Browsing by Author "Pearn, Wen Lea"

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A batch arrival queue under randomised multi-vacation policy with unreliable server and repair
(2012)
Ke, Jau-Chuan
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Huang, Kai-Bin
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This article examines an M([x])/G/1 queueing system with an unreliable server and a repair, in which the server operates a randomised vacation policy with multiple available vacations. Upon the system being found to be empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 - p. When one or more customers arrive when the server is idle, the server immediately starts providing service for the arrivals. It is possible that an unpredictable breakdown may occur in the server, in which case a repair time is requested. For such a system, we derive the distributions of several important system characteristics, such as the system size distribution at a random epoch and at a departure epoch, the system size distribution at the busy period initiation epoch, and the distribution of the idle and busy periods. We perform a numerical analysis for changes in the system characteristics, along with changes in specific values of the system parameters. A cost effectiveness maximisation model is constructed to show the benefits of such a queueing system.
A heuristic algorithm for the optimization of a retrial system with Bernoulli vacation
(2013-03-01)
Ke, Jau-Chuan
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Wu, Chia-Huang
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Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
In this study, we consider an M/M/c retrial queue with Bernoulli vacation under a single vacation policy. When an arrived customer finds a free server, the customer receives the service immediately; otherwise the customer would enter into an orbit. After the server completes the service, the server may go on a vacation or become idle (waiting for the next arriving, retrying customer). The retrial system is analysed as a quasi-birth-and-death process. The sufficient and necessary condition of system equilibrium is obtained. The formulae for computing the rate matrix and stationary probabilities are derived. The explicit close forms for system performance measures are developed. A cost model is constructed to determine the optimal values of the number of servers, service rate, and vacation rate for minimizing the total expected cost per unit time. Numerical examples are given to demonstrate this optimization approach. The effects of various parameters in the cost model on system performance are investigated.
Algorithmic analysis of the multi-server system with a modified Bernoulli vacation schedule
(2011-05-01)
Ke, Jau-Chuan
;
Wu, Chia-Huang
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper considers an infinite-capacity M/M/c queueing system with modified Bernoulli vacation under a single vacation policy. At each service completion of a server, the server may go for a vacation or may continue to serve the next customer, if any in the queue. The system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition of system equilibrium is obtained. The explicit closed-form of the rate matrix is derived and the useful formula for computing stationary probabilities is developed by using matrix analytic approach. System performance measures are explicitly developed in terms of computable forms. A cost model is derived to determine the optimal values of the number of servers, service rate and vacation rate simultaneously at the minimum total expected cost per unit time. Illustrative numerical examples demonstrate the optimization approach as well as the effect of various parameters on system performance measures. (c) 2010 Elsevier Inc. All rights reserved.
An improved measure of quality loss for notching processes
(1970-01-01)
Wu, Chia Huang
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Hsu, Ya Chen
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Pearn, Wen Lea
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工業工程與管理學系
;
Department of Industrial Engineering and Management
Nowadays, electronic products are progressively becoming thinner, lighter, and more convenient for people to use. Printed circuit boards, and especially integrated circuit (IC) substrates, are among the essential component of these products. The IC substrate not only protects circuits, fixes lines, and conducts heat, but is also the critical component that provides signal connectivity between the chip, the printed circuit boards, and other crucial parts during the packaging process. The process capability indexC(pm)is commonly used to assess the product quality loss for decision making in modern semiconductor packaging manufacturing. For high-definition products, packaging processes often have very strict quality requirements and thus the quality inspection procedure is time-consuming and complicated. Therefore, because of the limitation of manpower and capacity of the inspection instruments, the collected sample for quality assessment may be with small to moderate sample sizes. In this paper, we introduce an unbiased estimator forC(pm)and provide a step-by-step parametric bootstrap procedure for obtaining a composite lower confidence bound onC(pm). To compare with the approaches discussed in the literature, numerical simulations are conducted under various process parameter settings. The results show that for small to moderate sample sizes, the proposed method applying the unbiased estimator has more accurate coverage rates than the existing methods. At the end of this paper, an application of quality loss assessment in notching processes is demonstrated.
