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The Robust Economic Statistical Design of the Hotelling’s T^2 Chart Faraz, Alireza ; ; et al in Communications in Statistics : Theory & Methods (2016) Economic statistical designs aim at minimizing the cost of process monitoring when a specific scenario or a set of estimated process and cost parameters is given. However, in practical situations the ... [more ▼] Economic statistical designs aim at minimizing the cost of process monitoring when a specific scenario or a set of estimated process and cost parameters is given. However, in practical situations the process may be affected by more than one scenario which may lead to severe cost penalties for upsetting the true scenario. This paper presents the robust economic statistical design (RESD) of the T^2 chart to reduce the monetary losses when there are multiple distinct scenarios. The genetic algorithm optimization method is employed here to minimize the total expected monitoring cost across all distinct scenarios. Through two numerical examples the proposed method is illustrated. Simulation studies indicate that the robust economic statistical designs should be encouraged in practice. [less ▲] Detailed reference viewed: 68 (3 ULg)Monitoring supply chains with multivariate control charts: an economic-statistical design approach Heuchenne, Cédric ; Faraz, Alireza ; Scientific conference (2015, June 02) Detailed reference viewed: 17 (1 ULg)Characteristics of Economically Designed CUSUM and \bar{X} Control Charts ; ; Faraz, Alireza et al in Knoth, Sven; Schmid, Wolfgang (Eds.) Frontiers in Statistical Quality Control 11 (2015) In this paper we investigate the characteristics of economic control chart designs for both Shewhart (¯X ) and CUSUM control charts. Authors in the past have made some suggestions regarding the design of ... [more ▼] In this paper we investigate the characteristics of economic control chart designs for both Shewhart (¯X ) and CUSUM control charts. Authors in the past have made some suggestions regarding the design of these charts, where design is defined as finding the values of sample size, intersample interval and control limit (Shewhart chart) or control parameters (k and h) for the CUSUM chart. Here, we run a large number of experiments consisting of many configurations of the parameters and describe and model the results in terms of the actual economic designs. [less ▲] Detailed reference viewed: 15 (3 ULg)Shewhart Control Charts for Monitoring Reliability with Weibull Lifetimes Faraz, Alireza ; ; Heuchenne, Cédric in Quality and Reliability Engineering International (2015), 31 In this paper, we present Shewhart type Z ̅ and S2 control charts for monitoring individual or joint shifts in the scale and shape parameters of a Weibull distributed process. The advantage of this method ... [more ▼] In this paper, we present Shewhart type Z ̅ and S2 control charts for monitoring individual or joint shifts in the scale and shape parameters of a Weibull distributed process. The advantage of this method is its ease of use and flexibility for the case where the process distribution is Weibull, although the method can be applied to any distribution. We illustrate the performance of our method through simulation and the application through the use of an actual data set. Our results indicate that Z ̅ and S2 control charts perform well in detecting shifts in the scale and shape parameters. We also provide a guide that would enable a user to interpret out-of-control signals. [less ▲] Detailed reference viewed: 49 (2 ULg)Control Charts monitoring product’s loss to society ; Faraz, Alireza ; in Quality and Reliability Engineering International (2014), 30(8), 1393-1407 Taguchi introduced a new philosophy in quality control that accounts for the economic loss associated to process variation measured by deviations from the target value of a product quality characteristic ... [more ▼] Taguchi introduced a new philosophy in quality control that accounts for the economic loss associated to process variation measured by deviations from the target value of a product quality characteristic. The Taguchi loss function has been considered in the design of control charts only for the computation of costs associated with nonconformities. This paper considers sample statistics based on the Taguchi loss function as a means to implement Shewhart control charts monitoring both the deviation from the target and dispersion of normally distributed quality characteristics. The aim of this proposed control chart is to perform on-line quality control of a process by monitoring its quality loss cost performance over time. To compute the quality loss performance, we consider a nominal-the-best quality characteristic. The statistical performance of the proposed control charts has been evaluated and compared with that of widely used control charts. Implementing target costing philosophy by means of one of the proposed charts is also discussed. An example illustrates the Taguchi control chart in a practical implementation. [less ▲] Detailed reference viewed: 64 (25 ULg)Economic Statistical Design of the VP( X) ̅ Control Charts for Monitoring a Process under Non-normality ; Faraz, Alireza ; in International Journal of Production Research (2014), 53(14), 4218-4230 Recent studies proved that variable parameters (VP) X ̅ control charts not only detects process mean shifts