Browsing by Author "Pearn, WL"

Now showing 1 - 20 of 83

A Bayesian approach for assessing process precision based on multiple samples
(2005-09-16)
Pearn, WL
;
Wu, CW
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Using process capability indices to quantify manufacturing process precision (consistency) and performance, is an essential part of implementing any quality improvement program. Most research works for testing the capability indices have focused on using the traditional distribution frequency approaches. Cheng and Spiring [IIE Trans. 21 (1) 97) proposed a Bayesian procedure for assessing process capability index C-P based on one single sample. In practice, manufacturing information regarding product quality characteristic is often derived from multiple samples, particularly, when a routine-based quality control plan is implemented for monitoring process stability. In this paper, we consider estimating and testing C-P with multiple samples using Bayesian approach, and propose accordingly a Bayesian procedure for capability testing. The posterior probability, p, for which the process under investigation is capable, is derived. The credible interval, a Bayesian analogue of the classical lower confidence interval, is obtained. The results obtained in this paper, are generalizations of those obtained in Cheng and Spiring [IIE Trans. 21 (1), 97]. Practitioners can use the proposed procedure to Cheng and Spiring determine whether their manufacturing processes are capable of reproducing products satisfying the preset precision requirement. (c) 2004 Elsevier B.V. All rights reserved.
A Bayesian approach to obtain a lower bound for the C-pm capability index
(2005-10-01)
Lin, GH
;
Pearn, WL
;
Yang, YS
;
工業工程與管理學系
;
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 C-pk
(1996)
Pearn, WL
;
Chen, KS
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Bissell (1990) proposed an estimator for the process capability index C-pk assuming the knowledge whether the process mean mu < m or mu greater than or equal to m is available, where m is the mid-point between the upper and lower specification limits. Kotz, Pearn and Johnson (1993) showed that for the index C-pk, the natural estimator gives values for the standard deviation smaller than those of Bissell's. In this paper we show that by adding a well-known correction factor to Bissell's estimator, we obtain an unbiased estimator of C-pk whose standard deviation is smaller than those given in Kotz, Pearn and Johnson (1993). In addition, we propose a Bayesian-like estimator which relaxes Bissell's assumption on the process mean. The distribution of the new estimator is shown to be identical to that of Bissell's estimator.
A Bayesian-like estimator of the process capability index C-pmk
(2003)
Pearn, WL
;
Lin, GH
;
工業工程與管理學系
;
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 case study on the multistage IC final testing scheduling problem with reentry
(2004-04-18)
Pearn, WL
;
Chung, SH
;
Chen, AY
;
Yang, MH
;
工業工程與管理學系
The integrated-circuit final testing scheduling problem (ICFTSP) with reentry is a variation of the complex flow-shop scheduling problem, which is also a generalization of the classical reentrant flow batch process problem, and the identical parallel machine problem. In this paper, we present a case study on the ICFTSP with reentry, which is taken from a final testing shop floor in an integrated circuit manufacturing factory. For the case investigated, the jobs are clustered by their product types, which must be processed on groups of parallel machines at various process stages following the manufacturing sequence, which must be completed before the due dates. The job processing time depends on the product type, and the machine setup time is sequentially dependent on the orders of jobs processed. The objective is to schedule jobs without violating all constraints, while the total machine workload is minimized. Since the ICFTSP has reentry characteristic, and involves job processing precedence, serial-processing stage, batch-processing stage, job clusters, job-cluster dependent processing time, due dates, machine capacity, and sequence dependent setup time, it is more difficult to solve than the classical flow-shop scheduling problem. We present three fast network algorithms to efficiently solve the ICFTSP with reentry and provide a performance comparison between the three algorithms on eight test problems. (C) 2003 Elsevier B.V. All rights reserved.
A case study on the wafer probing scheduling problem
(2002-01-01)
Pearn, WL
;
Chung, SH
;
Yang, MH
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
The wafer probing scheduling problem (WPSP) is a practical generalization of the classical parallel-machine scheduling problem, which has many real-world applications, particularly, in the integrated circuit (IC) manufacturing industry. In this paper, a case study on the WPSP is presented, which is taken from a wafer probing shop floor in an IC manufacturing factory. For the WPSP case investigated, the jobs are clustered by their product types, which are processed on groups of identical parallel machines and must be completed before the due dates. The job processing time depends on the product type, and the machine setup time is sequentially dependent on the orders of jobs processed. The objective in this case is to seek a probing job schedule with minimum total machine workload. Since the WPSP case investigated involves constraints on job clusters, job-cluster dependent processing time, due dates, machine capacity, and sequentially dependent setup time, it is more difficult to solve than the classical parallel-machine scheduling problem. The WPSP is formulated as an integer programming problem and the problem solved using the powerful CPLEX with effective implementation strategies. An efficient solution procedure to solve the WPSP near-optimally is proposed.
