Ppk versus Cpk

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    We are having a lot of heated discussions about the difference between Ppk and Cpk and when you should use each.  I have searched the web several times and found conflicting opinions and definitions of each! Can anyone help? Thanks!



    The definitions used in Six Sigma come from the AIAG SPC manual (page 79 – 81). Minitab is programed using the definitions given there.



     MiniTab accepted definition used in my company is:
    Cpk, Process Capability, often referred to as ‘Short term’ capability, the potential (within) capability indices are associated with the within-subgroup standard deviation. These indices reflect how the process could perform relative to the specification limits, if the shifts and drifts between subgroups could be eliminated.  The calculation of Cpk in MiniTab takes in to account the effect of time ordering by using the observed level of variation taken from a Moving Range, Range or Sigma control charts.  
    Ppk, Process Performance, often referred to as ‘Long term’ capability, the overall capability indices are associated with the overall sample standard deviation. These indices depict how the process is actually performing relative to the specification limits.  Ppk is calculated by Minitab using the mathematical standard deviation of all the data.  This is the figure that should be reported for Component Proving
     A substantial difference between the overall and within capability indices may indicate that the process is out of control, or the sources of variation are not estimated by within capability.  Ppk will always be less than or equal to Cpk because the process spread predicted by Ppk will always be larger than (or equal to) as it does not take into account the time ordered behaviour of the process. 
    Just to complicate the issue the definitions are reversed in some texts!


    Reigle Stewart

    Sgollus: To help answer your question, I refer you to the
    “Ask Dr. Harry” forum on this site. He states: “One must
    necessarily understand that the short-term standard
    deviation reports on the “instantaneous reproducibility” of
    a process whereas the long-term standard deviation
    reflects the “sustainable reproducibility.” To this end, the
    short-term standard deviation is comprised of the “within
    group” sums-of-squares (SSW). The long-term standard
    deviation incorporates the “total” sums-of-squares (SST).
    Of course, the difference between the two constitutes the
    “between group” sums-of-squares (SSB). By employing a
    rational sampling strategy it is possible to effectively block
    the noises due to assignable causes from those due to
    random causes. In this context, we recognize that SST =
    SSW + SSB. By considering the degrees-of-freedom
    associated with SST and SSW, we are able to compute
    the corresponding variances and then establish the
    respective standard deviations. In the case of a process
    characterization study, we note that the short-term
    standard deviation is given by the quantity Sqrt(SSW / g(n
    – 1)). The long-term standard deviation is defined as
    Sqrt(SST / ng– 1). When computing Cp and Cpk, it is
    necessary to employ the short-term standard deviation.
    This ensures that the given index of capability reports on
    the instantaneous reproducibility of the process under
    investigation. So as to reflect the sustainable
    reproducibility of the process, the long-term standard
    deviation must be employed to compute Pp and Ppk.
    Oddly enough, many practitioners confuse these two
    overlapping sets of performance indices.”

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