Cpk and Ppk ?

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    Dear 6 Sigma guys,
    I’ve confused in the Cpk and Ppk in some areas. If the former is long term and sigma is wtihin subgroup, the latter is short term. and sigma is overall (within and between subgroup). Meanwhile we know the Ppk is for let’s say one lot, that is no subgroups. If in that case, how come with between subgroup variations.
    2nd, Can we say, if the process is stable, Ppk would be almost equal to Cpk.
    P.s. Cpk (sigma=R bar/D2)
           Ppk (sigma=total individual variation)    



    Short term variablility is within-subgroup and should display only common-cause variation. Long Term variability is characterized by the between-group shift and may display both common and special-cause variability.
    Many statistical software pakages estimate short-term using Pooled Std. Deviation in the case of subgroups > 1 or Avg. Moving Range assuming a subgroup = 1.
    If you have a stable process (i.e. no special-cause variability and hence no shift between-groups) then yes, Ppk would be almost equal to Cpk.



    Further to Matt’s answer ..
    – Few process engineers would estimate a process capability or process performance on any less than 30 subgroups – typically a single page of a X-bar and R chart. No one in their right mind would base any of the above on a subgroup size of n = 3 to 5.
    – Years ago, process sigma was often estimated using a rule of thumb, n = 30. But typically this was only to compare equipment, or types of processes, before starting a ‘full characterisation.’ ( A procedure to find sources of variation and to find out what happens when control factors are disturbed.)
    – The question of a subroup bias (or shift) arose when considering how to ‘set ‘ a process using Pre-Control, using a small subgroup of n = 3 to 5, instead of a single ‘first off.’
    What advocates of the bias or (shift) do not take into account is the fact that the outcome of a process is higly autocorrelated to previous runs – for the same set of control factors – unlike random numbers. Since the usual statistical approach is to use a null hypothesis, once an X-bar and R chart has been constructed; special causes removed; and control limits calculated; very small shifts can be detected, and there seems to be little justification for a constant bias (shift.)
    – In my opinion, the introducation of the bias or shift along with the comcommitant Ppp and Ppk has done more harm than good. Prior to about 1990, there was none of this confusion -until you know who tried to ‘improve’ the original six sigma.
    Since 1990, there has been a continual decline in Moto’s quality so that now their mobile phones are widely considered to have the worst reliablity. Anyone for a t-test?



    Cpk is short term = process capability. Sigma estimated as per Matt posted.
    Ppk is long term = process performance. Sigma estimated using all data point.
    If only 1 group or data is using, the calculated is Cpk, can substract by 0.5 (=1.5 sigma shift in mean) as Ppk.



    Thank you for stating the obvious ..
    You are quite right … a subgroup of 1 would be subject to a bias or shift of 1.5 sigma. But how would a process engineer interpret this on  an X-bar and R chart with control limits are based on 30 subgroups, or even 10 subgroups of n = 3?
    What do most process engineers do when they detect a pre-control subgroup with a subgroup average outside control limits – they run more tests, and the reason is that process output is correlated through the process settings. And the proof of the pudding is in the results. In 1989. we achieved Cpk = 2 over an eight month period for effective channel lengths by not ‘tweaking’ the original control limits, and always taking ‘immediate corrective action.’
    I look forward to continuing this debate with you ..
    Best regards,



    Be careful with the term “term”.
    Cpk is withins subgroup, as you said. The within subgroup variation is also called “short term variation” in the Six Sigma argot, because it is a measure of the “repeatability” or “part to part” variation (and part to part is short term).
    Cpk is NOT between subgrups. It is TOTAL (between + within). Wether you have subgroups or not, the variation of a process (for example during a lot) will have part to part variation and also variation that cannot be explained due to part-to-pat variation only (imagine, for example, a process that difts). If you plotted a control chart you will see the “between subgroups variation” as out-of-control signals. If you don’t plot a control chart, that variation will be there anyway.
    If the process was perfectly stable, then the real process’ Cpk and Ppk would be identical, not almost equal. The problem is that you never know the real values, just estimations based on the sample which are affected by sampling variation. If the process was fully stable, the estimations will be close one from the other, but small sample sizes (few subgroups of few parts) can make this difference pretty big due to sampling variation.

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