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Control Limits

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  • #26274

    Bob Lowe
    Participant

    I am new to SS and am using minitab to run an IM-R chart.  I read that the control limits are set at +- 3 sigma from the mean.  Yet, when I calculate this from the descriptive statistics that minitab gives me, it is never exact.  It sometimes gives me 2 sigma, sometimes 3 sigma plus n and other times no logical explanations….Can someone please explain how minitab calc’s the limits?

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    #63847

    francobaez
    Participant

    read the help files from minitab, it is explained
     

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    #63848

    melvin
    Participant

    I did check the help files in minitab and it references that the limits are set at 3 sigma.  Reality is that the limits are set at 2.66 times mean of the moving range plus mean of the individual value chart. Do not understand this logic.

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    #63849

    Franco
    Participant

    Stat > Control Charts > Xbar, Individuals, Xbar-R, Xbar-S, I-MR-R/S (Between/Within), I-MR > Tests
    Stat > Quality Tools > Capability Sixpack (Normal), Capability Sixpack (Between/Within) > Tests
    Lets you select a subset of the eight tests for special causes shown in Eight Tests for Special Causes. Each test detects a specific pattern in the data plotted on the chart. The occurrence of a pattern suggests a special cause for the variation, one that should be investigated.
    When a point fails a test, Minitab marks it with the test number on the plot. If a point fails more than one test, Minitab marks it by the lowest numbered test, and prints a summary table with complete information in the Session window. See [5] and [25] for guidance on using these tests that detect specific patterns in the data plotted on the chart.You can adjust the sensitivity of the tests with Stat > Control Charts > Define Tests.
    Subgroup sizes must be equal to perform the tests.
    Stat > Control Charts > Define Tests
    You can define the sensitivity of the tests for special causes used with quality control charts. The test definitions stay in effect until you restart Minitab. The range of acceptable values you can enter depends on the test number, as shown below.
    Test  K can be…(default in parentheses)1 One point more than K sigmas from the center line 1-6 (3)2 K points in a row on same side of center line 7-11 (9)3 K points in a row, all increasing or all decreasing 5-8 (6)4 K points in a row, alternating up and down 12-14 (14)5 K out of K + 1 points in a row more than 2 sigmas from the center line (same side)  2-4 (2)6 K out of K + 1 points in a row more than 1 sigma from the center line (same side)  3-6 (4)7 K points in a row within 1 sigma of the center line (either side) 12-15 (15)8 K points in a row more than 1 sigma from the center line (either side) 6-10 (8)
     

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    #63850

    Chaturvedi
    Participant

    The value of UCL and LCL are computed as X bar + 3 sigma and X bar – 3 sigma. Here the sigma is equal to the standard deviation of the sample / root n. To know more on this read book on quality control. This is the basic of control charts.

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    #63851

    Savage
    Participant

    Control limits are calculated depending on the type of control chart you are using.  In a typical X-bar R chart the constant A2 is used to calculate the limits.  For the I-MR chart of individuals, they use a constant called E2 because there is only one sample in each subgroup.  For individuals, use the constant E2=2.66 multiplied my R-bar, or the average of the moving range chart.  This +/- the mean will get your limits.
    For all the E2 constants, you should be able to get on the internet.  They are also in the BB Pocket Guide and most books.  Or, see this:
    http://www.qualityadvisor.com/sqc/formulas/x-mr-f.htm
     

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    #63855

    Paul Aaron
    Participant

    Give Minitab a call at 814-231-2682.  They are very helpful.

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    #63858

    Dale Doyle
    Participant

    Matt’s answer is correct in that an IM-R chart uses a constant in the formula.  Keep in mind control limits are based on the data.  Because the IM-R is looking at one data point to the next, we loose much of the power of the “C L T”.  It will take a number of data points for the contol limits to level out.  Mini Tab calculates the CL each time a new data point is entered.  Depending on the type of data you are collecting you may want to check to see if this chart is the best fit for the process you are charting. 

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    #63859

    Adam
    Participant

    First of all you have to understand the logic of the control charts. By means of control charts you can compare long term variation against short term variations. In the case of X-MR chart, the short term variation is estimated by a difference between two or more successive individual values moving with time. If the long term variation is significantly larger than short term variation (existence of variation other than common casue) then the dfference between the ways of control limit calculation will be bigger.

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    #63862

    Harini V
    Participant

    Please refer to the book by Donald Wheeler “Understanding Variation – The key to manageing Chaos”.
    For IMR charts, with adjacent values, n=2, the k value becomes 2.66, which is nothing but 3/Hartley’s constant. Replacing Harley’s constant (1.128) for n=2 will give 2.66

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