Browsing by Author "Lin, GH"

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A Bayesian approach to obtain a lower bound for the C-pm capability index
(2005-10-01)
Lin, GH
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Pearn, WL
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Yang, YS
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工業工程與管理學系
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Department of Industrial Engineering and Management
The Taguchi capability index C-pm, which incorporates the departure of the process mean from the target value, has been proposed to the manufacturing industry for measuring manufacturing capability. A Bayesian procedure has been considered for testing process performance assuming mu = T, which was generalized without assuming mu = T. Statistical properties of the natural estimator of the index C-pm for normal processes have been investigated extensively. However, the investigation was restricted to processes with symmetric tolerances. Recently, a generalized C-pm, referred to as C-pm", was proposed to cover processes with asymmetric tolerances. Under the normality assumption, the statistical properties of the estimated C-pm" including the exact sampling distribution, the rth moment, expected value, variance, and the mean-squared error were obtained. In this paper, we use a Bayesian approach to obtain the interval estimation for the generalized Taguchi capability index C-pm" Consequently, the manufacturing capability testing can be performed for quality assurance. Copyright (c) 2005 John Wiley & Sons, Ltd.
A Bayesian-like estimator of the process capability index C-pmk
(2003)
Pearn, WL
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Lin, GH
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工業工程與管理學系
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Department of Industrial Engineering and Management
Pearn et al. (1992) proposed the capability index C-pmk, and investigated the statistical properties of its natural estimator (C) over cap (pmk) for stable normal processes with constant mean mu. Chen and Hsu (1995) showed that under general conditions the asymptotic distribution of (C) over cap (pmk) is normal if munot equalm, and is a linear combination of the normal and the folded-normal distributions if mu=m, where m is the mid-point between the upper and the lower specification limits. In this paper, we consider a new estimator (C) over tilde (pmk) for stable processes under a different (more realistic) condition on process mean, namely, P (mugreater than or equal tom)=p, 0less than or equal topless than or equal to1. We obtain the exact distribution, the expected value, and the variance of (C) over tilde (pmk) under normality assumption. We show that for P (mugreater than or equal tom)=0, or 1, the new estimator (C) over tilde (pmk) is the MLE of C-pmk, which is asymptotically efficient. In addition, we show that under general conditions (C) over tilde (pmk) is consistent and is asymptotically unbiased. We also show that the asymptotic distribution of (C) over tilde (pmk) is a mixture of two normal distributions.
A note on the interval estimation of C-pk with asymmetric tolerances
(2002-12-01)
Lin, GH
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Pearn, WL
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工業工程與管理學系
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Department of Industrial Engineering and Management
Pearn and Chen (1998) proposed a generalization of the widely used process capability index (PCI) C-pk to handle processes with asymmetric tolerances. They investigated the sampling distribution and obtained the exact formulae for the expected value and variance of its natural estimator. Recently, Pearn and Lin (2000) considered a different estimator under different process condition, and investigated the statistical properties of the new estimator. However, their efforts focused on the small sample properties under the normality assumption. In this paper, we investigate the large sample properties of its natural estimator under the general condition. Based on the limiting distribution of the new estimator, we provide an approximate 100(1 - alpha)% confidence interval of the considered PCI. The obtained confidence interval provides great benefit to quality engineers on monitoring the process and assessing process performance.
A reliable procedure for testing linear regulators with one-sided specification limits based on multiple samples
(2003-04-01)
Pearn, WL
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Lin, GH
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工業工程與管理學系
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Department of Industrial Engineering and Management
Process capability indices C-PU and C-PL are developed in the manufacturing industry to provide quantitative measures on process potential and performance. for processes with one-sided specification limits. Statistical properties of the estimators of C-PU and C-PL have been investigated extensively, but only restricted to cases with single samples. In this paper, we consider the estimation and capability testing of C-PU and C-PL based on multiple samples. We show that the proposed estimator of C-PU and C-PL are indeed the uniformly minimum variance unbiased estimators (UMVUEs). A simple procedure based on a hypothesis testing using the UMVUE is developed for the practitioners to use for judging whether a stable process meets the preset capability requirement. (C) 2002 Elsevier Science Ltd. All rights reserved.
Distributional and inferential properties of the process accuracy and process precision indices
(1998)
Pearn, WL
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Lin, GH
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Chen, KS
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工業工程與管理學系
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Department of Industrial Engineering and Management
Process capability indices such as C-p, k, and C-pk, have been widely used in manufacturing industry to provide numerical measures on process potential and performance. While C-p measures overall process variation, k measures the degree of process departure. In this paper, we consider the index C-p and a transformation of k defined as C-a = 1 - k which measures the degree of process centering. We refer to C-p as the process precision index, and C-a as the process accuracy index. We consider the estimators of C-p and C-a, and investigate their statistical properties. For C-p, we obtain the UMVUE and the MLE. We show that this UMVUE is consistent, and asymptotically efficient. For C-a, we investigate its natural estimator. We obtain the first two moments of this estimator, and show that the natural estimator is the MLE, which is asymptotically unbiased and asymptotically efficient. We also propose an efficient test based on the UMVUE of C-p. We show that the proposed test is the UMP test.
