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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.
Testing process capability based on C-pm in the presence of random measurement errors
(2005-12-01)
Pearn, WL
;
Shu, MH
;
Hsu, BM
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Process capability indices have been widely used in the manufacturing industry providing numerical measures on process performance. The index C-p provides measures on process precision (or product consistency). The index C-pm,C- sometimes called the Taguchi index, meditates on process centring ability and process loss. Most research work related to C-p and C-pm assumes no gauge measurement errors. This assumption insufficiently reflects real situations even with highly advanced measuring instruments. Conclusions drawn from process capability analysis are therefore unreliable and misleading. In this paper, we conduct sensitivity investigation on process capability C-p and C-pm in the presence of gauge measurement errors. Due to the randomness of variations in the data, we consider capability testing for C-p and C-pm to obtain lower confidence bounds and critical values for true process capability when gauge measurement errors are unavoidable. The results show that the estimator with sample data contaminated by the measurement errors severely underestimates the true capability, resulting in imperceptible smaller test power. To obtain the true process capability, adjusted confidence bounds and critical values are presented to practitioners for their factory applications.
Tool replacement for production with a low fraction of defectives
(2006-06-15)
Pearn, WL
;
Hsu, YC
;
Wu, CW
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
In manufacturing industry, the tool replacement cost is, in many cases, a significant portion of the production cost. Early tool replacement increases the production cost. Overdue tool replacement, however, results in poor production quality. Accordingly, improving production quality while maintaining a low production cost is essential. The index C-pk is regarded as a yield-based index. For a fixed C-pk value, the production yield and fraction of defectives can be calculated. In this paper, we present an analytical approach using C-pk to determine the optimal tool replacement time. An accurate process capability must be calculated, particularly when the data contain assignable cause variation. Tool wear is a dominant and inseparable component in many machining processes (a systematic assignable cause), and ordinary capability measures become inaccurate because process data are contaminated by the assignable cause variation. Considering process capability changes dynamically, an estimator of C-pk is investigated. The closed form of the exact sampling distribution is derived. An effective tool management procedure for determining the optimal tool replacement time is presented for processes with a low fraction of defectives. For illustrative purposes, an application example involving tool wear is presented.
One-sided process capability assessment in the presence of measurement errors
(2006-11-01)
Pearn, W. L.
;
Liao, Mou-Yuan
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
In the manufacturing industry, many product characteristics are of one-sided specifications. The well-known process capability indices C-PU and C-PL are often used to measure process performance. Most capability research works have assumed no measurement errors. Unfortunately, such an assumption is not realistic even if the measurement is conducted using highly sophisticated advanced measuring instruments. Therefore, conclusions drawn regarding process capability are not reliable. In this paper, we consider the estimation and testing of C-PU and C-PL with the presence of measurement errors, to obtain adjusted lower confidence bounds and critical values for true process capability, which can be used to determine whether the factory processes meet the capability requirement when the measurement errors are unavoidable. Copyright (C) 2005 John Wiley & Sons, Ltd.
Multivariate capability indices: Distributional and inferential properties
(2007)
Pearn, W. L.
;
Wang, F. K.
;
Yen, C. H.
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Process capability indices have been widely used in the manufacturing industry for measuring process reproduction capability according to manufacturing specifications. Properties of the univariate processes have been investigated extensively, but are comparatively neglected for multivariate processes where multiple dependent characteristics are involved in quality measurement. In this paper, we consider two commonly used multivariate capability indices MCp and MCpm, to evaluate multivariate process capability. We investigate the statistical properties of the estimated MCp and obtain the lower confidence bound for MCp. We also consider testing MCp, and provide critical values for testing if a multivariate process meets the preset capability requirement. In addition, an approximate confidence interval for MCpm is derived. A simulation study is conducted to ascertain the accuracy of the approximation. Three examples are presented to illustrate the applicability of the obtained results.
Optimal tool replacement for processes with low fraction defective
(2007-08-01)
Pearn, W. L.
;
Hsu, Ya-Chen
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Tool wear is a frequent and natural part in many machining processes and is a systematic assignable cause. The fraction of defectives would rise as the tool deteriorates. When the fraction defective reaches a certain level, the tool must be replaced. To minimize the defective parts and the overall tool costs, the optimal tool replacement time needs to be determined. Process capability indices (PCIs) have been effectively used in the manufacturing industry to measure the fraction of defectives. Conventional methods of capability measurement become inaccurate since the process data is contaminated by the assignable cause variation. In order to determine the optimal tool replacement time to maintain maximum product quality, conventional capability calculation must be modified. Considering process capability changes dynamically, an estimator of C-pmk is investigated. We obtain an exact form of the sampling distribution in the presence of a systematic assignable cause. This study provides an effective management policy for optimal tool replacement under low fraction of defectives. To illustrate the application of this procedure, a case study involving the tool wear problem is presented. (c) 2006 Elsevier B.V. All rights reserved.
Measuring process capability based on Cpmk with gauge measurement errors
(2007-08-01)
Hsu, B. M.
;
Shu, M. H.
;
Pearn, W. L.
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Due to their effectiveness and simplicity of use, the process capability indices Cp, Cpk, and Cp. have been popularly accepted in the manufacturing industry as management tools for evaluating and improving process quality. Combining the merits of those indices, a more advanced index, C(pmk), is proposed that takes into account process variation, process centering, and the proximity to the target value, and has been shown to be a very useful index for manufacturing processes with two-sided specification limits. Most research works related to Cpmk assume no gauge measurement errors. However, such an assumption inadequately reflects real situations even when highly advanced measurement instruments are employed. Conclusions drawn regarding process capability are therefore unreliable and misleading. In this paper, we conduct a sensitivity investigation for the process capability index Cpmk in the presence of gauge measurement errors. We consider the use of capability testing Of C(pmk) as a method for obtaining lower confidence bounds and critical values for true process capability when gauge measurement errors are unavoidable. The results show that using the estimator with sample data contaminated by measurement errors severely underestimates the true capability, resulting in an imperceptibly smaller test power. To measure the true process capability, three methods for the adjusted confidence bounds are presented and their performances are compared using computer simulation. Copyright (C) 2006 John Wiley & Sons, Ltd.

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