Hafiz Zafar Nazir

Robust CUSUM control charting

ABSTRACT Cumulative sum (CUSUM) control charts are very effective in detecting special causes. In general, the underlying distribution is supposed to be normal. In designing a CUSUM chart, it is important to know how the chart will respond to disturbances of normality. The focus of this article is to control the location parameter using a CUSUM structure and the major concern is to identify the CUSUM control charts that are of more practical value under different normal, non-normal, contaminated normal, and special cause contaminated parent scenarios. In this study, we propose and compare the performance of different CUSUM control charts for phase II monitoring of location, based on mean, median, midrange, Hodges-Lehmann, and trimean statistics. The average run length is used as the performance measure of the CUSUM control charts.

EWMA Dispersion Control Charts for Normal and Non-normal Processes

Process monitoring through control charts is a quite popular practice in statistical process control. This study is planned for monitoring the process dispersion parameter using exponentially weighted moving average (EWMA) control chart scheme. Most of the EWMA dispersion charts that have been proposed are based on the assumption that the parent distribution of the quality characteristic is normal, which is not always the case. In this study, we develop new EWMA charts based on a wide range of dispersion estimates for processes following normal and non-normal parent distributions. The performance of all the charts is evaluated and compared using run length characteristics (such as the average run length). Extra quadratic loss, relative average run length, and performance comparison index measures are also used to examine the overall effectiveness of the EWMA dispersion charts. Copyright

An Efficient Nonparametric EWMA Wilcoxon Signed‐Rank Chart for Monitoring Location

The statistical performance of traditional control charts for monitoring the process shifts is doubtful if the underlying process will not follow a normal distribution. So, in this situation, the use of a nonparametric control charts is considered to be an efficient alternative. In this paper, a nonparametric exponentially weighted moving average (EWMA) control chart is developed based on Wilcoxon signed-rank statistic using ranked set sampling. The average run length and some other associated characteristics were used as the performance evaluation of the proposed chart. A major advantage of the proposed nonparametric EWMA signed-rank chart is the robustness of its in-control run length distribution. Moreover, it has been observed that the proposed version of the EWMA signed-rank chart using ranked set sampling shows better detection ability than some of the competing counterparts including EWMA sign chart, EWMA signed-rank chart, and the usual EWMA control chart using simple random sampling scheme. An illustrative example is also provided for practical consideration. Copyright

Use of ranked set sampling in nonparametric control charts

Abstract Control charts are widely used to identify changes in a production process. Nonparametric or distribution-free charts can be useful when there is a lack of underlying process distribution. A nonparametric exponentially weighted moving average (EWMA) control chart based on sign test using ranked set sampling (RSS) is proposed to monitor the possible small shifts in the process mean. The performance of the proposed chart is evaluated in terms of average run length, median run length, and standard deviation of the run length distribution. It has been observed that the proposed version of the EWMA sign chart, using RSS shows better detection ability than that version of the EWMA sign chart and the parametric EWMA control chart using simple random sampling scheme. An application with real data-set is also provided to explain the proposal for practical considerations.

Quality Quandaries: How to Set Up a Robust Shewhart Control Chart for Dispersion?

In this article, the authors have outlined procedures to construct Phase I and Phase II standard deviation control charts.

Investigating the Impact of Ranked Set Sampling in Nonparametric CUSUM Control Charts

Nonparametric control charts can be useful as an alternative in practice to the data expert when there is a lack of knowledge about the underlying distribution. In this study, a nonparametric cumulative sum (CUSUM) sign control chart for monitoring and detecting possible deviation from the process mean using ranked set sampling is proposed. Ranked set sampling is an effective method when the observations are inexpensive, and measurements are perhaps destructive. The average run length is used as performance measure for the proposed nonparametric CUSUM sign chart. Simulation study shows that the proposed version of the CUSUM sign chart using ranked set sampling generally outperforms than that version of the nonparametric CUSUM sign chart and the parametric CUSUM control chart using simple random sampling scheme. An illustrative example is also provided for practical consideration. Copyright

Robust CUSUM control charting for process dispersion

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 one that has an efficient design structure, but having resistance against unusual situations is of more practical importance. To have a compromise between the statistical and practical purposes, a natural desire is to have a control chart that can serve both purposes simultaneously in a good capacity. This study is planned for the same objective focusing on monitoring the dispersion parameter by using a Cumulative Sum (CUSUM) control chart scheme. We investigate the properties of the design structure of different control charts based on some already existing estimators as well as some new robust dispersion estimators. By evaluating the performance of these estimators-based CUSUM control charts in terms of average run length, we identify those charts that are more capable to make a good compromise between the aforementioned purposes in terms of statistical and practical needs.

Quality Quandaries: A Stepwise Approach for Setting Up a Robust Shewhart Location Control Chart

The main purpose of the present column is to give practitioners a stepwise procedure on how to set up a robust location control chart.

A comparative study of memory-type control charts under normal and contaminated normal environments

Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are commonly used to detect small changes in the parameters of production processes. Recently, a new control structure was introduced, named as mixed EWMA–CUSUM control chart, which combined both charts. The current study provides a detailed comparison of these three types of control charts when the process parameters are unknown under normal and contaminated normal environments. Performance measures average run length and different percentiles of run length distribution are used for comparison purposes. We investigate six different location estimators with the structures of the three memory charts and study their robustness properties.

In-control robustness comparison of different control charts

Control charts are widely used to monitor the process parameters. Proper design structure and implementation of a control chart requires its in-control robustness, otherwise, its performance cannot be fairly observed. It is important to know whether a chart is sensitive to disturbances to the model (e.g. normality under which it is developed) or not. This study, explores the robustness of Mixed EWMA-CUSUM (MEC) control chart for location parameter under different non-normal and contaminated environments and compares it with its counterparts. The robustness of the MEC scheme and counterparts is evaluated by using the run length distributions, and for better assessment not only is in-control average run length (ARL) used, but also standard deviation of run length (SDRL) and different percentiles – that is, 5th, 50th and 95th– are considered. A careful insight is necessary in selection and application of control charts in non-normal and contaminated environments. It is observed that the in-control robustness performance of the MEC scheme is quite good in the case of normal, non-normal and contaminated normal distributions as compared with its competitor’s schemes.