Stable process

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    Please define and explain a stable process in relation to usl, lsl, ucl,lcl and Cp.



    Hi Ganesh,
    You bring up a good question. It’s actually been beaten to death in the past :). You can view a the “best thoughts” here:
    And the full thread and comments on stable processes here:
    I hope these references help.



    I know that this subject was discussed deeply before, but I can’t resist to post again.
    About the links posted by Carol, the only thing that I agree is that not everybody agree about what a stable process is. But I think there is a general agreement about this:
    You can say if a process is stable or not even if no specification is available. For example, I could assess the stability of the UV radiation that reaches the ground. Of course, there is no specification for that, but if I see that suddenly the values goes beyond what it has been in the last years, I can say that there is some unstability in the “process” that makes the UV radiation hit the ground. Maybe there was a change in the ozone layer, or may be tere is a sun storm. But there is something “special” that makes the process behave different from how it was behaving. Another example can be the body temperature. Again, no doctor have ever specified “the temperature must be between 35ºC and 37ºC”, but it is ussually there. The “normal” variation is within this range. We don’t know why sometimes it is 35.7 and some times it is 36.2, but if it goes to 38 we know that that’s not normal, and we look for the “special cause” that pushed the temperature to that value (for example, a virus, an infection, etc.).
    Stability is related with behavior along the time. If the behavior is the same, then the process is stable. If it changes from what was the previous behaviour (or it is changing all the time) then it is non stbale. And non stability is related with this variation that goes beyond the “normal variation”, and then we call it “variation due to special causes”. There are statistical methods to assess stability, such as the control charts. Then we say that a stabyle process is “under statistical control”.
    In short, a stable process, or a process in statistical control (ot just in-control) is one that beaves the same way over the time, or one where only normal variation is pressent (or it is free from variation due to special causes), or one that shows no out-of-control signals in a set of control charts.
    There may be some disagreement about how we understand thas last paragraph, but there should not be much disagreement beyond that.
    Do I mean that a process can be perfectly stable, and still be awfull to meet the specification? Absolutely yes, I do. Imagine I have a turning process. The target value for a diameter is 8, and the process delivers all the time parts with a dimater that can be randomly anywhere between 7.95 an 8.05. Is this process stable? Yes. Does it mets the specification? I don’t know. If the specification is 8 +/-0.1, yes it does. If the specification is 8 +/-0.01, no it does not. BUT CHANGING THE SPECIFICATION DOES NOT CHANGE THE STABILITY CONDITION OF A PROCESS.
    Finally, of course that you don’t need Cp, Cpk, Pp or Ppk to say if a process is stable or not, because you need the specification to get those values (Had I already said that the specification was not needed for stability?).



    I like too much the way you explained it; sometimes you need to post again the same concept because the training is an ongoing process,,, everytime there is somebody that needs a feedback – help from the guys which have the knowledge/ experience..
    Continua asi…



    And I forgot one thing, that is another usual mistake:
    The term “normal variation” only common causes are pressent is sometime misleading, and can be wrongly taken for “normal distribution”. “Normal variation” (sometimes called “noise”, “white noise” or “background noise”) stands for the “variation where only common causes are pressent”, and is not related with the shape of the distribution. On the other hand, a normal distribution stands for the symetrical, bell shaped Gauss distribution, where you have about a 64% of the population within the average +/- 1 sigma, 95% in +/- 2 sigma, 99,7% in +/- 3 sigma and so on.
    If the process delivers the same rectangular shaped distribution in a consistent way over the time, than the process is stable, even when the distribution is not normal. Further more, if the same process sudennly changes to a normal distribution, then it become unstable, because it is not behaving as it was.
    That said, yet a histogram can help to assess the prssence of special causes, and therefore, of unstability. For example, if the histogram shows a well defined distribution (normal shaped or not) but one value is clearly far away from this distribution, probabliy there was a special cause that made this single value so different from the others. A bimodal distribution ussually (but not necessarily) is a signal of unstability too, when this behaviour is due to an overlapping of two different distributions. This is ussually because of mixing two sources of production, as two spindles of a multi-sipindle turning, or two cavities of a mould, or two process lines. But this is not allways the case, as sometimes one sigle source may deliver a bimodal distribution.
    A final concept on stability: You need unstability (meaning that you need a special cause of variation) to move from one stable state to another stable state. For example, imagine that I have a stable process with Cp=2 and Cpk=1.3. I follow the process with control charts that never show OOC signals. I keep the process uncentered because there is a technical limitation to shift the average any further. Then, an improvement team designs a solution for this issue and implement a change that allows to center the process. That is clearly a special cause of variation (making this change is not an inherent part of the process). Be sure, the control chart, with the limits for the previous condition, will show unstability. However, now we can calculate the new control limits and see that the process has reached a new stable condition (as Cp=Cpk=2). Here, the unstability was one single instant, as the “special cause” (the change in the  set-up) occurred only once.
    Other times, however, the unstability remains. For example, you have a stable process but one screw that fixates a stop get loosen, and the process begins to behave in an unpredictable way. Until the special cause remains there (the loosen screw) the process will continue to be unstable.
    As you see, unstability and special causes of variation allways match. The unstable condition will last what the special cause may last.



    Ganesh, read my other messages in this thread. But to focus on your question, it is not possible to either define or explain stability in terms of USL, LSL, UCL, LCL and Cp.
    USL, LSL and Cp have nothing to do with stability, except that you need the process to be stable to calculate Cp.
    UCL and LCL, in a control chart, let you identify one of the out-of-control signals: a point beyond control limits. An OOC signal is a sign of unstability, but there are several other OOC signals (such as trends) that are not related to the UCL or LCL.

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