M. A. Rahim

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Na'ama Pat-El

The University of Texas at Austin

Gabriel STOICIU

Romanian Academy of Science

Albert Bastardas-Boada

Universitat de Barcelona

Tatiana Nikitina

Centre National de la Recherche Scientifique / French National Centre for Scientific Research

Eitan Grossman

The Hebrew University of Jerusalem

Martin Haspelmath

Max Planck Institute for Evolutionary Anthropology

Alexander Lubotsky

Universiteit Leiden

Elsa Oréal

Centre National de la Recherche Scientifique / French National Centre for Scientific Research

Vít Boček

Academy of Sciences of the Czech Republic

Ambarish Khare

Tilak Maharashtra Vidyapeeth

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Papers by M. A. Rahim

The synthetic control chart based on two sample variances for monitoring the covariance matrix

Quality and Reliability Engineering International, 2009

Economic design of (X)over-bar and R charts under Weibull shock models

Monitoring the Coefficient of Variation Using a Variable Sampling Interval EWMA Chart

Journal of Quality Technology

In recent years, the coefficient of variation (CV) chart is receiving increasing attention in qua... more In recent years, the coefficient of variation (CV) chart is receiving increasing attention in quality control. A number of studies demonstrated that adaptive charts could detect process shifts faster than traditional charts. This paper proposes an EWMA chart with variable sampling interval (VSI) to monitor the CV. Formulas for computing the performance measures of the VSI EWMA-γ2 chart are derived using Markov chain, where γ2 denotes the CV squared. Comparative studies show that the VSI EWMA-γ2 chart significantly outperforms other competing charts. An example using real manufacturing data shows that the VSI EWMA-γ2 chart performs well in applications.

Effects of Measurement Error on Controlling Two Dependent Process Steps

Economic Quality Control, 2007

Imprecise measurements may seriously affect the efficiency of process control and production cost... more Imprecise measurements may seriously affect the efficiency of process control and production cost. For two dependent processes, the incoming quality variable in the first process may influence the outgoing quality variable in the second process. To effectively monitor and distinguish the state of the two dependent process steps with imprecise measurements, the EWMA control chart and cause-selecting control chart are constructed by taking account of the measurement errors. The EWMA control chart for imprecise measurements is constructed to monitor small shifts in the process mean on the first step, and the cause-selecting control chart for imprecise measurements, is constructed to monitor small shifts in the process mean in the second step. The effects of imprecise measurements on the performance of the two proposed control charts are examined for the case, where the mean of each process may be changed by the occurrence of a special cause. The performance of the proposed control charts is measured by the average run length. A sensitivity analysis indicates that a larger variation of imprecise measurements leads to a larger average run length for the out-of-control process and a larger average loss.

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Economic selection of optimal target values

Process Control and Quality, 2000

This paper considers economic models for the selection of target mean and variance of a process t... more This paper considers economic models for the selection of target mean and variance of a process that has both lower and upper specification limits. When the product quality characteristic falls within these limits, an item is classified as good, or non-defective. The problem of finding the target mean is solved by first making the assumption that variance is known for different conditions. The Taguchi loss function is then incorporated, and variance is optimized for minimum cost, based on the expected loss function which assumes the mean is on target. The paper suggests that the process is first optimized for the mean with a given variance, subsequently optimized for the variance with a given mean, and this process is repeated until their optimal values converge.

Economic Design of x̄-Control Charts under Weibull Shock Models

Technometrics, 1988

In this article, a moditied version of Duncan's (1956) model for the economic design of \-control... more In this article, a moditied version of Duncan's (1956) model for the economic design of \-control charts is extended to deal with situations involving the Weibull shock model. In the traditional Duncan approach to Markovian shock models, the length of sampling intervals is kept constant. When the process-failure mechanism follows a Weibull model or some other model having an increasing hazard rate. however, it may be desirable to have the frequency of sampling increased with the age of the system. This study proposes a cost model that uses variable sampling intervals as opposed to sampling intervals of fixed length. The computational results indicate that the proposed model under variable sampling intervals provides a lower cost than those obtained by using the existing model developed by Hu (1984) for a Welbull shock model having sampling intervals of fixed length.

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A generalized model for the economic design of ??control charts for production systems with increasing failure rate and early replacement

Naval Research Logistics, 1993

This article generalizes the model for the economic design of ?-control charts of Duncan [4], sta... more This article generalizes the model for the economic design of ?-control charts of Duncan [4], starting from the more recent papers of Lorenzen and Vance [8] and Banerjee and Rahim [3]. The classical model of Duncan [4] and its several extensions including the unified model of Lorenzen and Vance [8] assumed exponentially distributed in-control periods and provided uniform sampling schemes. Banerjee and Rahim [3], however, assumed a Weibull-distributed in-control period having an increasing failure rate and used variable sampling intervals. The present article is an extension of the work of Banerjee and Rahim [3], where a general distribution of in-control periods having an increasing failure rate is assumed and the possibility of age-dependent repair before failure is considered. Several different truncated and nontruncated probability models are chosen. It is proposed that economic benefits can be achieved by adopting a nonuniform inspection scheme and by truncating a production cycle when it attains a certain age. Numerical examples are presented to support this proposition. Finally, the effect of model specification in the choice of failure mechanism is investigated.

