Economic design of EWMA control charts based on loss function

Cataloged from PDF version of article.For monitoring the stability of a process, various control charts based on exponentially weighted moving average (EWMA) statistics have been proposed in the literature. We study the economic design of EWMA-based mean and dispersion charts when a linear, quadratic, or exponential loss function is used for computing the costs arising from poor quality. The chart parameters (sample size, sampling interval, control limits and smoothing constant) minimizing the overall cost of the control scheme are determined via computational methods. Using numerical examples, we compare the performances of the EWMA charts with Shewhart X and S charts, and investigate the sensitivity of the chart parameters to changes in process parameters and loss functions. Numerical results imply that rather than sample size or control limits, the users need to adjust the sampling interval in response to changes in the cost of poor quality. © 2008 Elsevier Ltd. All rights reserved

Joint economic design of EWMA control charts for mean and variance

Cataloged from PDF version of article.Control charts with exponentially weighted moving average (EWMA) statistics (mean and variance) are used to jointly monitor the mean and variance of a process. An EWMA cost minimization model is presented to design the joint control scheme based on pure economic or both economic and statistical performance criteria. The pure economic model is extended to the economic-statistical design by adding constraints associated with in-control and out-of-control average run lengths. The quality related production costs are calculated using Taguchi's quadratic loss function. The optimal values of smoothing constants, sampling interval, sample size, and control chart limits are determined by using a numerical search method. The average run length of the control scheme is computed by using the Markov chain approach. Computational study indicates that optimal sample sizes decrease as the magnitudes of shifts in mean and/or variance increase, and higher values of quality loss coefficient lead to shorter sampling intervals. The sensitivity analysis results regarding the effects of various inputs on the chart parameters provide useful guidelines for designing an EWMA-based process control scheme when there exists an assignable cause generating concurrent changes in process mean and variance. (C) 2006 Elsevier B.V. All rights reserved

Stochastics and Statistics Joint economic design of EWMA control charts for mean and variance

Abstract Control charts with exponentially weighted moving average (EWMA) statistics (mean and variance) are used to jointly monitor the mean and variance of a process. An EWMA cost minimization model is presented to design the joint control scheme based on pure economic or both economic and statistical performance criteria. The pure economic model is extended to the economic-statistical design by adding constraints associated with in-control and out-of-control average run lengths. The quality related production costs are calculated using Taguchi's quadratic loss function. The optimal values of smoothing constants, sampling interval, sample size, and control chart limits are determined by using a numerical search method. The average run length of the control scheme is computed by using the Markov chain approach. Computational study indicates that optimal sample sizes decrease as the magnitudes of shifts in mean and/or variance increase, and higher values of quality loss coefficient lead to shorter sampling intervals. The sensitivity analysis results regarding the effects of various inputs on the chart parameters provide useful guidelines for designing an EWMA-based process control scheme when there exists an assignable cause generating concurrent changes in process mean and variance

Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

Control charts for monitoring the mean of AR(1) data

New product development is one of the most powerful but difficult activities in business. It is also a very important factor affecting final product quality. There are many techniques available for new product development. Experimental design is now regarded as one of the most significant techniques. In this article, we will discuss how to use the technique of experimental design in developing a new product - an extrusion press. In order to provide a better understanding of this specific process, a brief description of the extrusion press is presented. To ensure the successful development of the extrusion press, customer requirements and expectations were obtained by detailed market research. The critical and non-critical factors affecting the performance of the extrusion press were identified in preliminary experiments. Through conducting single factorial experiments, the critical factorial levels were determined. The relationships between the performance indexes of the extrusion press and the four critical factors were determined on the basis of multi-factorial experiments. The mathematical models for the performance of the extrusion press were established according to a central composite rotatable design. The best combination of the four critical factors and the optimum performance indexes were determined by optimum design. The results were verified by conducting a confirmatory experiment. Finally, a number of conclusions became evident.

A Model for Maintenance Planning and Process Quality Control Optimization Based on EWMA and CUSUM Control Charts

The performance of a production system is highly dependent on the smooth operation of various equipment and processes. Thus, reducing failures of the equipment and processes in a cost-effective manner improves overall performance; this is often achieved by carrying out maintenance and quality control policies. In this study, an integrated optimization method that addresses both maintenance strategies and quality control practices is proposed using an exponentially weighted moving average (EWMA) chart, in which both corrective and preventive maintenance policies are considered. The integrated model has been proposed to find optimal decision variables of both the process quality decision parameters and the optimal interval of preventive maintenance (i.e., Ns, Hs, L, λ, and t_PM) to result in overall optimal expected hourly total system costs. A case study is then utilized to investigate the impact of cost criteria on the proposed integrated model and to compare the proposed model with a model using the cumulative sum (CUSUM) control chart. The improved model outputs indicate that there is a reduction of 34.6% in the total expected costs compared with those of the other model using the CUSUM chart. Finally, an analysis of sensitivity to present the effectiveness of the model parameters and the main variables in the overall costs of the system is provided

On the constrained economic design of control charts: a literature review

The economic design is an appealing approach to settle the design parameters of a control chart. Unfortunately, the economic models to design control charts have been scarcely implemented by quality practitioners due to the simplifying assumptions when representing the multifaceted complexity and constraints present within manufacturing and transactional environments. Although there has been an increasing scepticism about the economic models usefulness in practice, some recent studies proposed in literature face the problem of the control charts economic design from a new point of view: the objective is to achieve a well balanced trade-off between the operational and the statistical aspects. Under this perspective, the economic design problem can be intended in a broader sense as the constrained design of a SPC inspection procedure. This paper presents a discussion of some recent trends in the economic design stream of research and outlines the importance of considering the constraints related to SPC resources availability and modelling the occurrence of random shifts

Optimizing the Cost of Integrated Model for Fuzzy Failure Weibull Distribution Using Genetic Algorithm

This research applies the fuzzy concept in development of an integrated model (Statistical process control and Maintenance management) with Weibull distribution for Exponentially Weighted Moving Average (EWMA) control chart. Since sample data may contain uncertainties coming from measurement systems and environment conditions, fuzzy number is used to inspect these suspicions. Moreover, the Weibull distribution with fuzzy scale parameters is considers, and the genetic algorithm approach is used to determine the optimal values of six variables that minimize the fuzzy hourly cost. Finally, the fuzzy hourly cost is transformed to crisp number by the centroid defuzzification.This research applies the fuzzy concept in development of an integrated model (Statistical process control and Maintenance management) with Weibull distribution for Exponentially Weighted Moving Average (EWMA) control chart. Since sample data may contain uncertainties coming from measurement systems and environment conditions, fuzzy number is used to inspect these suspicions. Moreover, the Weibull distribution with fuzzy scale parameters is considers, and the genetic algorithm approach is used to determine the optimal values of six variables that minimize the fuzzy hourly cost. Finally, the fuzzy hourly cost is transformed to crisp number by the centroid defuzzification