Q 562. What is an Exponentially Weighted Moving Average (EWMA) control chart? How is it different from the traditional control charts? Highlight the advantages and disadvantages of EWMA chart using an example.

 

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The Exponentially Weighted Moving Average (EWMA) control chart used for observing the small changes in the process mean value. The highest weight is given to the latest observation whereas past values considered smallest. The EWMA glowingly stacked moving average graph for statistical control to measure variables to use all the outputs. This chart will identify sigma shift (0.5 – 2) quicker than other charts with same sample value. Its used mainly when the continuous values are available for the life cycle of the process.

Difference between EWMA vs traditional control charts:

Major difference between Exponentially Weighted Moving Average control chart and other traditional control charts are, a simple moving average chart focuses on similar weight to all the values, whereas EWMA is focused on latest values not the total historical data.

Also, EWMA is alert on smallest change in the process compared to trendy Xbar-R or other control charts

Advantages of EWMA:

Exponentially Weighted Moving Average control chart helps in exploring the variations which are regularly existed in the process.

EWMA helps in detecting the potential process failure, also projects the data shifts and patterns in the process.

It shows the process future performance potential and failure, very useful in statistical process control. With the help of EWMA, we can improve process quality by innovative ideas.

Disadvantages of EWMA:

This needed a lot of historical data maintenance for various times and every projected period

Mostly avoids complexity of the different variables from the data set

Fluctuations in the data goes unnoticed which occurs due to some reason, e.g., special causes, or abnormality due to shift in the work environment

EWMA (Exponentially Weighted Moving Average) control charts are used for monitoring attribute type of data. These charts can be used to plot individual data points or subgroup means. EMWA charts consider full history of the process under monitoring for its plotting. Compared to other control chart, EWMA differs in terms of, weightage of recent samples contribute higher towards moving average computation in EMWA. This helps to highlight even the smallest shift in the process average. If the process needs focus on smoothing out the effect of uncontrollable noise EWMA will help. Disadvantage of EWMA charts are, they are complex is its statistical computation. They are not appropriate for the processes where the shift is process are very large.

Control charts are used to identify any changes or shifts in the process and to determine if the process is in a state of statistical control. By tracking process performance over time, control charts can help identify trends, and other sources of variation that may affect the required quality of the output.

 An Exponentially Weighted Moving Average (EWMA) control chart is a statistical process control tool/chart that is also used to monitor the quality of a process over time however it is a type of moving average control chart that assigns more weight to recent data points than to older ones. This allows the chart to detect changes in the process more quickly than traditional moving average charts.

EWMA  charts and traditional control charts are used to monitor processes and detect changes in the quality of output. However, there are some important differences between EWMA and traditional charts.

 

 

Example of EWMA charts that they better at detecting small shifts in the process mean:

 

Moving range (Tradition chart ) measurement of 250 samples, where the data seems within control in the below chart. For the same data when EWMA chart is used, it shows test has failed at point 161 which implies that the data is out of control limit.

 

 

 

Test Failed at points:  161

 

 

Example:

 

Suppose a manufacturer wants to monitor the thickness of a optical film produced by a machine. They decide to use an EWMA chart to monitor the process. The advantages and disadvantages of using an EWMA chart for this application are:

 

Advantages:

 

Sensitivity to small shifts: The EWMA chart will be more sensitive to small changes in thickness than a traditional control chart, allowing the manufacturer to detect changes in the process sooner.

 

Flexibility: The weighting factor can be adjusted to give more or less weight to recent data points, depending on the specific process being monitored.

 

 

Disadvantages:

 

Complexity: The manufacturer will need to perform more complex calculations to determine the appropriate weighting factor and control limits for the EWMA chart.

 

False alarms: If the process is stable, the EWMA chart may generate more false alarms due to its sensitivity to small changes.

 

Limited detection of large shifts: The weighting factor used in the EWMA chart gives more weight to recent data, which may obscure longer-term trends in the process.

 

 

In summary, EWMA charts are a variation of traditional control charts that are designed to be more sensitive to small shifts in the process mean and respond more quickly to changes. However, one needs to be vigilant of the fact that  they require more complex calculations for control limits and can generate more false alarms.

The EWMA (Exponentially weighted Moving Average) chart takes all the data points into account, it plots weighted moving averages from Oldest to newest data points, Weightage increase exponentially from Oldest to newest data points.

Following is the typical formula to calculation: -

Zt=α ∗Xt+(1.0−α) ∗Zt−1

Where α is the smoothing coefficient and value lies between 0 to 1. If Value of α is taken close to 1, It will give more weight to newest data point, however its value α is chosen close to 0, it will give more weight to Old Data points.