Estimated incapability index: Reliability and decision making with sample information
(2002-03-01)
Pearn, WL
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Lin, GH
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工業工程與管理學系
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Department of Industrial Engineering and Management
The process incapability index C-pp, which provides an uncontaminated separation between information concerning the process precision and process accuracy, has been proposed to measure process performance for industry applications. In this paper, we investigate the reliability of the natural estimator computationally, based on the alpha-level confidence relative error for various sample sizes. We also develop a decision-making procedure for judging if the process satisfies the preset quality requirement. The investigation is useful to the practitioners in determining the sample sizes required in their applications for the decisions reliable to the desired level. Copyright (C) 2002 John Wiley Sons, Ltd.
Estimating capability index C-pk for processes with asymmetric tolerances
(2000)
Pearn, WL
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Lin, GH
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工業工程與管理學系
;
Department of Industrial Engineering and Management
Pearn and Chen (1996) considered the process capability index C-pk, and investigated the statistical properties of its natural estimator under various process conditions. Their investigation, however, was restricted to processes with symmetric tolerances. Recently, Pearn and Chen (1998) considered a generalization of C-pk, referred to as C-pk(.), to cover processes with asymmetric tolerances. They investigated the statistical properties of the natural estimator of C-pk(.), and obtained the exact formulae for the expected value and variance. In this paper, we consider a new estimator of C-pk*, assuming the knowledge on P(mu greater than or equal to T) = p is available, where 0 less than or equal to p less than or equal to 1, which can be obtained from historical information of a stable process. We obtain the exact distribution of the new estimator assuming the process characteristic follows the normal distribution. We show that the new estimator is consistent, asymptotically unbiased, which converges to a mixture of two normal distributions. We also show that by adding suitable correction factors to the new estimator, we may obtain the UMVUE and the MLE of the generalization C-pk(.).
Normal approximation to the distribution of the estimated yield index S-pk
(2004-02-01)
Pearn, WL
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Lin, GH
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Wang, KH
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工業工程與管理學系
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Department of Industrial Engineering and Management
Process yield is the most common criterion used in the manufacturing industry for measuring process performance. A measurement index, called S-pk, has been proposed to calculate the yield for normal processes. The measurement index S-pk establishes the relationship between the manufacturing specifications and the actual process performance, which provides an exact measure on process yield. Unfortunately, the sampling distribution of the estimated S-pk is mathematically intractable. Therefore, process performance testing cannot be performed. In this paper; we consider a normal approximation to the distribution of the estimated S-pk, and investigate its accuracy computationally. We compare the critical values calculated from the approximate distribution with those obtained using the standard simulation technique, for various commonly used quality requirements. Extensive computational results are provided and analyzed. The investigation is useful to the practitioners for making decisions in testing process performance based on the yield.
On the distributional properties of the estimated process accuracy index C-a
(2004-06-01)
Lin, GH
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Pearn, WL
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工業工程與管理學系
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Department of Industrial Engineering and Management
Pearn et al. (1998) introduced the process accuracy index C-a to measure the degree of process centering (the ability to cluster around the center). Assuming that the process runs under uniform process condition, so that the process mean may be assumed as an unknown constant, the distributional and inferential properties of the estimator of Ca are investigated for normal processes. In this paper, the distributional properties of an estimator are investigated under a different but practical condition for stable normal processes, in which the knowledge P{mu greater than or equal to m} = p epsilon [0, 1] is available. The sampling distribution of the new estimator is derived. It is shown that the proposed estimator under the new process condition investigated, follows the normal distribution. Consequently, process accuracy testing based on the ability to cluster around the center, can be easily performed. The expected value and the mean square error of the new estimator are also calculated for various values of two commonly-used process characteristic parameters, (mu - m)/sigma = 0.0(0.5)2.0, and d/sigma = 2(1)6. Significance: The sampling distribution of the proposed new estimator is derived. Consequently, process accuracy testing based on the ability to cluster around the center, can be easily performed, and decisions therefore can be made on whether actions should be taken to improve the process quality.
On the reliability of the estimated incapability index
(2001-07-01)
Pearn, WL
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Lin, GH
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工業工程與管理學系
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Department of Industrial Engineering and Management
Greenwich and Jahr-Schaffrath (1995) introduced the process incapability index C-pp = C-ip + C-ia, which provides an uncontaminated separation between information concerning the process precision (C-ip) and process accuracy (C-ia)- In this paper, we consider the three indices, and investigate the statistical properties of their natural estimators. For the three indices, we obtain their UMVUEs and MLEs, and compare the reliability of the two estimators based on the relative mean square errors. In addition, we construct 90%, 95%, and 99% upper confidence limits, and the maximum values of C-pp for which the process is capable 90%, 95%, and 99% of the time. The results obtained in this paper are useful to the practitioners in choosing good estimators and making reliable decisions on judging process capability. Copyright (C) 2001 John Wiley & Sons, Ltd.