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Joint determination of production quantity, inspection schedule, and quality control for an imperfect process with deteriorating products

Journal of the Operational Research Society, 2001

In this paper, we study the simultaneous effects of both deteriorating product items and deterior... more

Multivariate extension to the economical design of control chart under Weibull shock model

Journal of Statistical Computation and Simulation, 2006

ABSTRACT This article is an extension of research conducted by Banerjee and Rahim in 1988. Their ... more ABSTRACT This article is an extension of research conducted by Banerjee and Rahim in 1988. Their general approach is now applied to a multivariate control chart instead of a univariate control chart. A cost model for the economic-statistical design of a Hotelling T 2 control chart is derived to deal with situations involving a Weibull shock model with an increasing failure rate. Application of the proposed T 2 control chart design is demonstrated through a numerical example. A sensitivity analysis of the model is performed.

Determination of an Optimal Setting and Production Run Using Taguchi's Loss Function

International Journal of Reliability, Quality and Safety Engineering, 1999

This paper considers the problem of selecting an optimal setting of the process mean and an optim... more This paper considers the problem of selecting an optimal setting of the process mean and an optimal production run for a continuous production process. The process is subject to gradual shifts in the process mean due to occurrences of some random shocks. The product output becomes nonconforming only when the process experiences a certain number of accumulated shocks. The changes in the process mean are assumed to follow a nonhomogeneous Poisson process. A quadratic loss function, which is a general form of Taguchi's loss function, is utilized for developing the economic model in determining an initial resetting process mean and an optimal production run. Some new results are derived and some interesting findings are reported.

A generalized economic model for joint determination of production run, inspection schedule and control chart design

International Journal of Production Research, 1998

... MA RAHIM² * and M. BEN-DAYA ... The model consists of the following cost components: (1) the ... more

Economic statistical process control for multivariate quality characteristics under Weibull shock model

International Journal of Production Economics, 2005

This paper is an extension of research conducted by Banerjee and Rahim (Technometrics 29(6) (1988... more This paper is an extension of research conducted by Banerjee and Rahim (Technometrics 29(6) (1988) 404). Their general approach is now applied to a multivariate control chart instead of a univariate control chart. A cost model for the economic statistical design of a Hotelling T2 control chart is derived to deal with situations involving a Weibull shock model with an

$Research paper thumbnail of An optimal production run for an imperfect production process with allowable shortages and time-varying fraction defective rate$

An optimal production run for an imperfect production process with allowable shortages and time-varying fraction defective rate

The International Journal of Advanced Manufacturing Technology, 2006

The effects of an imperfect production process on the optimal production run by assuming that an ... more The effects of an imperfect production process on the optimal production run by assuming that an elapsed time until the process shift is exponentially distributed have been studied. This problem was extended by assuming that the elapsed time until the process shift is arbitrarily distributed. The models, however, do not allow for shortages. This work has been generalized by assuming that shortages were allowed. The common assumption of all the above-mentioned models is that a fixed percentage of defective items are produced during the out-of-control period. This assumption may not be applicable in many industrial situations. Intuitively, the percentage of defective rate should increase with an increase in the duration of the out-of-control period. In fact, other research has considered an imperfect production process model with a variable rate of defective units produced when the process is in an out-of-control state. The defective rate is assumed to be a function of detection delay. The main purpose of this paper is to further generalize earlier work by introducing a time-varying percentage defective rate. This paper develops a model to determine the optimal production run for a deteriorating production system, with allowable shortages, and time-varying fraction defective rate. However, the elapsed time until the production process shift is assumed to be exponentially distributed. A unique optimal production run is found that minimizes the total expected cost. A numerical example is provided to illustrate the application of the model and to prove the convexity of the total cost function. A sensitivity analysis is also conducted to study the effects of various model parameters on the optimal production run and the total cost.

Joint Determination of Production Quantity, Inspection Schedule, and Control Chart Design

IIE Transactions, 1994

Abstract This paper presents a model for jointly determining an economic production quantity, ins... more

Optimal process levels for the joint control of variables and attributes

European Journal of Operational Research, 1990

Abstract This paper presents an economic model which incorporates the joint control of both varia... more Abstract This paper presents an economic model which incorporates the joint control of both variable and attribute quality characteristics of a product. Items are acceptable if they meet the specifications for both types of characteristics at the same time. Otherwise, the items are reprocessed or sold as scrap at a reduced price. A lot is acceptable if the number of rejected items does not exceed a given limit. The objective is to simultaneously select the appropriate target values for the characteristics, so as to maximize the expected income per lot. Optimality conditions are derived for various probability distributions of the number of defects in a lot and computational experience is reported.