Analysis of an infinite multi-server queue with an optional service
(2013-06-01)
Ke, Jau-Chuan
;
Wu, Chia-Huang
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper deals with an infinite-capacity multi-server queueing system with a second optional service (SOS) channel. The inter-arrival times of arriving customers, the service times of the first essential service (FES) and the SOS channel are all exponentially distributed. A customer may leave the system after the FES channel with a probability (1 - theta), or the completion of the FES may immediately require a SOS with a probability theta (0 <= theta <= 1). The formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is developed to simultaneously determine the optimal values of the number of servers and the two service rates at the minimal total expected cost per unit time. Quasi-Newton method and Particle Swarm Optimization (PSO) method are employed to deal with the optimization problem. Under optimal operating conditions, numerical results are provided from which several system performance measures are calculated based on the assumed numerical values of the system parameters. (c) 2013 Elsevier Ltd. All rights reserved.
Analytic Solution to Product Acceptance Determination for Gold Bumping Process With Multiple Manufacturing Lines
(2013-11-01)
Pearn, Wen Lea
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Tai, Yu Ting
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Wu, Chia Huang
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Chuang, Ching Ching
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工業工程與管理學系
In recent years, gold bumping process has been applied extensively for the package technology of liquid crystal display driver integrated circuit, which is an essential component in portable devices. Because the increasing requirement of high-definition display devices, the gold bumping process has become more difficult and it is requested to be of high quality with very low fraction of defectives. Unfortunately, conventional methods for product acceptance determination no longer work because any sample of reasonable size probably contains no defective gold bump product items. In addition, in the globally competitive manufacturing environment, gold bumping processes involving multiple manufacturing lines are quite common in the Science-Based Industrial Park in Hsinchu, Taiwan, because of economic scale considerations. In this paper, we provide analytical solutions to gold bump product acceptance determination, which provide both manufacturers and customers to reserve their own rights by compromising on a rule for gold bumping process with multiple manufacturing lines. For the convenience of inplant applications, we tabulate the number of required inspection units, the critical acceptance values for various manufacturer's risks and consumer's risks, and various number of manufacturing lines. For illustration purpose, a real application in a gold bumping factory, which is located in the Science-Based Industrial Park in Hsinchu, Taiwan, is included.
Capability Assessment for Weibull In-Cell Touch Panel Manufacturing Processes With Variance Change
(2014-05-01)
Tai, Yu-Ting
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Pearn, Wen Lea
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Huang, Kai-Bin
;
Liao, Lu-Wei
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工業工程與管理學系
Since touch panels can provide natural user-interface, including fluent multipoint touch or advance gesture recognition, recently they have been extensively applied in various portable devices, such as smart phones and tablet PCs. In-cell touch panel is the highest integration touch technology as compared to the on-cell and typical touch panel manufacturing technologies for the thinnest and lightest structure. In in-cell manufacturing processes, manufacturing yield assessment is an essential issue. However, inevitable process variance changes could arise from equipment, material, and operation, and may not be detected within a short time. In addition, the process output usually has a Weibull distribution. To circumvent the undetected variance change causing the inaccurate manufacturing yield calculation, we provide a yield measure index to avoid overestimating when the underlying distribution is Weibull with variance change. We also show that the accommodation of the process capability index would not be affected by the scale parameter of Weibull distribution. Applying this method, the magnitudes of the undetected variance change are incorporated into the evaluation of manufacturing yield. For illustration purposes, a real application in an in-cell manufacturing factory, which is located in the Science-based Industrial Park in Hsinchu, Taiwan, is presented.
