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Testing process performance based on capability index C-pk with critical values
(2004-12-01)
Pearn, WL
;
Lin, PC
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Process capability index C-pk has been widely used in the manufacturing industry as a process performance measure. In this paper, we investigate the natural estimator of the index C-pk, and show that under the assumption of normality its distribution can be expressed as a mixture of the chi-square and the normal distributions. We also implement the theory of hypothesis testing using the natural estimator of C-pk, and provide efficient Maple programs to calculate the p-values as well as the critical values for various values of alpha-risk, capability requirements, and sample sizes. The behavior of the p-values and critical values as functions of the distribution parameters are investigated to obtain tight critical values for reliable testing. Based on the test, we develop a simple and practical procedure for in-plant applications. The practitioners can use the proposed procedure to determine whether their process meets the preset capability requirement, and make reliable decisions. (C) 2004 Elsevier Ltd. All rights reserved.
A note on production yield measure for multiple lines
(2016)
Pearn, W. L.
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Tai, Y. T.
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Wu, C. H.
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工業工程與管理學系
;
Department of Industrial Engineering and Management
In today\'s globally competitive environment, processes involving multiple manufacturing lines are quite common due to economies of scale considerations. Production yield measure indices C-pk and C-pu are the most popular yield-based indices and have been widely used in manufacturing industries for two-sided and one-sided specification limits, respectively. In this paper, two production yield indices for multiple lines C-pk(M) and C-pu(M) are considered and the approximate distributions of two natural estimators C-pk(M) and C-pu(M) are derived. For the convenience of industry applications, the lower confidence bounds and critical values are provided.
Convenient Ratio Approach for Industrial Implementation in Estimating and Testing Process Yield
(2015-07-01)
Pearn, W. L.
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Tai, Y. T.
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Kao, C. M.
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統計學研究所
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工業工程與管理學系
In recent years, since portable devices with thin and light designs are essential, the applications of the thin-film transistor liquid crystal display (TFT-LCD) have been applied extensively. Process yield is the most common criterion used in the TFT-LCD manufacturing industry for measuring process performance. The measurement index Spk establishes the relationship between the manufacturing specifications and the actual process performance, which provides an exact measure on process yield. In this paper, we provide two convenient ratio approaches to calculate the lower confidence bounds and critical values extensively for various values of alpha-risk, capability requirements, and sample sizes. Practitioners can use the proposed ratio approaches and procedures to determine whether their process meets the preset capability requirement and make reliable decisions. The convenient ratio approaches can bridge the gap between the theoretical development and factory applications for evaluation of process yields.
Estimating Process Capability Index C-p with Various Sample Types: A Practical Implementation
(2015-07-01)
Wu, C. H.
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Pearn, W. L.
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工業工程與管理學系
;
Department of Industrial Engineering and Management
Process precision index Cp has been used widely in the manufacturing industry for measuring process potential and precision. In practice, sample data with various types such as one single random sample, multiple random samples, control chart samples, and samples with gauge measurement errors may be employed to estimate the Cp index for evaluating the process potential capability. If the process is perfectly centered in the specification range, the percentage of process non-conforming (%NC) can be expressed by Cp index. In this paper, a review for estimating and testing of Cp index is presented. Some efficient MATLAB programs and illustrative examples are also provided for each type of sample data.
An Effective Procedure for Supplier Selection Applied to Glass Substrate Processes with Multiple Lines
(2014-11-01)
Pearn, W. L.
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Wu, C. H.
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Chuang, C. C.
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工業工程與管理學系
;
Department of Industrial Engineering and Management
In this paper, we consider a supplier selection problem, which compares two glass substrate processes with multiple lines and selects the one that has a higher capability. A test statistic obtained by a subtraction method is employed to establish a hypothesis test with two phases. Critical values of the test are obtained to determine the selection decisions. Sample sizes required for various designated selection powers and confidence levels are also investigated. Practitioners can use the proposed method to make reliable decisions. This paper presents a real-world case of a glass substrate process. The selection procedure uses data to reach a decision in supplier selection. We compare the results of the division method to the proposed subtraction method. The results show that the proposed subtraction method is indeed more powerful than the division method.
