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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.

In this paper, the authors design accelerated life test and provide its application in the field of accelerated life test. The authors use maximum likelihood estimation method as a parameter estimation method.

In this paper we design accelerated life test and provide its application in the field of accelerated life test. The authors use maximum likelihood estimation method as a parameter estimation method.

In this study, the authors design accelerated life test under Type-I censoring when the lifetime of test items follows PID and also provides its application in the field of warranty policy. The following conclusion is made on the basis of this study. (1) An inverse relationship is shown between the shape parameter with the expected total cost and expected cycle time, while the shape parameter directly relates to the expected cost rate (see Table 5). (2) A direct relationship is shown between the scale parameter with the expected total cost and expected time cycle, while the inverse relationship is shown with the expected cost rate (see Table 5). (3) An inverse relationship is shown between the replacement age and the expected cost rate, while there are direct relationships between expected total cost and expected time cycle (see Table 5).

This paper is neither published or neither accepted anywhere.

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.

The purpose of this paper is to design an optimal reliability acceptance sampling plan (RASP) using the Type-I generalized hybrid censoring scheme (GHCS) for non-repairable products sold under the general rebate warranty. A cost function approach is proposed for products having Weibull distributed lifetimes incorporating relevant costs.

For Weibull distributed product lifetimes, acceptance criterion introduced by Lieberman and Resnikoff (1955) is derived for Type-I GHCS. A cost function is formulated using expected warranty cost and other relevant cost components incorporating the acceptance criterion. The cost function is optimized following a constrained optimization approach to arrive at the optimum RASP. The constraint ensures that the producer's and the consumer's risks are maintained at agreed-upon levels.

Optimal solution using the above approach is obtained for Type-I GHCS. As a special case of Type-I GHCS, the proposed approach is also used to arrive at the optimal design for Type-I hybrid censoring scheme as shown in Chakrabarty et al. (2019). Observations regarding the change in optimal design and computational times between the two censoring schemes are noted. An extensive simulation study is performed to validate the model for finite sample sizes and the results obtained are found to be in strong agreement. In order to analyze the sensitivity of the optimal solution due to misspecification of parameter values and cost components, a well-designed sensitivity analysis is carried out using a real-life failure data set from Lawless (2003). Interesting observations are made regarding the change in optimal cost due to change in parameter values, the impact of warranty cost in optimal design and change in optimal design due to change in lot sizes.

The research presents an approach for designing optimal RASPs using Type-I generalized hybrid censoring. The study formulates optimum life test sampling plans by minimizing the average aggregate costs involved, which makes it valuable in dealing with real-life problems pertaining to product quality management.

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.

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.

In order to reduce avoidably lengthy duration required to test highly reliable products under usage stress, accelerated life test sampling plans (ALTSPs) are employed. This paper aims to build a decision model for obtaining optimal sampling plan under accelerated life test setting using Type-I hybrid censoring scheme for products covered under warranty.

The primary decision model proposed in this paper determines ALTSP by minimizing the relevant costs involved. To arrive at the decision model, the Fisher information matrix for Type-I hybrid censoring scheme under accelerated life test setting is derived. The optimal solution is attained by utilizing appropriate techniques following a nonlinear constrained optimization approach. As a special case, ALTSP for Type-I censoring is obtained using the same approach. ALTSP under Type-I hybrid censoring using the variance minimization approach is also derived.

On comparing the optimal results obtained using the above mentioned approaches, it is found that the cost minimization approach does better in reducing the total cost incurred. Results also show that the proposed ALTSP model under cost function setting has considerably lower expected testing time. Interesting findings from the sensitivity analysis conducted using a newly introduced failure dataset pertaining to locomotive controls are highlighted.

The research introduces a model to design optimum ALTSP for Type-I hybrid censoring scheme. The practical viability of the model makes it valuable for real-life situations. The practical application of the proposed model is exemplified using a real-life case.

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.

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.

Knight's Industrial Law Reports goes into a new style and format as Managerial Law This issue of KILR is restyled Managerial Law and it now appears on a continuous updating basis rather than as a monthly routine affair.