Estimating process capability index C-pk: classical approach versus Bayesian approach
(2015-07-03)
Pearn, Wen Lea
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Wu, Chin Chieh
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Wu, Chia Huang
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統計學研究所
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工業工程與管理學系
Process capability index C-pk has been the most popular one used in the manufacturing industry dealing with problems of measuring reproduction capability of processes to enhance product development with very low fraction of defectives. In the manufacturing industry, lower confidence bound (LCB) estimates the minimum process capability providing pivotal information for quality engineers to monitoring the process and assessing process performance for quality assurance. The main objective of this paper is to compare and contrast the LCBs on C-pk using two approaches, Classical method and Bayesian method.
Group selection for production yield among k manufacturing lines
(2011-04-01)
Lin, Chen-ju
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Pearn, Wen Lea
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工業工程與管理學系
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Department of Industrial Engineering and Management
Producing qualified items or products is essential to meet the requirement preset by customers. Evaluation and selection of desired manufacturing lines become challenging tasks for decision makers. Production yield is one of the important factors in measuring production performance. The goal of this paper is to screen a group of manufacturing lines and identify the best one with the highest yield. For the production lines with extremely low fraction of defectives, the yield index, S(pk), is an efficient indicator for quality level. This paper considers the production selection problem by using S(pk) to compare k (k > 2) manufacturing lines. A subset is constructed to contain the production lines with the highest yield. A systematic approach of test order k compares selected pairs of manufacturing lines along with the Bonferroni method is proposed to solve this problem. Each pair of production yields is compared by taking ratio. The paper provides critical values and required sample sizes of the group selection procedure. An application example on evaluating four power inductor productions is presented to illustrate the practicality of the proposed approach. (C) 2010 Elsevier B.V. All rights reserved.
Lower confidence bounds as precision measure for truncated processes
(2017)
Wu, Chia Huang
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Pearn, Wen Lea
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Tai, Yu Ting
;
Lin, Pi Chuan
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工業工程與管理學系
Process capability index C-p has been the most popular one used in the manufacturing industry to provide numerical measures on process precision. For normally distributed processes with automatic fully inspections, the inspected processes follow truncated normal distributions. In this article, we provide the formulae of moments used for the Edgeworth approximation on the precision measurement C-p for truncated normally distributed processes. Based on the developed moments, lower confidence bounds with various sample sizes and confidence levels are provided and tabulated. Consequently, practitioners can use lower confidence bounds to determine whether their manufacturing processes are capable of preset precision requirements.
Measuring production performance of different product mixes in semiconductor fabrication
(2006-03-01)
Chung, Shu-Hsing
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Pearn, Wen Lea
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Lee, Amy H. I.
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工業工程與管理學系
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Department of Industrial Engineering and Management
In a competitive market, a company needs to fully utilize its current capacity in order to acquire higher profit. The purpose of this paper is to present an effective approach to find a set of product mix efficient for the company to achieve the optimal production. Simulation is first used to generate the data of performance measures of different product mixes in a semiconductor fabricator. Data Envelopment Analysis (DEA) is applied next to measure multiple inputs and outputs, without pre-assigning weights, for product mixes, and an efficiency score for producing each product mix relative to other mixes can be obtained. The results provide guidance for a fab in accepting orders when its capacity cannot fully satisfy all the product demand. Significance: This paper applied the DEA method to evaluate the production performance with different product mixes in a semiconductor fabricator. The results provide guidance to the fabricator regarding accepting orders to maximize the production efficiency and the profit, while considering several other important input and output factors that maintain production smoothing.
Multi-server retrial queue with second optional service: algorithmic computation and optimisation
(2011)
Ke, Jau-Chuan
;
Wu, Chia-Huang
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
We consider an infinite-capacity M/M/c retrial queue with second optional service (SOS) channel. An arriving customer finds a free server would enter the service (namely, the first essential service, denoted by FES) immediately; otherwise, the customer enters into an orbit and starts generating requests for service in an exponentially distributed time interval until he finds a free server and begins receiving service. After the completion of FES, only some of them receive SOS. The retrial system is modelled by a quasi-birth-and-death process and some system performance measures are derived. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix-analytic approach. A cost model is derived to determine the optimal values of the number of servers and the two different service rates simultaneously at the minimal total expected cost per unit time. Illustrative numerical examples demonstrate the optimisation approach as well as the effect of various parameters on system performance measures.
