• Journal of Korean Society for Quality Management
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• v.31 no.4
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• pp.219-225
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• 2003

Two­dimensional warranty data can be modelled using two different approaches： two­dimensional point process and one­dimensional point process with usage as a function of age. The first approach has three different models. First of all, bivariate model is appealing but is not appropriate for explaining warranty claims. Next, the rest of the two models (marked point process, and counting and matching on both directions independently) are more appropriate for explaining warranty claims. However, the second one (counting and matching on both directions independently) assumes that the two variables (variables representing the two­dimensions) are independent. Last of all, one­dimensional point process with usage as a function of age is also promising to explain the two­dimensional warranty claims. But the models or variations of them need more investigation to be applicable to real warranty claim data.

• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.555-560
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• 2010

One-dimensional approach to two-dimensional warranty data involves modeling us- age as a function of time. Iskandar (1993) suggests a simple linear model for usage. However, simple linear form of intensity function is of limited value to model the situa-tion where the intensity varies over time. In this study Weibull intensity is considered where the scale parameter is expressed in terms of different models. We will nd out how each parameter in the model a ects the warranty cost and which model gives a bigger number of failures within the two-dimensional warranty region.

• Communications for Statistical Applications and Methods
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• v.18 no.3
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• pp.277-286
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• 2011

Global companies can sell their products with dierent warranty periods based on location and times. Customers can select the length of warranty on their own if they pay an additional fee. In this paper, we consider the warranty period and the repair time limit as random variables. A two-dimensional warranty policy is considered with repair times and failure times. The repair times are considered within the repair time limit and the failure times are considered within the warranty period. Under the non-renewable warranty policy, we obtain the expected number of warranty services and their variances in the censored area by warranty period and repair time limit to conduct a warranty cost analysis. Numerical examples are discussed to demonstrate the applicability of the methodologies and results using field data based on the proposed approach in the paper.

• Journal of Applied Reliability
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• v.11 no.1
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• pp.43-57
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• 2011

In the paper, we consider two-dimensional warranty policy with failure times and repair times. The failure times are considered within the warranty period and the repair times are considered within the repair time limit. Under the renewable warranty policy and non-renewable warranty policy, we consider the number of warranty services in the censored area by warranty period and repair time limit to conduct warranty cost analysis. We investigate the field data to check their dependency and implement our proposed approaches to conduct warranty cost analysis using the parametric methods. Numerical examples are discussed to demonstrate the applicability of the methodologies and results based on the proposed approach in the paper.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2002.05a
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• pp.762-766
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• 2002

This paper proposes a method or estimating lifetime distribution for products under two-dimensional warranty in which age and usage are used simultaneously to determine the eligibility of a warranty claim. For such a case, existing methods reduce the two-dimensional time stale to a single stale assuming that the two variables have a functional relationship. This assumption is, however, not appropriate since the functional relationship is unknown in practice. In this paper, the field age and usage data are modeled with a bivariate lifetime distribution. Method of obtaining maximum likelihood estimators is outlined, their asymptotic properties are studied and specific formulas for a bivariate Weibull distribution are obtained. The proposed model is compared with the existing one which assumes a lineal relationship between the two variables Simulation studios are performed to investigate the effect of the degree of dependency between the two variables.

• Journal of Applied Reliability
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• v.10 no.4
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• pp.251-263
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• 2010

Modelling for failures is important for reliability analysis since failures of products such as automobiles occur as both time and usage progress and the results from the proper analysis of the two-dimensional data can be used for establishing warranty assurance policy. Hence, in this paper general issues which concern modelling failures are discussed, and both one-dimensional approaches and two-dimensional approaches to two-dimensional data are investigated. Finally non-parametric approaches to two-dimensional data are presented as a means of exploratory data analyses.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.10 no.6
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• pp.1346-1352
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• 2009

Warranty cost of automobile parts varies depending on the parts failure rate in a warranty region of individual markets. Parts failure rate is significantly affected by usage-rate given that other stressors of individual markets are similar. Accordingly, warranty cost can be predicted by failure modeling which reflects usage-rate and using a stochastic process. In this paper, one-dimensional approach is used by applying accelerated failure time model on the assumption that the usage-rate is linear. Such model can explain changes in parts failure rate depending on the changes in usage-rate since it can be expressed as a function of usage-rate. Therefore, acquisition of usage-rate in a new market will automatically lead to estimate of failure rate even without warranty data and warranty cost of parts can be predicted through a renewal process in replacement cases. A case study using warranty data of two real markets is presented in the application part of this paper.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.12 no.3
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• pp.123-131
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• 2012

As the price of traditional fuels soar, the alternatives are becoming more viable. And manufacturers are promoting the growing viability of electric and biofuel-powered vehicles through longer warranties. Now, these longer green environment (emission)warranties, sometimes called extended warranties or "super warranties," have been adapted. The main result of this paper is to present a new method to approximate a bivariate warranty function by using Radial Basis Function Network with application of Radon Transform and its inverse which is used to reduce the dimension of the warranty space. This method consist of the following stages: First, by using the Radon Transform, the bivariate warranty function can be reduced to one dimensional function. Second, each of the one dimensional functions is approximated by using neural network technique into neural sub-networks. Third, these neural sub-networks are combined together to form the final approximation neural network. Four, by using the inverse of radon transform to this final approximation neural network we get the approximation to the given function. Also, we apply the above method to some green warranty data of automotive vehicle company.