• International Journal of Reliability and Applications
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• v.2 no.4
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• pp.241-251
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• 2001

In this paper, optimal bum-in time to minimize the total mean cost, which is the sum of manufacturing cost with burn-in and cumulative warranty-related cost, is obtained. When the products with cumulative pro-rata warranty have high failure rate in the early period (infant mortality period), a burn-in procedure is adopted to eliminate early product failures. After burn-in, the posterior product life distribution and the warranty-related cost are dependent on burn-in time; long burn-in period may reduce the warranty-related cost, but it increases the manufacturing cost. The paper provides a methodology to obtain total mean cost under burn-in and cumulative pro-rata warranty. Property of the optimal burn-in time is analyzed, and numerical examples and sensitivity analysis are studied.

• Journal of Korean Society for Quality Management
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• v.24 no.1
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• pp.1-9
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• 1996

Ritchken(1985) analyzes free replacement and pro-rata warranty policies for products receiving renewable warranies. He shows that for constant failure rates pro-rata warranty policies are more attractive to risk-averse manufacturers than shorter term free replacement policies that result in the same average warranty cost. This paper considers the case when product lifetimes distributions are of phase-type. When this is so, Ritchken's performance measures can be simplified considerably. It is found, that irrespective of the pattern of failure rates, pro-rata warranty policies are preferable to free replacement policies. But the warranty period of the equivalent free replacement policy decreases and then increases, as product reliability(the average time between failures) increases.

• The Korean Journal of Applied Statistics
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• v.26 no.1
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• pp.151-162
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• 2013

Due to a growing demand for the second-hand product, especially for the expensive one, the warranty and maintenance policies for such products have been studied to improve the product reliability of late. In this paper we study a periodic maintenance model for the second-hand product which is purchased by the customer at the age of $x$. When purchased, the dealer provides a warranty of a fixed length during which the product is maintained periodically to reduce the failure rate of the product and thus, to improve the reliability after each maintenance is served. If a failure occurs between two successive maintenances, only minimal repair is conducted. As for the warranty policy, we adopt free non-renewing repair action on each failure, in addition to the periodic maintenance service during the warranty period. Thus, under the given warranty policy, all the maintenance and repair costs incurred during the warranty period are charged to the dealer. For the proposed periodic maintenance scheme, we formulate a cost model to evaluate the expected total cost charged to the dealer during the warranty period and derive an optimal upgrade level of the failure rate at each maintenance to minimize the expected total warranty cost from the perspective of the dealer. We also present numerical results for an optimal upgrade level based on the proposed methods.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.12 no.20
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• pp.39-45
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• 1989

This article is concerned with cost analysis in product warranty policy. The warranty cost can be different according to warranty rate and warranty renewal policy. In this paper the stepdown warranty is used. The warranty renewal policy is considered when the warranty is received upon free replacement period as item failing. Assuming the non repairable item as one item is sold, investigated manufacturer's cost in stepdown warranty policy. Also manufacturer's cost is calculated in the free replacement. pro-rata. hybrid policy. Numerical example is given over Weibull time to failure distribution, comparing stepdown warranty policy with free replacement, pro-rata, hybrid one in the manufacturer's point of view. The sensitivity analysis of warranty cost according to the number of warranty period step is included.

• Journal of Korean Society for Quality Management
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• v.42 no.1
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• pp.1-14
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• 2014

Purpose: In this paper, the minimal repair-replacement warranty policy is used to carry out a warranty cost analysis with warranty servicing times and failure times that are statistically correlated to bivariate distributions. Methods: Based on the developed approach by Park and Pham (2012a), we investigate the property of the Freund's bivariate exponential distribution and obtain the number of warranty services using the field data to conduct the warranty cost analysis. Results: Maximum likelihood estimates are presented to estimate the parameters and the warranty model is investigated using a Freund's bivariate exponential distribution. A numerical example is discussed to deal with the applicability of the developed approach in the paper. Conclusion: A novel approach of analyzing the warranty cost is proposed for a product in which failure times and warranty servicing times are used simultaneously to investigate the eligibility of a warranty claim.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.4
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• pp.368-378
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• 2002

As more companies are equipped with data aquisition systems for their products, huge amount of field warranty data has been accumulated. We focus on the case when the field data for a given product comprise with the number of sales and the number of the first failures for each period. The number of censored items and their ages are assumed to be given. This type of data are incomplete in the sense that the age of a failed item is unknown. We construct a model for this type of data and propose an algorithm for nonparametric maximum likelihood estimation of the product reliability. Unlike the nonhomogeneous Poisson process(NHPP) model, our method can handle the data with censored items as well as those with small population. A few examples are investigated to characterize our model, and a real field warranty data set is analyzed by the method.

• Journal of Applied Reliability
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• v.15 no.1
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• pp.6-11
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• 2015

Maintenance plays an important role in keeping product availability, reliability and quality at an appropriate level. In this paper, two-types of maintenance policies are studied following the expiration of two-dimensional (2D) free replacement warranty. Both the fixed-maintenance-period policy and the variable-maintenance-period policy are based on a specified region of the warranty defined in terms of age and usage where all failures are minimally repaired. An accelerating failure time (AFT) model is used to allow for the effect of usage rate on product degradation. The maintenance model that arises following the expiration of 2D warranty is discussed. The expected cost rates per unit time from the user's point of view are formulated and the optimal maintenance policies are determined to minimize the expected cost rate to the user. Finally numerical examples are given to illustrate the optimal maintenance polices.

• Journal of Korean Institute of Industrial Engineers
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• v.14 no.2
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• pp.81-90
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• 1988

This paper is concerned with warranty cost models for a product with two types of failure ; type 1 failures corrected by minimal repair and type 2 failures removed only by replacement. Two warranty policies involving an initial free service period followed by a pro-rata period are considered ; the difference is whether the warranty is renewed or not when type 2 failure occures during its free service period. Expected warranty costs under the two policies are obtained, and their behaviors are examined for the case where type 1 and 2 failure distributions are Weibull and exponential, respectively.

• Proceedings of the Korean Reliability Society Conference
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• 2000.11a
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• pp.299-311
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• 2000

This paper is concerned with the method of estimating lifetime distribution for field data in warranty period and for a situation where some additional field data can be gathered after the warranty period. Implementing the proposed methods in this paper will result in obtaining the more precise product life time estimation and product improvement.

• Journal of Korean Society for Quality Management
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• v.15 no.1
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• pp.2-12
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• 1987

Warranty cost usually involves complex factors paticularly when the product concerned consists of a great deal of parts. In spite of that it can be assessed by means of rather simple mathematical expression, it is possible to realistically appraise the sensitivity to any type of quality policy. This paper thus presents the mathematical concept related to the warranty cost and the general relationship showing that quality policy can be established in connection with the economic quality level.