Distribution-free mixed GWMA-CUSUM and CUSUM-GWMA Mann–Whitney charts to monitor unknown shifts in the process location
TL;DR: The Mann-Whitney (MW) test as mentioned in this paper is one of the most important nonparametric tests used in the comparison of the location parameters of two populations, and it can be used when the t-test can not be used.
Abstract: The Mann–Whitney (MW) test is one of the most important nonparametric tests used in the comparison of the location parameters of two populations. Unlike the t-test, the MW test can be used when the...
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TL;DR: An overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided in this article, where a number of possible future GWMA-related schemes are documented and categorized in such a manner that it is easy to identify research gaps.
Abstract: An overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided. A GWMA scheme is an extended version of the exponentially weighted moving average (EWMA) scheme with an additional adjustment parameter that introduces more flexibility in the GWMA model as it adjusts the kurtosis of the weighting function so that the GWMA scheme can be designed such that it has an advantage over the corresponding EWMA scheme in the detection of certain shift values efficiently. The parametric and distribution-free GWMA schemes to monitor various quality characteristics and its existing enhanced versions (i.e. double GWMA, composite Shewhart-GWMA, mixed GWMA-CUSUM and mixed CUSUM-GWMA) have better performance than their corresponding EWMA counterparts in many situations; hence, all such existing research works discussing GWMA-related schemes (i.e. 61 publications in total) are documented and categorized in such a manner that it is easy to identify research gaps. Finally, a number of possible future research ideas are provided.
20 citations
TL;DR: Many extensions and modifications have been made to standard process monitoring methods such as the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart as mentioned in this paper , usually to put greater emphasis on past data and less weight on current and recent data.
Abstract: Many extensions and modifications have been made to standard process monitoring methods such as the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart. In addition, new schemes have been proposed based on alternative weighting of past data, usually to put greater emphasis on past data and less weight on current and recent data. In other cases, the output of one process monitoring method, such as the EWMA statistic, is used as the input to another method, such as the CUSUM chart. Often the recursive formula for a control chart statistic is itself used recursively to form a new control chart statistic. We find the use of these ad hoc methods to be unjustified. Statistical performance comparisons justifying the use of these methods have been either flawed by focusing only on zero-state run length metrics or by making comparisons to an unnecessarily weak competitor.
15 citations
TL;DR: From applying the proposed Tukey Moving Average-Exponentially Weighted Moving Average control chart to two sets of real data, the mine explosion period in the UK during 1875–1951 and data of diameter of the workpiece from an industrial factory, it was found that the MME-TCC was able to more quickly detect the change than the other control charts.
Abstract: Control charts are a type of statistical tool used to control a production process in order to obtain the quality products that can fulfill the demands of both the manufacturer and the consumers. In this paper, we propose the Tukey Moving Average-Exponentially Weighted Moving Average control chart (MME-TCC) to detect the change of average of the process with symmetric and asymmetric distribution and to compare the efficiency in detecting the change of the MME-TCC to the MA, MME, MEM, MA-TCC and MEM-TCC at the various change levels of the parameter. The criteria to measure the efficiency were average run length (ARL), standard deviation of run length (SDRL), and median run length (MRL) which evaluated by using Monte Carlo simulation (MC), The research results showed that the proposed control chart has the highest efficiency in detecting the change when the change level was at $-0.75\le \delta \le 0.75$ . However, if the change of parameter increased ( $\delta \ge 1.00$ ), the MME had more efficiency. In the case where the observation was logistic distributions, the MA-TCC had more efficiency to detect the change. Moreover, from applying the proposed control chart to two sets of real data, the mine explosion period in the UK during 1875–1951 and data of diameter of the workpiece from an industrial factory, it was found that the MME-TCC was able to more quickly detect the change than the other control charts.
9 citations
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Book•
01 Jan 1985
TL;DR: In this article, the authors present a survey of statistical process control and capability analysis techniques for improving the quality of a business process in the modern business environment, using a variety of techniques.
Abstract: Quality Improvement in the Modern Business Environment.STAISTICAL METHODS USEFUL IN QUALITY IMPROVEMENT.Modeling Process Quality.Inferences About Process Quality.BASIC METHODS OF STATISTICAL PROCESS CONTROL AND CAPABILITY ANALYSIS.Methods and Philosophy of Statistical Process Control.Control Charts for Variables.Control Charts for Attributes.Process and Measurement Systems System Capability Analysis.OTHER STATISTICAL PROCESS MONITORING AND CONTROL TECHNIQUES.Cumulative Sum and Exponentially Weighted Moving Average Control Charts.Other Univariate SPC Techniques.Multivariate Process Monitoring and Control.Engineering Process Control and SPC.PROCESS DESIGN AND IMPROVEMENT WITH DESIGNED EXPERIMENTS.Factorial and Fractional Factorial Designs for Process Design and Improvement.Process Optimization with Designed Experiments.ACCEPTANCE SAMPLING.Lot--by--Lot Acceptance Sampling for Attributes.Other Acceptance Sampling Techniques.Appendix.Bibliography.Answers to Selected Exercises.Index.
7,312 citations
4,805 citations
Journal Article•
TL;DR: The recognition that an EWMA control scheme can be represented as a Markov chain allows its properties to be evaluated more easily and completely than has previously been done.
1,624 citations
TL;DR: In this article, a graphical procedure for generating geometric moving averages is described in which the most recent observation is assigned a weight r, and all previous observations weights decreasing in geometric progression from the most recently back to the first.
Abstract: A geometrical moving average gives the most recent observation the greatest weight, and all previous observations weights decreasing in geometric progression from the most recent back to the first. A graphical procedure for generating geometric moving averages is described in which the most recent observation is assigned a weight r. The properties of control chart tests based on geometric moving averages are compared to tests based on ordinary moving averages.
1,490 citations