Need Help Analyzing Non-Normal Data

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    We had a project to find if an acid leveling machine was Capable or not. After taking the samples we found that
    1-our data was NON-NORMALLY because our measuring device wasn’t accurate enough and this device is the best that we can afford.
    2-There were some points out of control (Using minitab)

    What should we do next? and do we need to do hypothesis test or not? and if Yes then how to do it?

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    Robert Butler

    I would recommend you re-examine your data. The IMR plot gives a visual impression of three distinct shifts downward in your data. The first cut point occurs at about data point 44, and the second at about data point 83. It also gives the impression the process is drifting back toward the target around data point 93. In short, the plot would suggest you don’t have the process in control. One of the requirements of a capability study is that the data needs to be from a stable process.

    Before worrying about issues of normality or capability I would want to go back and see if I could identify the reasons for what appears to be special cause variation and change the process so that the data is exhibiting only ordinary process variation. In the interim, if you want to use the data to give yourself a measure of expected ordinary variation (and also check to see if the visual appearance really is signalling the presence of special cause variation) you could generate an estimate of ordinary variability using the method of successive differences.



    Prerequisites for Capability studies are that the data is normal and stable, over time. Additionally, you can’t perform capability studies until you have an acceptable GR&R, so that would be the first step. To Mr. Robert’s point above, there’s obviously “special cause” variation included in the study. Also, you need to think about how the sample data was collected. What variation sources were inherent to the data? Was this a representative sample? Lot’s of unanswered questions.


    Chris Seider

    Non normality (bi-modal) is rarely caused by the gage but go ahead and perform a gage R&R. You realize the graphs shown don’t discuss process capability. You may be chasing your tail about a problem that doesn’t exist depending on if the specs are real and where they are.

    I’d encourage you to use your process map to get other X’s and gather them simultaneously and use the 6S process to help solve the problem–do you have a problem in process capability?



    Great points above regarding the shifts in the data. It looks like a batch operation, someone is adjusting a process to a target. As for the gage accuracy driving non normality; that should not be a factor for the distribution, only the bucketing. I would guess that is why there are gaps in the buckets every 5 bars.
    There is a distinct bump at the left tail of your data set. I have seen this many times in the past and it is a great indicator that operators are “raking in” the test result to meet the spec. That hump will skew your mean. I’d be willing to bet your spec is right around 20.75.
    I have run capability studies on processes that were similar, Baseline capabilities are pre-improvement effort and as such are often not on processes that are stable or in control. they are however the reality that the business is feeling. Consider that if the gage is not capable, but it’s what is being used to accept or reject products, the capability is an accurate reflection of the process. The same can be said regarding process shift due to the current practices, they should be included in the study.


    Mike Carnell

    @karimsalem I do not believe that your normality issue is a function of your gage. That looks a lot more like a sample selection issue.

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