• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2005년도 춘계공동학술대회 발표논문
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• pp.678-685
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• 2005

Estimating parameters of the lifetime distribution is investigated when field failure data are not completely reported. To take into account the reality and the accuracy of the estimates in such a case, the failure reporting probability is incorporated in estimating parameters. Firstly, method of maximum likelihood estimate(MLE) is used to estimate parameters of the lifetime distribution when failure reporting probability is known. Secondly, Expectation and Maximization(EM) algorithm is used to estimate the failure reporting probability and parameters of the lifetime distribution simultaneously when failure reporting probability is unknown. For both case, procedures of estimation are illustrated for single Weibull distribution and mixed Weibull distribution. Simulation results show that MLE obtained by the proposed method is more accurate than the conventional MLE.

• 산업경영시스템학회지
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• 제23권57호
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• pp.113-122
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• 2000

A mixture of two distributions, each belonging to the same known Weibull distributions, is proposed and a simple graphical method for estimating the parameters of the Weibull distribution is applied. It appears from the results of this study that the mixed Weibull distribution is an appropriate expression for describing industrial property mortality characteristics.

• 대한산업공학회지
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• 제33권1호
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• pp.52-60
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• 2007

Estimating parameters of the lifetime distribution is investigated when field failure data are not completelyreported. To take into account the reality and the accuracy of the estimates in such a case, the failure reportingprobability is incorporated in estimating parameters, Firstly, method of maximum likelihood estimate (MLE) isused to estimate parameters of the lifetime distribution when failure reporting probability is known, Secondly,Expectation and Maximization (EM) algorithm is used to estimate the failure reporting probability and parame-ters of the lifetime distribution simultaneously when failure reporting probability is unknown. For both cases,procedures of estimation are illustrated for single Weibull distribution and mixed Weibull distribution. Simula-tion results show that MLE obtained by the proposed method is more accurate than the conventional MLE.

• 한국신뢰성학회지:신뢰성응용연구
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• 제15권3호
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• pp.170-175
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• 2015

Reliability demonstration tests (RDT's) are widely employed in design verification and process validation stages of industry. New mixed attribute-variable RDT plans that compromise demerits of the corresponding zero and zero or one failure plans which are common in practice are developed for the exponential distribution. The proposed mixed plans are compared with the typical RDT plans in terms of probability of acceptance and expected test termination time. A numerical example is provided to illustrate the mixed plans and a procedure to extend these plans to the Weibull distribution with known shape parameter is also presented.

• 대한안전경영과학회지
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• 제1권1호
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• pp.135-143
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• 1999

This paper discusses an optimal burn-in procedure to minimize total costs based on the assumption that the failure rate pattern follows a bimodal mixed Weibull distribution. The procedure will consider warranty period as a factor of the total expected bum-in cost. A cost model is formulated to find the optimal burn-in time that minimizes the expected burn-in cost. Conditional reliability for warranty period will be discussed. An illustrative example is included to show how to use the cost model in practice.

• 품질경영학회지
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• 제24권2호
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• pp.65-76
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• 1996

In general, most industrial products exhibit bath-tub shaped curve for their failure rate functions. This distributional life model can be obtained by the Piecewise Weibull distribution. The least squares, maximum likelihood, and mixed methods of estimating the parameters of the Piecewise Weibull distribution are compared. The comparison is made by using the empirical mean squared errors of (a) the parameter estimates and (b) the estimated change-points, to summarize the results of 1000 simulated samples of three sizes - each 100, 150 and 200. The results are that the mixed method estimation comes to be the best as the sample sizes increase.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 1998년도 The 12th Asia Quality Management Symposium* Total Quality Management for Restoring Competitiveness
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• pp.544-555
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• 1998

Although the bimodal mixed weibull distribution is used to developing burn-in model widely, the failure times for a component or a system is often truncated at some time, T, due to the obsolescence in the electronics industry. In this paper, we will determine minimum total cost and burn-in time by using the bimodal mixed weibull distribution and the truncated bimodal mixed weibull distribution under the free warranty policy. The results of this study are summarized as follows. First, when products or system is not repairable, the width of the change of burn-in time can be larger by ${\beta}_1,\;{\beta}_2$ Second, if burn-in time become longer, it will be impossible to consider the bum-in in a long time, and in this case, the burn-in time should be shorten by the acceleration burn-in. Third, in case that opportunity loss cost or repair cost is exceed the warranty cost, or the total cost of considering burn-in is larger than that of not considering burn-in, it is not existed burn-in time which makes total cost to minimize. Forth, the shorter life-cycle of product, the more burn-in times will be decreased and the cost in considering burn-in will be increased

• 한국국방경영분석학회지
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• 제22권2호
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• pp.215-226
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• 1996

The estimation of lifetimes are examined when the distribution of lifetimes are Weibull. It is assumed that, due to physical restrictions and/or economic requirements, the lifetimes are investigated only at certain time intervals during the test period with 'mixed replacement' experiment, even though it is well known that 'with replacement' experiment produces better accuracy than 'without replacement' one. The maximum likelihood estimators are derived through the iterative method like as Lawless(1982). Also Cramer-Rao lower bounds are found as the asymptotic variances of the estimates.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 1999년도 추계학술대회
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• pp.147-155
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• 1999

This paper discusses an optimal burn-in procedure to minimize total costs based on the assumption that the failure rate pattern follows a bimodal mixed Weibull distribution. The procedure will consider warranty period as a factor of the total expected burn-in cost. A cost model is formulated to find the optimal burn-in time that minimizes the expected burn-in cost. Conditional reliability for warranty period will be discussed. An illustrative example is included to show how to use the cost model in practice.

• Journal of the Korean Statistical Society
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• 제28권4호
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• pp.399-413
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• 1999