Optimal control of the N policy M/G/1 queueing system with server breakdowns and general startup times
(2007-10-01)
Wang, Kuo-Hsiung
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Wang, Tsung-Yin
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Pearn, Wen Lea
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工業工程與管理學系
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Department of Industrial Engineering and Management
This paper deals with an N policy M/G/1 queueing system with a single removable and unreliable server whose arrivals form a Poisson process. Service times, repair times, and startup times are assumed to be generally distributed. When the queue length reaches N(N >= 1), the server is immediately turned on but is temporarily unavailable to serve the waiting customers. The server needs a startup time before providing service until there are no customers in the system. We analyze various system performance measures and investigate some designated known expected cost function per unit time to determine the optimal threshold N at a minimum cost. Sensitivity analysis is also studied. (c) 2006 Elsevier Inc. All rights reserved.
Optimal randomized control policy of an unreliable server system with second optional service and startup
(2008)
Yang, Dong-Yuh
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Wang, Kuo-Hsiung
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Ke, Jau-Chuan
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Pearn, Wen Lea
;
工業工程與管理學系
Purpose - To study the optimization of a randomized control problem in an M/G/1 queue in which a removable and unreliable server may provide two phases of heterogeneous service to arriving customers. Design/methodology/approach - Arriving customers follow a Poisson process and require the first essential service (FES). As soon as FES of a customer is completed, the customer may leave the system or opt for the second optional service (SOS). The service times of FES channel and SOS channel are assumed to be general distribution functions. The server requires a startup time with random length before starting service. When the server is working, he may meet unpredictable breakdowns but is immediately repaired. The inter-breakdown time and repair time of the removable server are exponentially random variable and generally random variable, respectively. By the convex combination property and the renewal reward theorem, several system performances are obtained. A cost model is developed to search the optimal two-threshold policy at a minimum cost. Sensitivity analysis is performed. Findings - Expressions for various system performances are derived. Sensitivity analysis of optimal randomized control policy (based on the developed expected cost function) with respect to system parameters is investigated. Originality/value - It is the first time that analytic results of sensitivity analysis of optimal randomized control policy for the complex system have been obtained which is quite useful and significant for engineers.
Optimization of the T policy M/G/1 queue with server breakdowns and general startup times
(2009-06-01)
Wang, Tsung-Yin
;
Wang, Kuo-Hsiung
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper investigates the T policy M/G/1 queue with server breakdowns, and startup times. Customers arrive at the system according to a Poisson process. Service times, repair times, and startup times are assumed to be generally distributed. The server is turned on after a fixed length of time T repeatedly until at least one customer is present in the waiting line. The server needs a startup time before starting the service. We analyze various system performance measures and develop the total expected cost function per unit time in which T is a decision variable. We determine the optimum threshold T* and derive analytical results for sensitivity investigations. The sensitivity analysis is particularly valuable to the system analyst when evaluating future conditions. We also present extensive numerical computation for illustration purpose. (c) 2008 Elsevier B.V. All rights reserved.
Product selection for newsboy-type products with normal demands and unequal costs
(2011-08-01)
Su, Rung Hung
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Pearn, Wen Lea
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工業工程與管理學系
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Department of Industrial Engineering and Management
In this paper, we consider two newsboy-type products with unequal prices and costs. Both demands are independent and follow normal distributions with unknown parameters it and a. We study the product selection problem which deals with comparing two products and selecting the one that has a significantly higher profitability, in which the profitability is defined to the probability of achieving a target profit under the optimal ordering policy. The statistical hypothesis testing methodology is performed to tackle this selection problem. Critical value of the test is calculated to determine the selection decision. Sample size required for a designated power and confidence level is also investigated. An application example on comparing English-teaching magazines is presented to illustrate the practicality of our approach. (C) 2011 Elsevier B.V. All rights reserved.
