Statistical Challenge

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    Hi, I am working on a training project to measure the performance on a small feature for an injection folded feature on a component.

    The feature is a rib of height 1.5mm and the gage is accurate to 0.005mm. The range of variability is 0.004mm so I only have a discrimination level of 4.

    What is troubling me is that the data is coming out as non-normal. I am wondering whether this should be a one sided distribution as the metal prevents the part from being bigger. I have been told that longer dimensions are normal and again wonder if the shrinkage would be the more dominant factor making it normal.

    So far I have 20 samples and it is quite difficult to get more as the parts are very low volume.

    Please can you tell me what distribution should be used to describe the data?


    Robert Butler

    Why do you need a specific name for your distribution? You are dealing with data that is guaranteed to be non-normal and there are all kinds of distributions for which no name exists. Take your 20 samples, plot them on normal probability paper, as a box plot, and as a histogram, determine the mean and the median and present your graphical and summary statistics findings and press on.



    Hi Robert,
    Thanks for this. Would you expect the data from an inject moulding process to be non normal?

    Reason for asking is that one of the stakeholders is expecting normal data and believes that the non normality represents variability signalling the process is out of control. I am not sure that I would expect normal data and believe that the low variability (almost to the point it can’t be measured) would mean that the normality test doesn’t really tell us anything. Am I right in thinking you are saying that it is less important what distribution it is as the variability is low?


    Daniel Sims

    I’ll just throw my hat in to say that just because a process produces non-normal data does not mean it’s out of control. Perhaps he has been trying to run SPC with non-normal data without realising and has experienced some false alarms, but that is speculation on my part.

    My opinion when thinking of your mould process is that it will most likely create non-normal data, as you’ve alluded to the tool cavity will be limiting the upper limits of the rib dimensions, the data on the longer dimensions will most likely tend to normality as factors such as shrinkage will have a more noticeable effect over the larger dimension.

    You really should plot the points as a histogram and boxplot to get an idea of what the data is showing you. If it’s starkly non-normal you can start to look at the median and range to describe your distribution, using the 25/75th percentile, and I bet you’ll find a tight box in there. You could then take this to the stakeholder and explain to him why you expect non-normal data, but also why it isn’t necessarily a cause for concern.

    I’m not expert though, but just trying to help


    Robert Butler

    Yes, your process guarantees the data will be non-normal because you have a physical lower bound to the measurement you are taking and you are doing your best to have all of your product right at the lower bound (the lower bound being 0 shrinkage – you can’t have negative shrinkage) and shrinkage measures are naturally non-normal in distribution.

    Rather than get in a shouting match with your stakeholder see if you can borrow a copy of Measuring Process Capability by Bothe and make a copy of the first page of Chapter 8 – Measuring Capability for Non-Normal data.

    On the first page of Chapter 8 Bothe states “…there are many manufacturing processes that typically generate non-normally distributed outputs, even when in control. Below is a list of twenty such characteristics:
    1. Taper
    2. Flatness
    3. Surface Finish
    4. Concentricity
    5. Eccentricity
    6. Perpendicularity
    7. Angularity
    8. Roundness
    9. Warpage
    10. Straightness
    11. Squareness
    12. Weld or Bond Strength
    13. Tensile Strength
    14. Casting Hardness
    15. Particle Contamination
    16. Hole Location
    17. Shrinkage
    18. Dynamic Imbalance
    19.Insertion Depth
    20. Parallelism”

    …I’m sure your stakeholder will find #17 to be of interest. :-)

    As for non-normality indicating an out of control process – sorry no. The reverse is also true for a normal distribution – by itself a distribution tells you nothing about a process being in or out of control.

    If you need a quick proof of this for your stakeholder with respect to the normal distribution indicating an in control process get a random number generator based on a normal distribution and generate 100 numbers. Order the numbers from lowest to highest and assign the identifer number 1 to the first 25, 2 to the second 25, 3 to the third 25, and 4 to the last 25. Now run a one way ANOVA on the 4 groups to test for significant differences in means – you will find significant differences which means the distribution of perfectly normal numbers is hiding the results of an unstable process.


    Miguel Pereda

    Can you provide that raw data so people can help you ID the distribution? A transformation may also work if no distribution is fit. Or the process may be unstable and measurements are just erratic. Hard to say without looking at the data.



    Looking the scenario I suggest
    1. Calculate process capability cavity wise. There must be variation in dimensions cavity wise.i know there is sample size constraint. If you can produce some more samples, it will be good.
    2. Also, you can plot control chart (Xbar R chart) to get feel that your process is in control.
    3. Transformation of data – box Cox plot.

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