Q 561. I-MR, Xbar-R, Xbar-S: These are three control charts for continuous data. All the three have 2 control charts each. Why do we have 2 control charts in each one of them? What is the order in which these 2 control charts should be studied and why? Explain with illustrations.

 

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I-MR

Individual Chart – Depicts the individual values and observes the shifts in the mean value in the process, wherein data values are gathered at periodic frequency of time. I-Chart also helps to determine the obvious causes in the process

Moving Range Chart helps in observing the process variation wherein data values are gathered at periodic frequency of time.

X-bar-R When sample size is >2 – 9<

Xbar chart helps in study the changes in the mean value over the period. This chart is commonly used in combination with R-Chart to observe the process variation.

R-Chart depicts the data range changes periodically in the sub-group. Typically, this chart study the range and process variations. R values shows the defects in measurements and illustrates the sample data range.

Xbar-S when sample size is more than >10

X-bar chart depicts the process mean and changes in the process overtime.

S-Chart is the scale of standard deviation in the process over period, estimated by data sample moving range.

Control charts provides us powerful insights into process performance, variability, and stability, and help us in making data-driven decisions to improve the quality of our outputs.

 

Typically, control charts help us in getting below insights 

• Identifying process stability
• Detecting process variation 
• Predicting future process performance 
• Comparing different processes
• Communicating process performance 

We have 2 charts, the upper chart typically displays the process data in the form of a line graph or scatter plot, while the lower chart displays a measure of the variation in the data.

 

The two charts are typically complementary and together help to monitor the performance of a process over time, and to detect any unusual variation or changes that might be occurring.

 

Using two charts together helps us in understanding the comprehensive picture of the performance of a process. 

 

In Xbar-R, the Xbar chart can help us see whether the process is stable and centered around a target value, while the R chart can help us see whether the variation within subgroups is consistent over time.

If the variation in the process is consistent, the R chart should show relatively small and consistent ranges.

If the variation is not consistent, the R chart may show large and/or inconsistent ranges.

 

In I-MR, the I chart shows the individual data points plotted over time, and the MR chart shows the moving range between each successive data point. By using both charts together, we can monitor both the average level of the process and the variation in the data.

 

In Xbar-S, Xbar chart shows the average value of the process data within each subgroup, and the S chart shows the variation within each subgroup.

 

To conclude, using both control charts together can help us identify potential problems or changes in our processes, and take corrective action before the process goes out of control.

In Statistic control Process, to analyze Variable Data, we need to use mean, range and standard deviation. Control charts are used to Monitor these Parameters to study whether the process is out of control or not. Any of the Parameter outside the Control limit means special cause variation is present in the process.

When we deal with any Variable, it is necessary to control the mean and dispersion for process stability. For Average we have X bar chart however to check the variability either Range (MR, R Chart) or Standard deviation (S Chart) to be calculated based on rational Subgrouping of Sample Data.

Hence two charts required to check the process means and variation over a time.

I-MR is chart is used when there no subgrouping in the Data. Following is chart depicts Sample of 500 ML size Bottle Filled over a period.

From the above I-MR chart analysis, MR chart is stable, however Individual chart is out of control. MR chart must be analyzed before analyzing I-Chart as I-chart control limits are calculated based on MR charts variation and average. MR chart depicts the variation of range calculated from consecutive data points. If MR chart is out of control, then it is irrelevant to Analyze the I-Chart as control limits for I chart will be incorrect.

X bar R (X bar R chart is required to calculate average and Range when Rational Subgroup Size is 2 to 8.)

The following charts (Average Call Handling time for 5 Calls for 30 Days) for X bar and R show the process is in control. R-chart should be in control before analyzing the X bar chart because X bar control limits are derived from R control chart. If R chart is out of control, then X bar charts limits are inaccurate, and it is irrelevant to analyze the X bar chart. For process to be in control, Both X bar and R charts must be in control.

 

X bar S (X bar S chart is required when subgroup size is greater than 8. When number of subgroups are large, S chart (Standard deviation) is more efficient than R (range) chart as X bar S charts can provide more accurate depictions of small variation a process.

The following charts (Average Call Handling time for 12 Calls for 30 Days) for X bar and R show the process is in control. S-chart should be in control before analyzing the X bar chart because X bar control limits are derived from S control chart. If S-charts value are out of control, then X bar charts limits are inaccurate. For process to be in control, Both X bar and S-charts must be in control.

 

OH MY GOD. There were about 8 answers to this question, however, you are able to see only 3 answers because most of the other were incorrect 

 

Even from the published answers, there are 2 answers that have not tried to answer the question, however they are not incorrect. The only answer which is correct is from Vijay Tomar and hence has been selected as the best answer. Great answer Vijay.

 

Note: Some people seem to be using ChatGPT to find forum answers. This is a risky approach as ChatGPT is error prone as our questions are application questions (they are never straightforward).

Have a look at this funny example - https://www.benchmarksixsigma.com/forum/topic/39458-using-ai-to-respond-to-forum-questions/ 

Recommendation is to research with caution and write correct answers.