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The X̄ Chart

The X̄ Chart

The x̄ chart is a statistical tool for monitoring the means in a process.
The x̄ chart, often known as the individual control chart, is a crucial tool in statistical process control. It is designed to monitor process behavior and performance over time and is widely used in various industries to ensure that processes are operating at their optimum capacity and within specified limits.
A x̄ chart is constructed by plotting individual measurements of a quality...

Interpreting X̄ Charts

Interpreting X̄ Charts

Interpreting x̄ charts, a type of control chart used in statistical process control helps monitor the variation in processes over time. The x̄ chart is based on the sample mean and allows for monitoring variations in the process mean over time. These charts are pivotal for quality assurance in manufacturing and other sectors.
An x̄ chart plots the values of individual measurements over time against control limits calculated from historical data. The central line...

Interpreting R Charts

Interpreting R Charts

R chart, or range chart, is a fundamental tool in statistical process control used to monitor the variability within a process. It complements the X-bar (x̄) chart by focusing on the range of the data, rather than individual values, providing a clear picture of the process dispersion over time.
An R chart plots the range of subsets of measurements collected from a process. Each point on the chart represents the range—defined as the difference between the maximum and minimum...

The R Chart

The R Chart

In statistical process control, control charts, particularly R charts, are instrumental in monitoring process variations and identifying non-random patterns that run charts might miss. R charts track the variability within process subgroups, which is crucial when standard deviation use is impractical or unknown process variations exist.
R charts are pivotal for pinpointing shifts in process variability. Stability is indicated when all data points remain within the defined upper and lower...

Regression Toward the Mean

Regression Toward the Mean

Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...

Weighted Mean

Weighted Mean

While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...

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Monitoring process mean and dispersion with one double generally weighted moving average control chart.

Kashinath Chatterjee¹, Christos Koukouvinos², Angeliki Lappa²

¹Department of Population Health Sciences, Division of Biostatistics and Data Science, Augusta University, Augusta, Georgia.

Journal of Applied Statistics

|December 19, 2022

Summary

A new Maximum Double Generally Weighted Moving Average (Max-DGWMA) control chart effectively detects process mean and dispersion shifts. This statistical process control tool shows improved efficiency in industrial quality management.

Keywords:

Average run length (ARL)Max-DEWMA chart Max-DGWMA chart Max-EWMA chart Max-GWMA chart standard deviation of run length (SDRL)

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Area of Science:

Industrial Engineering
Statistical Quality Control
Operations Research

Background:

Statistical Process Control (SPC) utilizes control charts to monitor and manage industrial process variations.
Existing control charts like EWMA and GWMA have limitations in simultaneously detecting shifts in process mean and dispersion.

Purpose of the Study:

To introduce a novel memory-type control chart, the Maximum Double Generally Weighted Moving Average (Max-DGWMA) chart.
To evaluate the run length performance of the Max-DGWMA chart against other advanced control charts.

Main Methods:

Development of the Max-DGWMA control chart for simultaneous detection of mean and dispersion shifts.
Utilized Monte-Carlo simulations to compare the run length performance of various control charts.
Employed time-varying control limits for enhanced chart sensitivity.

Main Results:

The proposed Max-DGWMA chart demonstrated superior efficiency compared to Max-EWMA, Max-DEWMA, and Max-GWMA charts.
Performance of the Max-DGWMA chart was found to be comparable to the SS-DGWMA chart.
The chart successfully identified shifts in an automotive engine piston ring manufacturing process.

Conclusions:

The Max-DGWMA chart is an effective tool for enhancing statistical control in manufacturing processes.
Its ability to detect shifts in both process mean and dispersion offers significant advantages in quality management.
The chart proved efficient in identifying out-of-control signals rapidly within an industrial application.