iSixSigma

SPC: Interpreting a Value on the Lower Bound

Six Sigma – iSixSigma Forums General Forums Tools & Templates SPC: Interpreting a Value on the Lower Bound

Viewing 7 posts - 1 through 7 (of 7 total)
  • Author
    Posts
  • #55715

    Marcus
    Participant

    Hi,

    I have a process which has a lower bound of zero (meaning that the theoretical LCL is less than zero, but the series cannot have a negative value). One of the values observed in the series for which I am constructing the control chart is, in fact, zero.

    I have two questions: 1. In terms of Rule One of the Nelson Rules, how does one interpret a value which is exactly equal to the UCL or LCL? In theory, I would suppose that this would not meet Rule 1, because the value does not lie outside the line. But this seems like a bit of a semantic distinction. I suppose this is a bit like the “what if the p-value is exactly 0.05?” question.

    2. In any case, if there is a lower bound on a process, does it have the same status as the LCL?

    If the answer to both of these questions is yes, then theoretically, my process is out of control if one of the values is zero.

    To me, the answer seems likely to be “yes” to the first question and “no” to the second – that is, a value which is exactly equal to the control limit might not technically meet Rule 1, but that it would be acceptable to exercise a degree of common sense/qualitative interpretation and say that it did. However, on the second point, logically, if a process is bounded by zero and the theoretical control limit is negative, then a value which is zero is not indicative of a process being out of control.

    However, I would be keen to hear others’ thoughts.

    0
    #201300

    Chris Seider
    Participant

    Typically lower bounds are physical boundaries so it’s not even possible to violate that limit if it’s set appropriately.

    e.g. cycle time can never be less than 0 minutes/0 seconds in manufacturing in our world.

    0
    #201301

    Marcus
    Participant

    Yes, that’s my question. The value of the data point is precisely zero, which is also the lower bound. I am assuming that, since the lower bound is greater than the LCL, this does not indicate that the process is out of control. I.e. the lower bound does not have the same meaning as the LCL. Is this the case?

    0
    #201302

    Robert Butler
    Participant

    You’re not computing your limits correctly. If, as @cseider noted, you have a process that has a physical limitation which cannot be exceeded then that is your lower bound. What you need to do is run an analysis on the log of the measured variable and then back transform the mean and the control limits. When you do this you will not have meaningless negative control limits.

    As for the point on the line – If you have a data point that is exactly on the lower bound then there is nothing to worry about because the rule is that you are out of control if you exceed a bound…and this you have not done.

    0
    #201306

    Strayer
    Participant

    You might do some research on one-sided control charts.

    0
    #201307

    MBBinWI
    Participant

    @8sigma – depending on where your data lies compared to the boundary condition (in this case the lower bound being zero), you may or may not have a distribution that is reasonably normal. If very close to the boundary (as yours appears to be), you at the very least have a clipped distribution (this would occur when you have an actual normal distribution, but some portion – that under the LSL for example – is excluded from the data set), or more likely you have a non-normal distribution. Time and physical boundaries can exist where zero is an absolute. If your data always resides sufficiently far away from the boundary (at least three std dev or more) then you should not run into a boundary issue with a control chart. If closer, then you can run into problems. And you always want to check for normality and evaluate for special cause issues.

    0
    #201312

    Rip Stauffer
    Guest

    It’s really not that complicated, for a couple of reasons. Rule 1 of the Western Electric Zone Tests applies to observations outside the limits. So if a value falls exactly on the limit, we usually would not evaluate that value as an assignable cause signal.

    In this case, your lower bound is zero…the usual interpretation of that boundary is that it’s the lowest value the measurement can take. So, if a zero is a possibility in your process, then having a zero appear is not unexpected (and would not be considered an unusual event), right?

    0
Viewing 7 posts - 1 through 7 (of 7 total)

You must be logged in to reply to this topic.