventive maintenance (PM) behavioral components in different ways. The influence paths of the two warranty periods affected by PM behavior were also different.

This study introduced PM behavior to trace the ex-post control of “curling” back to the ex-post control of “self-healing.” This study adopted the human–machine interaction mode to improve durable goods' self-healing ability during operation and enable a more effective and sustainable development.

This study’s conclusions may help manufacturers guide PM behavior in a way that achieves “self-healing” of the durable goods.

The author opened a “black box” of PM behaviors and analyzed their components. The internal structure relation of PM behavior is built and the closed-loop system of spatial structure is formed.

Public reports of provider-specific patient outcomes aim to help consumers select suppliers of medical services. Yet, in an environment of rapidly changing medical technology and increasingly heterogeneous patient populations, and because they necessarily reflect the experience of other patients who received care in the past, such reports may be of limited value in helping patients forecast the probability of an adverse outcome for each provider they are considering. I propose that providers underwrite insurance policies that promptly pay patients a predetermined sum after an adverse outcome. Patients can use such outcome warranties to infer quality differences among providers easily and reliably. In addition, outcome warranties efficiently reward both providers and patients for reducing the risk of adverse outcomes and thereby improve the safety and affordability of health care. As such, outcome warranties help advance four important goals of health care management: reduction of financial risk, recruitment and retention of physicians, remediation of adverse outcomes, and raising the provider's reputation.

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.

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.