A linear programming model for the control wafers downgrading problem
(2005-02-01)
Chung, SH
;
Pearn, WL
;
Kang, HY
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper considers the control wafers downgrading problem (CWDP) in the wafer fabrication photolithography area. The objective of the research is to minimize the total cost of control wafers, while maintaining the same level of production throughput. For the problem under a pulling control production environment, a linear programming model is presented to set the supply rate of new control wafers and the recycle and downgrading rates so as to minimize the total cost of control wafers. A numerical example is given to illustrate the practicality of the model. The sensitivity of the linear programming model solution to changes in the underlying parameter values is also investigated. The results demonstrate that the proposed model is an effective tool for determining the control wafers downgrading policy. This paper presents a linear programming model that considers the cost of new control wafers, recycle and downgrading control wafers in wafer fabrication. The proposed model improved the performance of control wafers management, and served as the basis for setting the usage rates of control wafers.
A multiprocess performance analysis chart based on the incapability index C-pp: an application to the chip resistors
(2002-07-01)
Pearn, WL
;
Ko, CH
;
Wang, KH
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Statistical process control charts, such as the (X) over bar, R, S-2, S, and MR charts, have been widely used in the manufacturing industry for controlling/monitoring process performance, which are essential tools for any quality improvement activities. Those charts are easy to understand, which effectively communicate critical process information without using words and formula. In this paper, we introduce a new control chart, called the C-pp multiple process performance analysis chart (MPPAC), using the incapability index C-pp. The C-pp MPPAC displays multiple processes with the departure, and process variability relative to the specification tolerances, on one single chart. We demonstrate the use of the C-pp MPPAC by presenting a case study on some resistor component manufacturing processes, to evaluate the factory performance. (C) 2002 Elsevier Science Ltd. All rights reserved.
A note on the interval estimation of C-pk with asymmetric tolerances
(2002-12-01)
Lin, GH
;
Pearn, WL
;
工業工程與管理學系
;
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 practical implementation of the incapability index C-pp
(2002-12-01)
Pearn, WL
;
Chen, KL
;
Chen, KS
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Process capability index C-pp has been introduced to measure process performance. In practice, since sample data must be collected in order to calculate the index value, then a great degree of uncertainty may be introduced into capability assessments due to sampling errors. In current practice, the practitioners would simply look at the index value calculated from the sample data then make a conclusion on whether the given process meets the capability requirement. This approach is not reliable since the sampling errors are ignored. In this paper, we take into account the sampling errors and develop a simple procedure using the UMVUE (uniformly minimum variance unbiased estimator) of C-pp, for practitioners to use in determining whether a process meets the capability requirement. The decisions made based on the proposed procedure are, of course, more reliable.
A reliable procedure for testing linear regulators with one-sided specification limits based on multiple samples
(2003-04-01)
Pearn, WL
;
Lin, GH
;
工業工程與管理學系
;
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.
A service level model for the control wafers safety inventory problem
(2005-09-01)
Chung, SH
;
Kang, HY
;
Pearn, WL
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper considers the control wafers safety inventory problem (CWSIP) in the wafer fabrication photolithography area. The objective is to minimize the total cost of control wafers, where the cost includes new wafers cost, re-entrant cost and holding cost while maintaining the same level of production throughput. For the problem under pulling control production environment, a nonlinear programming model is presented to set safety inventory levels so as to minimize total cost of control wafers. A numerical example is given to illustrate the practicality of the model. The results demonstrate that the proposed model is an effective tool for determining the service level of safety inventory of control wafers for each grade.
Accuracy analysis of the estimated process treld based onS(pk)
(2004-06-01)
Pearn, WL
;
Chuang, CC
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Process yield has been the most basic and common criterion used in the manufacturing industry as a base for measuring process performance. Boyles considered a measurement formula called S-pk, which establishes the relationship between the manufacturing specification and the actual process performance, providing an exact (rather than approximate) measure of process yield. Unfortunately, the sampling distribution and the associated statistical properties of Spk are analytically intractable. In this paper, we consider the natural estimator of the measure S-pk. We investigate the accuracy of the natural estimator of S-pk computationally, using a simulation technique to find the relative bias and the relative mean square error for some commonly used quality requirements. Extensive simulation results are provided and analyzed, which are useful to the engineers for factory applications in measuring process performance. Copyright (C) 2004 John Wiley Sons, Ltd.
Algorithms for the wafer probing scheduling problem with sequence-dependent set-up time and due date restrictions
(2004-11-01)
Pearn, WL
;
Chung, SH
;
Yang, MH
;
Chen, YH
;
交大名義發表
In this paper, we consider the wafer probing scheduling problem (WPSP) to sequence families of jobs on identical parallel machines with due date restrictions. The machine set-up time is sequentially dependent on the product types of the jobs processed on the machine. The objective is to minimize the total machine workload without violating the machine capacity and job due date restrictions. The WPSP is a variation of the classical parallel-machine scheduling problem, that can be transformed into the vehicle-routing problem with time windows (VRPTW). One can therefore solve the WPSP efficiently using existing VRPTW algorithms. We apply four existing savings algorithms presented in the literature including sequential, parallel, generalized, and matching based savings, and develop three modifications called the modified sequential, the compound matching based, and the modified compound matching-based savings algorithms, to solve the WPSP. Based on the characteristics of the wafer probing process, a set of test problems is generated for testing purposes. Computational results show that the three proposed modified algorithms perform remarkably well.
