Descrete data with varying sample size.

Six Sigma – iSixSigma Forums Old Forums General Descrete data with varying sample size.

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    Ken Sweat

    I am looking at machine availability where there are 3 shift operations. Sometimes the machine is only staffed 2 shifts and occasionally only one. I am considering an hour of staffed time as an opportunity and an hour lost to maintenance as an error. What would be the best way to chart this considering varying sample size on a daily basis? Could you control chart the % x 100 day to day? Open to good suggestions. We will soon DOE and I want a rational baseline that is defendable. Thanks Ken


    Ranganadha Erra

    Since you have identified an hour as an opportunity, I would suggest you calculate your dpmo ( defects per million opportunities )
    dpmo = (defects/(no. of units*no. of opportunities)*1000000
    dpmo happens to be a measure of how good or how bad your process is ( unavailability of the machine ). Since you have data for 100 days, you would get an accurate measurement of your process quality level.
    Control charts are used as indicators of the process deviation. It would tell you how may no of hours your machine is unavailable in a day. For that you got a fix up a specification limit. So if you draw the chart with number of days in the X axis, and no of hours of unavailability/day on Y axis, you would get a control chart. You may have qualitative comparision between the data points. It may also inform you when the process is deviating, the causes for the same ( random Vs assignable). This is a C chart.
    Your case, I would recommend dpmo compared to a c chart


    Tom Griffin

    I believe you have a few different options:
    Option 1
    1) Count scheduled but not produced units as errors
    or its time equivielent –
    2) Count percent of production time offline (units produced X unit time to produce / units scheduled X unit time to produce,
    Opton 2 – reduce the entire metric system to a per shift basis – each 8 hour block records its down time.
    If your machine is fully utilized, I would condier option 2, if it has spare capacity, option 1. 
    The assumption in the uptime metric you are suggesting is that any downtime is bad, that is that it will result in a loss of throughput.   My concern with the metric is that if the machine is not fully utilized, the measure may drive me to spend money to mitigate a risk that does not exist.  i.e. I have to keep the machine up every available minute or we will not be able to ship goods.
    Some thoughts, Tg


    Marc Richardson

    Tg has some good thoughts. The machine is theoretically available 24 hours a day, 7 days a week. It may not be operating for any number of reasons, one of which is ‘not scheduled’. Why is the press not scheduled? Because sales hasn’t sold the capacity. Now we are looking at press uptime with a global perspective. We are no longer limiting the scope of what can be improved to fixing internal lost opportunities.
    Marc Richardson
    Sr. Q.A. Engineer



    I agree with Tom and Marc – they present some viable options. 
    However:  Don’t forget to validate your measurement system before conducting the DOE.  Sounds like this is a brand new key measure that you are considering tracking so, before you perform an analysis such as a DOE, you need to be aware of the amount of variation that your measurement system is contributing to the overall measure.  For objective data like yours, a Gage R&R study or a similar study where sigma of the measurement system is compared to sigma of the measured process should be used.
    Without a validated measurement system, any results that are presented in a DOE can not be trusted!
    Good luck!



    Well, a p chart may SEEM the best, but I don’t believe that you meet the statistical assumptions behind the p chart – ie that each event is independant etc. So, consider the continuous data control charts. From what I understand of your project, I don’t think that there is a perfect chart – each one has its advantages & disadvantages. You will want to think through subgrouping strategies – what are the main driver of downtime – perhaps they do not change for shift 1,2,3…but more day to day? You may do an IMR w/ (the percentage?) I would have to know more about your project to really make any suggestions. So, What questions are you trying to answer? Why are you only considering the staffed machines? a measurement constraint or more due to production requirements? Good luck Ken.


    Rusty Lamont

    Using lean techniques, why not measure Overall Equipment Effectiveness?  This single measure encompases quality, scheduled time, etc. and represents a holistic view.  A project could work to improve OEE by working on key inputs to the equation (i.e. unscheduled downtime, cycle time, etc.).  This represents a fundamental difference in thinking but is worth considering.

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