quicker than the classical X ̅ control chart but also has better economic properties ... [more ▼] Recent studies proved that variable parameters (VP) X ̅ control charts not only detects process mean shifts quicker than the classical X ̅ control chart but also has better economic properties. Furthermore, like most papers in control chart design, the fundamental assumption is that process data are normally distributed. Nevertheless, process quality variables may not be normal in application. In this paper, we investigate the economic statistical design of the VP X ̅ control chart when the underlying process distribution is non-normal. We illustrate the design procedure and perform a sensitivity analysis on the process and cost parameters based upon the degrees of skewness and kurtosis of the population using an industrial application. [less ▲] Detailed reference viewed: 60 (12 ULg)The variable parameters T2 chart with run rules Faraz, Alireza ; ; Heuchenne, Cédric et al in Statistical Papers (2014), 55(4), 933-950 The Hotelling’s T2 control chart with variable parameters (VP T2) has been shown to have better statistical performance than other adaptive control schemes in detecting small to moderate process mean ... [more ▼] The Hotelling’s T2 control chart with variable parameters (VP T2) has been shown to have better statistical performance than other adaptive control schemes in detecting small to moderate process mean shifts. In this paper, we investigate the statistical performance of the VP T2 control chart coupled with run rules. We consider two well-known run rules schemes. Statistical performance is evaluated by using a Markov chain modeling the random shock mechanism of the monitored process. The in-control time interval of the process is assumed to follow an exponential distribution. A Genetic Algorithm has been designed to select the optimal chart design parameters. We provide an extensive numerical analysis indicating that the VP T2 control chart with run rules outperforms other charts for small sizes of the mean shift expressed through the Mahalanobis distance. [less ▲] Detailed reference viewed: 139 (14 ULg)Double Objective Economic Statistical Design of the VPT2 Control Chart: Wald’s identity approach Faraz, Alireza ; Heuchenne, Cédric ; et al in Journal of Statistical Computation & Simulation (2014), 84 Recent studies have shown that applying the control chart by using a variable parameters (VP) scheme yields more rapid detection of assignable causes than the classical method of taking fixed sample sizes ... [more ▼] Recent studies have shown that applying the control chart by using a variable parameters (VP) scheme yields more rapid detection of assignable causes than the classical method of taking fixed sample sizes at fixed intervals of time. In this paper, the problem of economical statistical design of the VP T2 control chart is considered as a double-objective minimization problem with the statistical objective adjusted average time to signal and the economic objective expected cost per hour. Then we strive to find the Pareto-optimal designs in which the two objectives are met simultaneously by using a multi-objective Genetic Algorithm or GA. Through an illustrative example, we show that relatively large benefits accrue to the VP method relative to the classical policy; further another advantage of our approach is to provide a list of alternative solutions that can be explored graphically. This then ensures flexibility and adaptability, an important attribute of contemporary control chart design. [less ▲] Detailed reference viewed: 68 (10 ULg)Characteristics of Economically Designed CUSUM and \bar{X} Control Charts ; ; Faraz, Alireza et al Conference (2013, August 22) In this paper we investigate the characteristics of economic control chart designs for both Shewhart (¯X ) and CUSUM control charts. Authors in the past have made some suggestions regarding the design of ... [more ▼] In this paper we investigate the characteristics of economic control chart designs for both Shewhart (¯X ) and CUSUM control charts. Authors in the past have made some suggestions regarding the design of these charts, where design is defined as finding the values of sample size, intersample interval and control limit (Shewhart chart) or control parameters (k and h) for the CUSUM chart. Here, we run a large number of experiments consisting of many configurations of the parameters and describe and model the results in terms of the actual economic designs. [less ▲] Detailed reference viewed: 14 (1 ULg)Double-objective Economic Statistical Design of the Adaptive T2 Control Charts Faraz, Alireza ; Heuchenne, Cédric ; et al Conference (2013, July 09) Detailed reference viewed: 30 (4 ULg)Monitoring delivery chains using multivariate control charts Faraz, Alireza ; Heuchenne, Cédric ; et al in European Journal of Operational Research (2013), 228(1), 282289 Delivery chains are concerned with the delivery of goods and services to customers within a specific time interval; this time constraint is added to the usual consumer demand for product or service ... [more ▼] Delivery chains are concerned with the delivery of goods and services to customers within a specific time interval; this time constraint is added to the usual consumer demand for product or service quality. In this context, we address the idea of using process control tools to monitor this key variable