An algorithm for calculating the lower confidence bounds of C-PU and C-PL with application to low-drop-out linear regulators
(2003-03-01)
Pearn, WL
;
Shu, MH
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
In assessing the performance of normal stable manufacturing processes with one-sided specification limits, process capability indices C-PU and C-PL have been widely used to measure the process capability. The purpose of this paper is to develop an algorithm to compute the lower confidence bounds on C-PU and C-PL using the UMVUEs of C-PU and C-PL. The lower confidence bound presents a measure on the minimum capability of the process based on the sample data. We also provide tables for the engineers/practitioners to use in measuring their processes. A real-world example taken from a microelectronics device manufacturing process is investigated to illustrate the applicability of the algorithm. Implementation of the existing statistical theory for capability assessment fills the gap between the theoretical development and the in-plant applications. (C) 2003 Elsevier Science Ltd. All rights reserved.
An algorithm for calculating the lower confidence bounds of C-PU and C-PL with application to low-drop-out linear regulators (vol 43, pg 495, 2003)
(2003-08-01)
Pearn, WL
;
Shu, MH
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
An application of non-normal process capability indices
(1997-11-01)
Chen, KS
;
Pearn, WL
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Numerous process capability indices, including C-p, C-pk, C-pm, and C-pmk, have been proposed to provide measures of process potential and performance. In this paper, we consider some generalizations of these four basic indices to cover non-normal distributions. The proposed generalizations are compared with the four basic indices. The results show that the proposed generalizations are more accurate than those basic indices and other generalizations in measuring process capability. We also consider an estimation method based on sample percentiles to calculate the proposed generalizations, and give an example to illustrate how we apply the proposed generalizations to actual data collected from the factory. (C) 1997 John Wiley & Sons, Ltd.
Analytic network process (ANP) approach for product mix planning in semiconductor fabricator
(2005-04-18)
Chung, SH
;
Lee, AHI
;
Pearn, WL
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper proposes an application of the analytic network process (ANP) for the selection of product mix for efficient manufacturing in a semiconductor fabricator. In order to evaluate different product mixes, a hierarchical network model based on various factors and the interactions of factors is presented. By incorporating experts' opinion, a priority index can be calculated for each product mix studied, and a performance ranking of product mixes can be generated. The results provide guidance to a fab regarding strategies for accepting orders to maximize the manufacturing efficiency in considering the aspects of product, equipment efficiency and finance. The model can be easily understood and followed by administrators to determine the most efficient product mix for a fab. (c) 2004 Elsevier B.V. All rights reserved.
Approximate solutions for the Maximum Benefit Chinese Postman Problem
(2005-10-20)
Pearn, WL
;
Chiu, WC
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
The Maximum Benefit Chinese Postman Problem (MBCPP) is an interesting and practical generalization of the classical Chinese Postman Problem, which has many real-world applications. Each arc on the MBCPP network is associated with a service cost for the traversal with service, a deadhead cost for the traversal with no service, and a set of benefits. Each time an arc is traversed, a benefit is generated. The objective of the MBCPP is to find a postman tour traversing a selected set of arcs with the total net benefit maximized. Such a generalization reflects real-world situations more closely. The MBCPP has been shown to be more complicated than the Rural Postman Problem, which is an NP-hard problem. Therefore, it is difficult to find polynomial-time bounded algorithms to solve the problem exactly. In this paper, we first review an existing exact solution procedure, and introduce several heuristic algorithms including the Branch-Scan algorithm, the Connection algorithm with various connection strategies, and the Directed Tree algorithm, to solve the MBCPP approximately. We also apply one-opt, two-opt, component exchange, and component-drop procedures to improve the solutions. The proposed algorithms are tested and compared. Extensive computational results are provided and analysed.
Assessing process performance based on the incapability index C-pp
(2005-06-01)
Lin, PC
;
Pearn, WL
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Process incapability index C-pp has been introduced to the manufacturing industry to measure process performance. But all existing methods for testing C-pp require further estimation of the distribution parameters when calculating the p-values and critical values causing additional sampling errors, which is unreliable. In this paper, an efficient SAS computer program is provided to calculate the p-values. Extensive calculations were performed to examine the behavior of the p-values and the critical values c(0) against the distribution parameter. Useful critical values for commonly used capability requirements are also tabulated. A simple but practical step-by-step hypothesis-testing procedure is developed for in-plant applications. Significance: Complicated statistical theory for the uniformly minimum variance unbiased estimator (UMVUE) of C-pp is implemented for testing normal processes. An efficient computer program and useful critical values are given. A practical procedure is developed for the practitioners to determine whether their process meets the preset capability requirement. Since the proposed procedure does not require further estimation of the distribution parameter, the decisions made are more reliable than that using other approaches.