An Investigation of Economic Design of -Charts to Control Non-Normal Process Means

Engineering Optimization, 1985

In this paper Duncan's model for the economic design of an X¯-control chart is generalized us... more In this paper Duncan's model for the economic design of an X¯-control chart is generalized using the Edgewarth approximation to the normal distribution. A single assignable cause process model is considered and its expected loss-cost function is presented. An improved version of the existing approximate analytical solution procedure to obtain the value of the design parameters (i.e., sample size n, sampling interval S. control limits coefficient k), is provided. Also, an oplimization technique based on Hooke and Jeeves's pattern search is developed and is employed on the loss-cost function to obtain the optimal design parameter values. Furthermore, a simplified scheme is proposed for selecting the design parameters so that the expected loss-cost is minimal for a specified level of consumer's risk. The proposed simplified scheme can be easily handled by a quality control practitioner at the workshop level.

Economically Optimal Design of a Multivariate Synthetic T 2 Chart

Communications in Statistics - Simulation and Computation, 2014

The accuracy of the Content should not be relied upon and should be independently verified with p... more The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &

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Joint determination of production quantity, inspection schedule, and quality control for an imperfect process with deteriorating products

Journal of the Operational Research Society, 2001

In this paper, we study the simultaneous effects of both deteriorating product items and deterior... more

Joint determination of production quantity, inspection schedule, and control chart design

IIE transactions, 1994

This paper presents a model for jointly determining an economic production quantity, inspection s... more

A generalized economic model for joint determination of production run, inspection schedule and control chart design

International Journal of Production Research, 1998

... MA RAHIM² * and M. BEN-DAYA ... The model consists of the following cost components: (1) the ... more

The synthetic control chart based on two sample variances for monitoring the covariance matrix

Quality and Reliability Engineering International, 2009

Economic design of (X)over-bar and R charts under Weibull shock models

Monitoring the Coefficient of Variation Using a Variable Sampling Interval EWMA Chart

Journal of Quality Technology

Effects of Measurement Error on Controlling Two Dependent Process Steps

Economic Quality Control, 2007

Download

Economic selection of optimal target values

Process Control and Quality, 2000

Economic Design of x̄-Control Charts under Weibull Shock Models

Technometrics, 1988

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A generalized model for the economic design of ??control charts for production systems with increasing failure rate and early replacement

Naval Research Logistics, 1993

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Joint determination of production quantity, inspection schedule, and quality control for an imperfect process with deteriorating products

Journal of the Operational Research Society, 2001

In this paper, we study the simultaneous effects of both deteriorating product items and deterior... more

Multivariate extension to the economical design of control chart under Weibull shock model

Journal of Statistical Computation and Simulation, 2006

Determination of an Optimal Setting and Production Run Using Taguchi's Loss Function

International Journal of Reliability, Quality and Safety Engineering, 1999

A generalized economic model for joint determination of production run, inspection schedule and control chart design

International Journal of Production Research, 1998

... MA RAHIM² * and M. BEN-DAYA ... The model consists of the following cost components: (1) the ... more

Economic statistical process control for multivariate quality characteristics under Weibull shock model

International Journal of Production Economics, 2005

$Research paper thumbnail of An optimal production run for an imperfect production process with allowable shortages and time-varying fraction defective rate$

An optimal production run for an imperfect production process with allowable shortages and time-varying fraction defective rate

The International Journal of Advanced Manufacturing Technology, 2006

Joint Determination of Production Quantity, Inspection Schedule, and Control Chart Design

IIE Transactions, 1994

Abstract This paper presents a model for jointly determining an economic production quantity, ins... more

Optimal process levels for the joint control of variables and attributes

European Journal of Operational Research, 1990

An Investigation of Economic Design of -Charts to Control Non-Normal Process Means

Engineering Optimization, 1985

Economically Optimal Design of a Multivariate Synthetic T 2 Chart

Communications in Statistics - Simulation and Computation, 2014

Download

Joint determination of production quantity, inspection schedule, and quality control for an imperfect process with deteriorating products

Journal of the Operational Research Society, 2001

In this paper, we study the simultaneous effects of both deteriorating product items and deterior... more

Joint determination of production quantity, inspection schedule, and control chart design

IIE transactions, 1994

This paper presents a model for jointly determining an economic production quantity, inspection s... more

A generalized economic model for joint determination of production run, inspection schedule and control chart design

International Journal of Production Research, 1998

... MA RAHIM² * and M. BEN-DAYA ... The model consists of the following cost components: (1) the ... more

M. A. Rahim

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