The following is an example of I-MR charts and EWMA charts for cricket ball circumference.

 

SN	Cricket Ball Circumference (mm)
1	224
2	225
3	227
4	226
5	224
6	228
7	227
8	225
9	229
10	227
11	224
12	226
13	227
14	224

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I-MR Chart:

EWMA Chart:

 

Difference between traditional control charts and EWMA:

Traditional charts use simple arithmetic averages hence give equal weightage to all data points, however EWMA charts use exponentially weighted moving averages and give weightage average from oldest to newest data points in increasing order.

Advantages and disadvantages of EWMA chart:

The EWMA is more efficient in detecting small shifts since it places more weightage on newest data points and less weightage on oldest data points. A major disadvantage is, EWMA charts don’t capture larger shifts.

Following is the example wherein I-MR showing the process in control for small shit however EWMA charts showing the out-of-control points with small shift

 

 

 

 

 

 

 

 

 

 

 

Exponentially weighted moving avg (EWMA) and control charts are both statistical tools used for monitoring process performance. However, they differ in their approach and applications.
EWMA is a time-series analysis which assigns a weight to each data point and gives greater weight to more recent data. Recent data points have greater influence on avg than older ones.
On the other hand, control charts plot the process data over time and indicate the upper and lower limits based on process variation. outliers require further investigation and corrective action.

Example:
Suppose a manufacturing company produces car batteries and uses an EWMA chart to monitor the average voltage of the batteries over time. The company has set a target voltage of 12 volts, and the control limits on the chart are +/- 0.5 volts.

Advantages:

    The EWMA chart can detect small changes in the average voltage, such as a gradual increase or decrease, which could indicate a problem with the production process.
    The chart can be easily customized to adjust the sensitivity to changes in voltage. For example, a smaller lambda value could be used to make the chart more sensitive to small changes, while a larger lambda value could be used to reduce the impact of outliers and noise.
    The chart can be easily interpreted by the operators on the production floor, who can quickly identify when the average voltage is trending towards the control limits.

Disadvantages:

    The choice of lambda can impact the results of the chart, and different values may be more appropriate for different situations. This requires some level of subjectivity and expertise.
    The chart may not react quickly to sudden changes in the process, such as a large increase or decrease in voltage caused by a specific issue.

Exponentially Weighted Moving Average (EWMA) Control chart

It is a statistical process control chart used to monitor and control a process. It is a modified version of the traditional control chart unlike traditional control charts, which use fixed time intervals to calculate the control limits. An EWMA chart uses exponentially decreasing weights to give greater emphasis to more recent data. It uses a moving average to detect changes in the mean value of a process.

 

An EWMA control chart is different from traditional control chart. The key difference between the EWMA control chart and the traditional control chart is that the EWMA places more weight on recent data points while gradually decreasing the weight given to older data points.

In an EWMA chart, each data point is given a weight based on its age, with older data points given smaller weights. The weight assigned to each data point is determined by a smoothing parameter called lambda (λ), which ranges between 0 and 1.

A larger value of lambda gives more weight to recent data

A smaller value of lambda gives more weight to historical data i.e. less weight to recent data

 

Advantages of EWMA chart:

- It can detect smaller shifts in the process mean and respond more quickly to these shifts.

- It is more sensitive to changes in the process than traditional control charts, reducing the risk of producing 

   non-conforming products

- It requires less data to establish the control limits.

 

Disadvantages of EWMA chart:

- It may not be appropriate for all types of processes.

- It may not be suitable for processes with long-term trends or seasonal patterns

- It is more complex to calculate than traditional control charts. It requires the selection of an appropriate           value of lambda, which can be subjective and may vary depending on the process.

- It may produce false alarms if there is a sudden increase in the data.

 

For example, let's say a manufacturing company produces ball bearings with a target diameter of 10 millimeters. The company uses an EWMA chart to monitor the process and detect any deviations from the target diameter. The company decides to set the value of lambda to 0.2 based on historical data.

After analyzing the data, the EWMA chart detects a shift in the process mean on the 6th day of production. The company investigates and finds that a machine was not calibrated properly, causing the deviation from the target diameter. The company quickly takes corrective action, reducing the risk of producing non-conforming products. Without the EWMA chart, the deviation may not have been detected until much later, resulting in more non-conforming products being produced.

Interesting answers to a tricky question. The best answer has been provided by Partho Karmakar. Well done!