RANDOMIZED POLICY OF A POISSON INPUT QUEUE WITH J VACATIONS
(2010-03-01)
Ke, Jau-Chuan
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Huang, Kai-Bin
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Pearn, Wen Lea
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工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper studies the operating characteristics of an M/G/1 queuing system with a randomized control policy and at most J vacations. After all the customers are served in the queue exhaustively, the server immediately takes at most J vacations repeatedly until at least N customers are waiting for service in the queue upon returning from a vacation. If the number of arrivals does not reach N by the end of the J(th) vacation, the server remains idle in the system until the number of arrivals in the queue reaches N. If the number of customers in the queue is exactly accumulated N since the server remains idle or returns from vacation, the server is activated for services with probability p and deactivated with probability (1-p). For such variant vacation model, other important system characteristics are derived, such as the expected number of customers, the expected length of the busy and idle period, and etc. Following the construction of the expected cost function per unit time, an efficient and fast procedure is developed for searching the joint optimum thresholds (N*, J*) that minimize the cost function. Some numerical examples are also presented.
The performance measures and randomized optimization for an unreliable server M([x])/G/1 vacation system
(2011-07-01)
Ke, Jau-Chuan
;
Huang, Kai-Bin
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper examines an M([x])/G/1 queueing system with a randomized vacation policy and at most J vacations. Whenever the system is empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be immediately activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 - p. This pattern continues until the number of vacations taken reaches J. If the system is empty by the end of the Jth vacation, the server becomes idle in the system. Whenever one or more customers arrive at server idle state, the server immediately starts providing service for the arrivals. Assume that the server may meet an unpredictable breakdown according to a Poisson process and the repair time has a general distribution. For such a system, we derive the distributions of important system characteristics, such as system size distribution at a random epoch and at a departure epoch, system size distribution at busy period initiation epoch, the distributions of idle period, busy period, etc. Finally, a cost model is developed to determine the joint suitable parameters (p*,J*) at a minimum cost, and some numerical examples are presented for illustrative purpose. (C) 2011 Elsevier Inc. All rights reserved.
The performance measures and randomized optimization for an unreliable server M-[x]/G/1 vacation system
(2011-07-01)
Ke, Jau-Chuan
;
Huang, Kai-Bin
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper examines an M-[x]/G/1 queueing system with a randomized vacation policy and at most J vacations. Whenever the system is empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be immediately activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 - p. This pattern continues until the number of vacations taken reaches J. If the system is empty by the end of the Jth vacation, the server becomes idle in the system. Whenever one or more customers arrive at server idle state, the server immediately starts providing service for the arrivals. Assume that the server may meet an unpredictable breakdown according to a Poisson process and the repair time has a general distribution. For such a system, we derive the distributions of important system characteristics, such as system size distribution at a random epoch and at a departure epoch, system size distribution at busy period initiation epoch, the distributions of idle period, busy period, etc. Finally, a cost model is developed to determine the joint suitable parameters (p*,J*) at a minimum cost, and some numerical examples are presented for illustrative purpose. (C) 2011 Elsevier Inc. All rights reserved.
The randomized vacation policy for a batch arrival queue
(2010-06-01)
Ke, Jau-Chuan
;
Huang, Kai-Bin
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper examines an M([x])/G/1 queueing system with a randomized vacation policy and at most J vacations. Whenever the system is empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be immediately activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 - p. This pattern continues until the number of vacations taken reaches J. If the system is empty by the end of the Jth vacation, the server is dormant idly in the system. If there is one or more customers arrive at server idle state, the server immediately starts his services for the arrivals. For such a system, we derive the distributions of important characteristics, such as system size distribution at a random epoch and at a departure epoch, system size distribution at busy period initiation epoch, idle period and busy period, etc. Finally, a cost model is developed to determine the joint suitable parameters (p*, J*) at a minimum cost, and some numerical examples are presented for illustrative purpose. (C) 2009 Elsevier Inc. All rights reserved.