Computer program for calculating the p-value in testing process capability index C-pmk
(2002-07-01)
Pearn, WL
;
Lin, PC
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Many process capability indices, including C-p, C-pk, and C-pm, have been proposed to provide numerical measures on the process potential and performance. Combining the advantages of these indices, Pearn et al. (1992) introduced a new capability index called C-pmk, which has been shown to be a useful capability index for processes with two-sided specification limits. In this paper, we implement the theory of a testing hypothesis using the natural estimator of C-pmk, and provide an efficient Maple computer program to calculate the p-values. We also provide tables of the critical values for some commonly used capability requirements. Based on the test we develop a simple step-by-step procedure for in-plant applications. The practitioners can use the proposed procedure to determine whether their process meets the preset capability requirement, and make reliable decisions. Copyright (C) 2002 John Wiley Sons, Ltd.
Normal approximation to the distribution of the estimated yield index S-pk
(2004-02-01)
Pearn, WL
;
Lin, GH
;
Wang, KH
;
工業工程與管理學系
;
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.
Procedures for testing manufacturing precision C(p)based on ((X)over-bar, R) or ((X)over-bar, S) control chart samples
(2005)
Pearn, WL
;
Wu, CW
;
Chuang, HC
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Process precision index C-p has been widely used in the manufacturing industry for measuring process potential and precision. Estimating and testing process precision based on one single sample have been investigated extensively. In this paper, we consider the problem of estimating and testing process precision based on multiple samples taken from ((X) over bar, R)or ((X) over bar, S)control chart. We first investigate the statistical properties of the natural estimator of C-p and implement the hypothesis testing procedure. We then develop efficient MAPLE programs to calculate the lower confidence bounds, critical values, and p-values based on m samples of size n. Based on the test, we develop a step-by-step procedure for practitioners to use in determining whether their manufacturing processes are capable of reproducing products satisfying the preset precision requirement.
Supplier Selection Critical Decision Values for Processes with Multiple Independent Lines
(2013-10-01)
Pearn, W. L.
;
Wu, C. H.
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
The process yield is the most common criterion considered for decision making in supplier selection problem. For normally distributed processes with multiple independent lines, the SpkM index provides an exact measurement for the overall yield. Therefore, the SpkM index can be implemented to deal with the supplier selection problem with processes having multiple independent lines. In this article, a test statistic obtained by a division method is employed to establish a hypothesis testing procedure, with two phases, which is developed to determine whether two suppliers are equally capable or not. The sampling distribution and the probability density function of the test statistic are derived. For various minimum requirements of process capability, number of lines, sample sizes, magnitudes of the difference between the two suppliers and the type I error, the critical values for decision making are presented. The required sample sizes for various designated powers at given type I error are tabulated. A thin-film transistor type liquid-crystal display application example is provided to demonstrate the testing procedure. Copyright (c) 2012 John Wiley & Sons, Ltd.
Supplier Selection for Processes with Multiple Characteristics Based on Testing Capability Index C-pk
(2013-07-01)
Pearn, W. L.
;
Wu, C. H.
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Supplier selection is the problem which deals with comparing two processes and selecting a better one that has a higher process capability. In this article, the generalization C-pk(T) index is employed to deal with this problem. The generalization C-pk(T) index measures the overall yield for the processes with multiple independent quality characteristics. Based on the generalization C-pk(T) index, a hypothesis testing with two phases is developed to determine whether or not new supplier is better. It allows one to select the supplier with better quality. A test statistic by division method and its corresponding sampling distribution are derived. For various process minimum requirements, magnitudes of the difference between the two processes, unequal sample sizes of two processes, and alpha-risk, the critical values of the tests are tabulated. An application example is presented to illustrate the practicality of the proposed approach. Practitioners can use the proposed method to make reliable decisions in supplier selection problem.

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