of delivery time. In applications, there are usually several production and delivery sites and a variety of different ways to transport, treat and provide goods and services; that makes the problem multivariate in nature. We therefore propose to control the process using multivariate T2 control charts economically designed with the addition of statistical constraints, a design method called economic-statistical design. We illustrate the application in general through an illustrative example. [less ▲] Detailed reference viewed: 145 (31 ULg)Multiobjective Genetic Algorithm Approach to the Economic Statistical Design of Control Charts with an application to Xbar and S2 charts Faraz, Alireza ; in Quality and Reliability Engineering International (2013), 29(3), 407-415 Control charts are the primary tools of statistical process control. These charts may be designed by using a simple rule suggested by Shewhart, by a statistical criterion, an economic criterion or a joint ... [more ▼] Control charts are the primary tools of statistical process control. These charts may be designed by using a simple rule suggested by Shewhart, by a statistical criterion, an economic criterion or a joint economic-statistical criterion. Each method has its strengths and weaknesses. One weakness of the methods of design listed above is their lack of flexibility and adaptability, a primary objective of practical mathematical models. In this paper, we explore multi objective models as an alternative for the methods listed above. These provide a set of optimal solutions rather than a single optimal solution and thus allow the user to tailor their solution to the temporal imperative of a specific industrial situation. We present a solution to a well known industrial problem and compare optimal multi objective designs to economic designs, statistical designs, economic statistical designs and heuristic designs. [less ▲] Detailed reference viewed: 85 (13 ULg)Optimal T2 control chart with double sampling scheme - an alternative to the MEWMA chart Faraz, Alireza ; Heuchenne, Cédric ; in Quality and Reliability Engineering International (2012), 28(7), 751-760 Recent studies have shown that the double sampling (DS) scheme yields rapid detection of out of control situations, but the economic consequences of applying the proposed method are not discussed in the ... [more ▼] Recent studies have shown that the double sampling (DS) scheme yields rapid detection of out of control situations, but the economic consequences of applying the proposed method are not discussed in the literature yet. In this paper, the economic statistical design of the DS T2 control chart is designed to address this issue. In this regard, upon the Lorenzen and Vance (1986)’s economic model, the problem is formulized and then the cost function is minimized using the genetic algorithm search method to obtain the optimal design parameters. Besides, we assumed that the length of the time that process remains in control is exponentially distributed. Through an illustrative example we show that by applying the proposed method relatively large benefits can be achieved in a comparison with the classical T2 and the statistical DS T2 charts. Furthermore the performance of the ESD DS T2 charts is compared to the MEWMA and other variable ratio sampling (VRS) T2 control charts in the literature. [less ▲] Detailed reference viewed: 80 (23 ULg)The Economic and Statistical Designs of Control charts for Censored and Non-Normal Data Faraz, Alireza ; Heuchenne, Cédric ; et al Scientific conference (2011, December) In this research, we are dealing with constructing the statistical design (SD) and economic statistical design (ESD) of Shewhart and CUSUM control charts for reliability data which are right censored ... [more ▼] In this research, we are dealing with constructing the statistical design (SD) and economic statistical design (ESD) of Shewhart and CUSUM control charts for reliability data which are right censored. This is the case which happens more frequently in the field. [less ▲] Detailed reference viewed: 39 (1 ULg)A unification and some corrections to Markov chain approaches to develop variable ratio sampling scheme control charts Faraz, Alireza ; in Statistical Papers (2011), 52(4), 799-811 We provide some unifying definitions, make some corrections to articles by Faraz and Parsian (J Stat Pap 47:569–593, 2006) and Costa (JQual Technol 26:155– 163, 1994; 29:197–204, 1997), and using these ... [more ▼] We provide some unifying definitions, make some corrections to articles by Faraz and Parsian (J Stat Pap 47:569–593, 2006) and Costa (JQual Technol 26:155– 163, 1994; 29:197–204, 1997), and using these provide more accurate tables of results and comparisons of control charts. We also investigate the impact of an incorrectly specified process shift on signal frequency. [less ▲] Detailed reference viewed: 25 (7 ULg)Monitoring delivery chains in a supply chain using multivariate control charts Faraz, Alireza ; Heuchenne, Cédric ; et al Conference (2011, July 13) The theory of the delivery chain considers the delivery of goods and services to customers within a specific time interval. Nowadays, organizations are focusing to satisfy their customers’ demands not ... [more ▼] The theory of the delivery chain considers the delivery of goods and services to customers within a specific time interval. Nowadays, organizations are