As a member of Minitab's Technical Support team, I get the opportunity to work with many people creating control charts. They know the importance of monitoring their processes with control charts, but many don’t realize that they themselves could play a vital role in improving the effectiveness of the control charts.
In this post I will show you how to take control of your charts by using Minitab Statistical Software to set the center line and control limits , which can make a control chart even more valuable.
When you add or change a value in the worksheet, by default the center line and control limits on a control chart are recalculated. This can be desirable in many cases—for example, when you have a new process. Once the process is stable, however, you may not want the center line and control limits continually recalculated.
Consider this stable process:
Now suppose the process has changed, but with the new re-calculated center line and control limits, the process is still shown to be in control (using the default Test 1: 1 point > 3 standard deviation from the center line).
If you have a stable control chart, and you do not want the center line or control limits to change (until you make a change to the process), you can set the center line and control limits. Here are two ways to do this.
Suppose you want the center line of your Xbar chart to be 118.29, UCL=138.32 and LCL=98.26.
Note: If you want to use the estimates from another data set, such as a similar process, you could obtain the estimates of the mean and standard deviation without solving for s. Choose Stat > Control Charts > Variables Charts for Subgroups > Xbar. Choose Xbar Options, then click the Storage tab. Check Means and Standard deviations. I'll use the data from the first 12 subgroups above for illustration:
These values are stored in the next available blank columns in the worksheet.
Using the center line and the control limits from the stable process (using either of the methods described above), the chart now reveals the new process is out of control.
As you can see, it's important to consider whether you are using the best center line and control limits for your control charts. Making sure you're using the best options, and setting the center line and control limits manually when desirable, will make your control charts even more beneficial.
I'm using this formula to calculate UCL & LCL, respectively:
Control limits, also known as natural process limits, are horizontal lines drawn on a statistical processcontrol chart, usually at a distance of ±3 standard deviations of the plotted statistic from the statistic's mean.
Control limits should not be confused with tolerance limits or specifications, which are completely independent of the distribution of the plotted sample statistic. Control limits describe what a process is capable of producing (sometimes referred to as the “voice of the process”), while tolerances and specifications describe how the product should perform to meet the customer's expectations (referred to as the “voice of the customer”).
Use[edit]
Control limits are used to detect signals in process data that indicate that a process is not in control and, therefore, not operating predictably.
There are several sets of rules for detecting signals - see Control chart - in one specification:
A signal is defined as any single point outside of the control limits. A process is also considered out of control if there are seven consecutive points, still inside the control limits but on one single side of the mean.
For normally distributed statistics, the area bracketed by the control limits will on average contain 99.73% of all the plot points on the chart, as long as the process is and remains in statistical control. A false-detection rate of at least 0.27% is therefore expected.
It is often not known whether a particular process generates data that conform to particular distributions, but the Chebyshev's inequality and the Vysochanskij–Petunin inequality allow the inference that for any unimodal distribution at least 95% of the data will be encapsulated by limits placed at 3 sigma.
See also[edit]References[edit]
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Control_limits&oldid=864066784'
Moving Range Chart - Formula, Example
This tutorial explains how to calculate Individual chart and Moving range chart values.
Formula:S = √Σ(x - x̄)2 / N-1Individual chart: UCL = X̄ + 3S, LCL = X̄ - 3SMoving range chart: UCL=3.668 * MR, LCL = 0 Where, X/N = Average X = Summation of measurement value N = The count of mean values S = Standard deviation X = Average Measurement UCL = Upper control limit LCL = Lower control limitExample :
College MCA five students grade point out of 10 for mean values are 2.0,3.5,4.2,3.0,5.5.
Given :
Measurement Values (X) = 2.0,3.5,4.2,3.0,5.5
N = 5
To Find :
Individual and Moving range chart
Solution :
Change txt to cfg. S = 1.31
How To Calculate Control Limits For SubgroupsIndividual chart
UCL = 3.63+(3*1.31) = 7.56 LCL=3.63-(3*1.31) = -0.29
Moving range chart
UCL=3.668*0.875 = 3.21 LCL = 0
Result :Individual chart
UCL = 7.56 LCL = -0.29
Moving range chart
UCL = 3.21 LCL = 0
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