Saddam Akber Abbasi

On Proper Choice of Variability Control Chart for Normal and Non-normal Processes

Control charts are an important statistical process control tool used to monitor changes in process location and variability. This study addresses issues regarding the proper choice of control chart for efficient monitoring of process variability. The choice of the best estimator to be used for variability charts has not been made clear in literature. We have analyzed the performance of eight control chart structures, based on different estimates of process standard deviation. The performance of control charts is investigated under the existence and violation of ideal assumptions of normality. Control chart constants and factors required for computing probability limits, considering normal and different non-normal parent distributions, are provided for all variability charts. This study aims at providing guidance to quality practitioners in choosing the appropriate variability control chart for normal and non-normal processes. Copyright

On efficient median control charting

In most manufacturing processes, we face sudden outliers, and in such situations, median control charts are more outliers-resistant than mean control charts. In ideal circumstances, a median chart presents less efficiency than a mean chart. In order to overcome the efficiency loss in uncontaminated environments by maintaining its resistance ability in contaminated environments, we have suggested an auxiliary information–based set of median type control charts using the coefficient of variation and coefficient of kurtosis of auxiliary characteristics for efficient process monitoring. The performances of these control charts are evaluated in terms of average run length (ARL) and extra quadratic loss (EQL) under the univariate, bivariate, and trivariate normally distributed process environments. The effects of contaminated environments are also examined on the ARL performance of different median-based charting structures. The illustrative examples concerning median type control structures are also provided for procedural details.

MDEWMA chart: an efficient and robust alternative to monitor process dispersion

Control chart is the most important statistical process control tool used to monitor changes in process location and dispersion. In this study, an EWMA control chart is proposed for efficient and robust monitoring of process dispersion. The proposed chart, namely the MDEWMA chart, is based on estimating the process standard deviation (σ) using the mean absolute deviations (MD), taken from the sample median. The performance of the proposed chart has been compared with the EWMASR chart (a dispersion EWMA chart based on sample range) and MD chart (a Shewhart-type dispersion chart based on MD), under the existence and violation of normality assumption. It has been observed that the proposed MDEWMA chart is more efficient and robust when compared with both EWMASR and MD charts in terms of run length (RL) characteristics such as average RL, median RL and standard deviation of the RL distribution.

On the Performance of EWMA Chart in the Presence of Two-Component Measurement Error

ABSTRACT Control charts are extensively used to monitor the stability of analytical processes. The presence of measurement error can seriously affect the outcome of any process and reduces the ability of control charts to detect a shift of a particular magnitude in the process parameters. Research has shown the superiority of exponentially weighted moving average (EWMA) control charts over Shewhart charts when it comes to quick and timely detection of small process shifts. In this study I examine the performance of the EWMA control chart in the presence of two-component measurement error due to its immense importance in analytical chemistry and environmental settings. It has been shown that effect of measurement error can be reduced by taking multiple measurements at each sample point.

Enhancing the performance of CUSUM scale chart

Control charts act as the most important statistical process monitoring tool, widely used for the purpose of identifying unusual variations in process parameters. Researchers have implemented different rules to increase the sensitivity of Shewhart, CUSUM and EWMA control charts for the detection of small shifts in process location. However, for the monitoring of process scale, the use of such rules has been limited to Shewhart charts. This study proposes the implementation of sensitizing rules in CUSUM scale charts to enhance their ability to detect smaller changes in process variability. The performance of the proposed schemes is evaluated and compared with the simple scale CUSUM scheme, the EWMS chart, the M-EWMS chart and the COMB chart, in terms of run length characteristics such as average run length (ARL) and standard deviation of the run length distribution (SDRL). Control chart coefficients to set the ARL at the desired level are also provided. Two numerical examples are given to illustrate the application of the proposed schemes on practical data sets.