focusing to satisfy their customers’ demands not only to meet the expectations for products quality but also in delivery times through managing delivery chains. Obviously it is desirable that a company has minimum delivery time of goods and services to its customers. Therefore, establishing economic and reliable control charts for monitoring the key characteristics of delivery chain is of great importance especially for managers to improve the whole delivery chains performance. On the other hand, as we shall see in the present paper, the performance of a delivery chain is multivariate in nature because customers do not evaluate a delivery performance with a univariate mindset and also there are usually several production and delivery sites, and variety of different methods of transportation of goods and services. In this paper, we propose a relatively new application of the economic statistical design of the multivariate T2 control chart to monitor the delivery chain performance and it is illustrated through a case study in the TNT express mail in Iran. [less ▲] Detailed reference viewed: 56 (8 ULg)Economic Statistical Design of a T2 Control Chart with Double Warning Lines Faraz, Alireza ; in Quality and Reliability Engineering International (2011), 27(2), 125-139 Recent studies have shown that enhancing the common T2 control chart by using variable sample sizes (VSS) and variable sample intervals (VSI) sampling policies with a double warning line scheme (DWL ... [more ▼] Recent studies have shown that enhancing the common T2 control chart by using variable sample sizes (VSS) and variable sample intervals (VSI) sampling policies with a double warning line scheme (DWL) yields improvements in shift detection times over either pure VSI or VSS schemes in detecting almost all shifts in the process mean. In this paper, we look at this problem from an economical perspective, certainly at least as an important criterion as shift detection time if one considers what occurs in the industry today. Our method is to first construct a cost model to find the economic statistical design (ESD) of the DWL T2 control chart using the general model of Lorenzen and Vance (Technometrics 1986; 28:3–11). Subsequently, we find the values of the chart parameters which minimize the cost model using a genetic algorithm optimization method. Cost comparisons of Fixed ratio sampling, VSI, VSS, VSIVSS with DWL, and multivariate exponentially weighted moving average (MEWMA) charts are made, which indicate the economic efficacy of using either VSIVSS with DWL or MEWMA charts in practice if cost minimization is of interest to the control chart user. [less ▲] Detailed reference viewed: 50 (12 ULg)Economic and Economical Statistical Design of Hotelling’s T2 Control Chart with Two-State Adaptive Sample Size Faraz, Alireza ; ; in Journal of Statistical Computation & Simulation (2010), 80(12), 12991316 The Hotelling’s T 2 control chart, a direct analogue of the univariate Shewhart ¯X chart, is perhaps the most commonly used tool in industry for simultaneous monitoring of several quality characteristics ... [more ▼] The Hotelling’s T 2 control chart, a direct analogue of the univariate Shewhart ¯X chart, is perhaps the most commonly used tool in industry for simultaneous monitoring of several quality characteristics. Recent studies have shown that using variable sampling size (VSS) schemes results in charts with more statistical power when detecting small to moderate shifts in the process mean vector. In this paper, we build a cost model of a VSS T 2 control chart for the economic and economic statistical design using the general model of Lorenzen and Vance [The economic design of control charts: A unified approach, Technometrics 28 (1986), pp. 3–11].We optimize this model using a genetic algorithm approach.We also study the effects of the costs and operating parameters on theVSS T 2 parameters, and show, through an example, the advantage of economic design over statistical design forVSS T 2 charts, and measure the economic advantage of VSS sampling versus fixed sample size sampling. [less ▲] Detailed reference viewed: 78 (4 ULg)The Optimal Design of the VSI T2 Control Chart Faraz, Alireza ; ; Heuchenne, Cédric et al in Journal of Iranian Statistical Society (2010), 9(1), 1-19 Recent studies have shown that the variable sampling interval (VSI) scheme helps practitioners detect process shifts more quickly than the classical scheme (FRS). In this paper, the economically and ... [more ▼] Recent studies have shown that the variable sampling interval (VSI) scheme helps practitioners detect process shifts more quickly than the classical scheme (FRS). In this paper, the economically and statistically optimal design of the VSI T2 control chart for monitoring the process mean vector is investigated. The cost model proposed by Lorenzen and Vance (1986) is minimized through a genetic algorithm (GA) approach. Then the effects of the costs and operating parameters on the optimal design (OD) of the chart parameters and resulting operating loss through a fractional factorial design is systematically studied and finally, based on the ANOVA results, a Meta model to facilitate implementation in industry is proposed to determine the OD of the VSI T2 control chart parameters from the process and cost parameters [less ▲] Detailed reference viewed: 53 (9 ULg) |
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