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How to Determine Process Capability with Non-Normal Data?

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This topic contains 4 replies, has 3 voices, and was last updated by  Chris Seider 6 months, 1 week ago.

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  • #237196

    tgause
    Participant

    I have a process improvement project related to a process that makes “widgets.” Sponsor suspects they are not meeting the customer’s contracted 3-day turnaround time (TAT) specification. (Note: the TAT is calculated from the day the order is received to the day the order is closed. In our company, it’s possible that a widget can have a TAT of 0 days, if the order is received, created, and closed in the same day.). My task: Determine how often we are meeting the 3-day TAT specification and if we aren’t, fix it so we are.

    I pulled data from 1/5/17-7/2/18 to see what TAT is for widgets created during this time. The data shows a TAT range of 0-36 days. I plugged the data into Minitab (v. 17), and attempted to run a capability analysis (constant size for subgroups=1 and Upper Spec=3, no Lower Spec entered). As you can see from the resulting Report Card, stability is an issue, the data failed the normality test miserably, and I can’t transform the data because, according to Minitab, “some data values are negative or zero.” (Sponsor’s suspicions confirmed.)

    I thought I might be able to solve the “zero data transformation” problem by increasing all values by 1, thereby eliminating all zeros in the data set. That didn’t help anything. The data was still off-the-charts non-normal and I still couldn’t transform the data.

    Correct me if I’m wrong, but you can’t run a process capability unless you have normal data and a stable process, right? And when the process owner asks me, “How capable is our process of meeting the customer’s SLA?” what do I tell him? Your process is so out of control that I can’t even run a test to tell you how capable it is? (Just kidding. Well, maybe not.)

    Is my only course of action at this point to do the following?
    Step 1: Identify outliers and determine special causes.
    Step 2: Get this process in control before we even think about running another process capability.

    Any other advice?

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    #237199

    Robert Butler
    Participant

    The standard calculation for Cpk requires normality in the data. Your data is naturally non-normal so what you need to do is use the methods for calculating Cpk for non-normal data. Chapter 8 of Bothe’s book Measuring Process Capability has the details of how to do this.

    The basic method consists of plotting the data on normal probability paper and identifying the .135 and 99.865 percentile values (Z = +-3). The difference between these two values is the span for producing the middle 99.73% of the process output. This is the equivalent 6 sigma spread. Use this value for computing the equivalent process capability.

    It is my understanding Minitab has included this method in its software. I’m not familiar with Minitab but I’m sure if you check the “help” section of the program you will find the necessary commands. If you can’t find it there you could contact Minitab help or, since this topic has been discussed time and again on this forum, you could use the search engine to locate older posts on this subject. As I recall, one or more of the older posts were made by people familiar with Minitab and they provided instructions on how to find this method in the Minitab package.

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    #237200

    tgause
    Participant

    @rbutler – Thank you for responding. I took your advice and found an article that I think will help: https://www.isixsigma.com/tools-templates/capability-indices-process-capability/process-capability-calculations-non-normal-data/

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    #237213

    Chris Seider
    Participant

    Check out in Minitab, Stat>capability analysis>non-normal and if you have a distribution you’re comfortable with, they do a great job of predicting ppm defective based on the distribution chosen.

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    #237214

    Chris Seider
    Participant

    @jennatlas might have some more info

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