On the Performance of Auxiliary‐based Control Charting under Normality and Nonnormality with Estimation Effects

Process monitoring through control charts is a quite popular practice in statistical process control. From a statistical point of view, a superior control chart is the one which has an efficient design structure, for the case of both known and unknown parameters. There are auxiliary information–based location charts for an improved monitoring of process mean level. These charting structures have some limitations like assuming normality, the parameters to be known and focusing mainly on phase I monitoring. In many practical situations, nonnormal process behaviors are more frequent. Information about process parameters is not available, and we have to rely on the limited data available from the process to establish the limits in phase I and then use them in phase II monitoring. To have a compromise between the statistical and the practical purposes, a natural desire is to have a control chart that can serve both the concerns efficiently. This study is planned for the same objective focusing the auxiliary-based Shewharts control charts for location parameter. We have investigated the properties of the design structures of different location charts based on some already used and some new estimators with known and unknown parameters for normal and nonnormally distributed processes. By evaluating the performance of different charting structures in terms of power and run length properties in phase I and phase II, we have identified those more capable of making a good compromise between the abovementioned purposes in terms of statistical efficiency and practical desires. Copyright

On efficient use of auxiliary information for control charting in SPC

In Statistical Process Control (SPC), monitoring of the process dispersion has a major impact on the performance of processes like manufacturing, management and services. Control charts act as the most important SPC tool, used to differentiate between common and special cause variations in the process. The use of auxiliary information can enhance the detection ability of control charts and hence an efficient monitoring of process parameter(s) can be done. This study deals with the Shewhart type variability control charts based on auxiliary characteristics for the non-cascading processes, assuming stability of auxiliary parameters. The control chart structures of these variability charts are provided and their performance evaluations are carried out in terms of average run length (ARL), relative average run length (RARL) and extra quadratic loss (EQL) under the normal and t distributed process environments. The comparisons have been made among different variability charts and superiorities are established based on their detection abilities for different amounts of shifts in process dispersion. An illustrative example is also provided in support of the theory, and finally the study ends with concluding remarks and suggestions for future research.

On median control charting under double sampling scheme

Standard Shewhart control charts are often based on the assumption that the observations follow a specific parametric distribution, such as the normal, and outlier-free samples are initially selected to construct control limits for future monitoring of process parameters, e.g., location, dispersion, etc. The median is a popular measure of location which is more robust than mean for heavily skewed distributions. In ideal circumstances (where all the underlying assumptions such as normality and independence are met), the median chart is shown to be less efficient that the mean chart. To overcome the efficiency loss of the median chart, this study presents a set of auxiliary information-based median type Shewhart charts based on parent normal, t and gamma distributed process environments under double sampling scheme. The performance of these charts is evaluated in terms of run length (RL) characteristics such as: average run length (ARL), median run length (MDRL), standard deviation of the run length distribution (SDRL), extra quadratic loss (EQL) and relative ARL (RARL). Moreover, the effects of Step 1 sample size and contaminated environments are examined on the ARL performance of different median-based charting structures, under double sampling scheme. Illustrative examples are also provided to explain the working of the said charts. [Received 24 March 2012; Revised 21 October 2012; Revised 27 January 2013; Accepted 12 February 2013]

Nonparametric Progressive Mean Control Chart for Monitoring Process Target

Nonparametric control charts are widely used when the parametric distribution of the quality characteristic of interest is questionable. In this study, we proposed a nonparametric progressive mean control chart, namely the nonparametric progressive mean chart, for efficient detection of disturbances in process location or target. The proposed chart is compared with the recently proposed nonparametric exponentially weighted moving average and nonparametric cumulative sum charts using different run length characteristics such as the average run length, standard deviation of the run length, and the percentile points of the run length distribution. The comparisons revealed that the proposed chart outperformed recent nonparametric exponentially weighted moving average and nonparametric cumulative sum charts, in terms of detecting the shifts in process target. A real life example concerning the fill heights of soft drink beverage bottles is also provided to illustrate the application of the proposed nonparametric control chart. Copyright

On Dual Use of Auxiliary Information for Efficient Monitoring

In this study, a new idea has been proposed in statistical process control by making dual use of auxiliary information, that is, for ranking as well as at the estimation stage. The control charts are proposed based on regression estimator in three basic ranked set schemes, that is, ranked-set sampling (RSS), median RSS, and extreme RSS. The power of detection is used as a performance measure for evaluation and comparison of control charts. Comparisons revealed that the newly proposed charts (making dual use of auxiliary information) performed significantly better compared with the existing location charts. An illustrative example is also provided for the application of the proposed charts. Copyright