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Cpk if data are exponential distribution

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  • #53421

    Grossmann
    Participant

    Hi

    Can you help me how is the right way through Minitab make a Capability analysis Cp,Cpk of measured data which have exponential distribution?
    Thanks for your help and support

    Michal

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    #190037

    Robert Butler
    Participant

    I don’t know Minitab but the easiest way I know for doing this is to use the plot function in Minitab and plot the data on the normal probability plot. Print out the graph and either eyeball the curve of the data points, or, if you’ve been around awhile, pull out your French curve and fit a line to the data points using the French curve and a lead pencil. Extend that curve until you cut the .135 and 99.865 percentiles. Use these two points to compute your equivalent six sigma spread and press on from there.

    Chapter 8 Measuring Capability for Non-Normal Variable Data in Measureing Process Capability by Bothe has additional details.

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    #190045

    Hody
    Member

    The first thing that you should do is determine which “non-normal” distribution your data set is a fit for. In Minitab, use
    Stat > Quality Tools > Individual Distribution Identification
    In that form you can compare your data to: exponential, weibull, lognormal, etc. and see which has the highest p-value. Beware that if you have any non-positive data points hidden in there it may not be able to do some of those (eg lognormal function blows up at zero mathematically).

    Stat > Quality Tools > Capability Analysis > Nonnormal
    would then allow you to specify which distribution you have determined. and show your capability.

    Also beware that these non-normals normally stick to Pp and Ppk instead of Cp and Cpk…

    Hope this helps

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    #190051

    Leader
    Participant

    And the reason we don’t get Cpk in non-normal process capabilities is that the magic d2 constant was based on a normal distribution. No worries, just go with Ppk and potentially explain in terms of ppm or percentage out of spec limits if Ppk is confusing to your audience.

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    #190052

    bbusa
    Participant

    pp , ppk are meaningless indices

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    #190065

    Leader
    Participant

    That was a greatly useful comment — thanks for your enlightenment and supporting data!

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    #190068

    bbusa
    Participant

    Thank you . refer to DC Montgomery’s Statistical Quality Control for more enlightenment !

    Quote

    …..Pp & Ppk are a waste of engineering and management effort – they tell you nothing . Kotz and Lovelace ( 1998 ) – — they refer to the mandated use of of Pp & Ppk through quality standards or industry guidelines as undiluted Statistical Terrorism” :angry:

    Unquote

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    #190078

    Leader
    Participant

    So, let’s put on our critical thinking caps here. Is there any reason to back up the above statement besides it being cooly dramatic? What quantitative data is the author(s) providing?

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    #190079

    Grossmann
    Participant

    I have issue with the correct way to do process analysis. Collect data looks according minitab as a exponential distribution. I need to check if process is capable and stable. Now I found the issue that minitab ver 13 is maybe old version because I can choose only Stat > Quality Tools > Capability Analysis 1.(Normal), 2. (Between/Within), 3. (Weibull). There isn’t choice nonnormal.

    I think I’m not able to do right analysis with this minitab software version.

    Thanks for your previous responds

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    #190082

    Hody
    Member

    Michal, If you don’t mind something “quick-and-dirty”…

    You can use your baseline’s yield and just translate it to Cpk since Z=3*Cpk
    (so in Excel you can use “=normsinv(yield) / 3”).

    P.S. Thanks to Delenn for taking the earlier conversational high ground

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    #190090

    Jonathon Andell
    Participant

    I agree with you. It goes back to the sigma shift baloney, which nobody has been able to validate to my satisfaction. Also, in Minitab, Ppk presumes that within-subgroup variation is “short term,” while between-subgroup variation is “long term.” I am not one bit comfortable allowing Minitab to make that distinction regarding my process or its data. And don’t even get me started on Cpk vs Ppk for autocorrelated data…

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    #190095

    Leader
    Participant

    1. Sounds like Minitab added some improvements since 13 – in 15 you can select your distribution. Can you upgrade? I hear 16 is almost out – you might call Mini and ask for timing.

    2. I also hate the “long term” vs “short term” designations – it tends to throw students off. I try to blow past that as quickly as possible and focus on the differences in the equations.

    3. In practically, when I get both Cpk and Ppk options, I’ll look at both. Better to have more data than less. You can always take the conservative route and use the worst-case scenario, although if the two numbers are significantly different you may have a control issue.

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