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Estimate Standard Deviation Between/Within Subgroup

Six Sigma – iSixSigma Forums General Forums Tools & Templates Estimate Standard Deviation Between/Within Subgroup

This topic contains 6 replies, has 5 voices, and was last updated by  Paul Keller 1 week, 4 days ago.

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  • #240860

    Carlos Garcia
    Participant

    I’m developing an Excel capability analysis data sheet but I have had some issues when I try to estimate standard deviation between/within subgroup (constant sample size) to calculate Cpk index. I need some help on calculations since the validation of Excel data sheet is not matching with the Minitab results.

    Could someone help me on this?

    Thanks in advance.

    • This topic was modified 2 weeks, 3 days ago by  Carlos Garcia.
    • This topic was modified 2 weeks, 3 days ago by  Katie Barry.
    • This topic was modified 2 weeks, 3 days ago by  Katie Barry.
    • This topic was modified 2 weeks, 3 days ago by  Katie Barry.
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    #240867

    Chris Seider
    Participant

    Did you check the help section of Minitab?  Pretty good info there but I wonder why not just use their awesome tools?

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    #240879

    Mike Carnell
    Participant

    @manray I got over 29,000,000 hits on Google in about .5 seconds. If you are using the same data set then you have a formula issue or so it would seem. I am sure if you contact the Minitab help line they can walk you through what they do.

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    #240880

    Chris Seider
    Participant

    @mike-carnell you have such fast internet…took me 0.71 seconds

    stay cool!

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    #240980

    Daniel Alfano
    Participant

    @manray mira este archivo, puedes ver las formulas que usa Minitab para valores individuales y para subgrupos.

    Saludos

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    #240999

    Paul Keller
    Participant

    Hi Carlos,

    You have a few things going on there. First, you shouldn’t use a Range chart to estimate variation for subgroup sizes >10. In fact, the subgroup standard deviation (i.e. X-bar Sigma chart) is always better. The Range chart was developed in the 1920’s before calculators or computers were prevalent, but better estimates are provided with the subgroup sigma nowadays.

    Second, specification limits should never be shown on an X-Bar chart. The X-bar chart plots subgroup averages, and the specifications apply to individual data measurements. Consider for example the subgroup consisting of the numbers 7,8.12, 13. The average is 10. If the specs are 9 and 11, then all observations are outside the specifications but the plotted mean is not. Stated differently, the  control limits on the Xbar chart are placed at +-3 standard deviation of the subgroup averages. The standard deviation of the subgroup averages is the standard deviation of the process divided by the square root of the subgroup size (i.e. A2 = 1/(d2*SQRT(n)). For a subgroup size of 5, the control limits on the Xbar chart are only 44% as wide as the control limits for the observations (when a normal distribution is used for the individuals control chart), so we’d expect that the specs (or any observation) are well outside the Xbar control limits. It’s apples and ranges, so don’t put specs on the X-bar chart.

    I didn’t go through all your calculations, and was going to paste the data into Minitab, but it doesn’t conveniently support the format you have. Instead, I’ve updated your file with a Sheet2 that shows two X-Bar Sigma charts developed with our SPC IV Excel software. (It’s only $299 so worth the hassle of trying to duplicate the formulas). The first “Standard X-bar-Sigma Chart” shows the X-Bar chart out of control. In this case, I’m suspecting that the within subgroup variation is not a good predictor of the longer term variation. This can happen in a variety of processes. For example, if you create a subgroup out of 16 cavities in an injection molding process, you will have this issue. The control chart is developed by using the within subgroup variation to estimate the short term variation, which is then used to calculate the control limits, so that the control limits test if the longer-term variation is similar to the short-term variation. In the injection molding example, the within subgroup variation is purely the differences between the cavities. It does not estimate short-term variation, so we need to use something different.

    The second chart shows a Batch Mean X-Bar Sigma chart. (Minitab calls this Between/Within). The Sigma chart shows the within subgroup variation, but the control limits on the X-Bar chart are based instead on the Moving Range between the subgroup averages. This provides a better estimate of short-term variation than the within group standard deviation.

    I hope this helps. Please let me know if you have any questions.

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    #241001

    Paul Keller
    Participant

    Better version of the charts attached.

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