Here are the definitions of the terms that you asked about:
Cp is a capability index defined as the ratio of the specification spread (USL - LSL) to the potential process spread (6 times the total (between and within) subgroup standard deviation).
Cp does not consider the location of the process mean in relation to the specification interval, so it is a measure of the capability your process could achieve if centered between the specification limits.
Cpk is a capability index that equals the minimum of CPU and CPL.
Cpk considers the location of the process mean relative to the specification interval, so it is a measure of how the process is actually performing.
Pp is a capability index calculated as follows:
Given the measurements for the whole process, the shape and scale parameters are estimated (if not specified by the user).
Given the lower specification limit (LSL) and the upper specification limit (USL), two probabilities are calculated:
· p1 is the probability that a randomly-selected measurement from the Weibull distribution is less than LSL
· p2 is the probability that a randomly-selected measurement from the Weibull distribution is greater than USL
Let Z1 = p1*100 th percentile, and Z2 = p2*100 th percentile of the standard normal distribution.
Then, Pp equals (Z2-Z1) / 6.
Ppk is another capability index. It equals the minimum of PPL and PPU.
PPL is a capability index defined as the ratio of the interval formed by the process mean and LSL to the one-sided spread of the process (represented by three times the overall standard deviation).
PPU is a capability index defined as the ratio of the interval formed by the process mean and USL to the one-sided spread of the process (represented by three times the overall standard deviation).
Cm is the ratio between the distance from to the target value M and half the range of the tolerance interval.
Cp/Cpk are capability indices that only apply to stable processes. The data must be free of special cause variation, and should be normally distributed. This is usually demonstrated by a control chart that is in statistical control (no out of control rules violations). Cp is a measure of how good the process could be if only common cause variation was present and the mean of the process was targeted at the nominal of the specification. Cpk includes the effect of targeting, and will always be less than or equal to Cp.
Pp/Ppk are performance indices. Stability is not a requirement for Pp/Ppk. Both common cause variation and special cause variation are included in the Pp/Ppk calculation.
Note, when sampling, common cause variation is from the within subgroup variation, and the special cause is between subgroup variation.
The formulas for Cp and Pp are essentially identical, as are the formulas for Ppk and Cpk. The only difference is how the standard deviation is calculated. For Cp and Cpk, the standard deviation is estimated by R-bar/d2 from a stable process. For Pp and Ppk, the standard deviation formulais used (SQRT of the sum of squares of xi - Xbar/n-1).
Pp/Ppk, because it can be used on data that is non-normal and unstable, is not a predictive indice. It can describe a finite set of data, but will not give any prediction in the future output of the process.
Cp/Cpk, because it is established from data that is stable (an in-control process where only common cause variation is present) is a predictive indice. You can expect the process to continue to run at the same capability until a process change occurs. It is important to continue sampling and utilizing control charts to identify when such a change has occurred.
Cm/Cmk are indices that were created by Q-Das, Inc. (a statistical software and process control software company) to differentiate between machine capability and process capability. There is no fundamental difference between these indices and Cp/Cpk. I would not recommend using them as they are not recognized outside of companies that do not use their software (although Q-Das methodology has been adopted by the VDA - the German equivalent of the AIAG).
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dlhunt 12/10/2003
Here are the definitions of the terms that you asked about:
Cp is a capability index defined as the ratio of the specification spread (USL - LSL) to the potential process spread (6 times the total (between and within) subgroup standard deviation).
Cp does not consider the location of the process mean in relation to the specification interval, so it is a measure of the capability your process could achieve if centered between the specification limits.
Cpk is a capability index that equals the minimum of CPU and CPL.
Cpk considers the location of the process mean relative to the specification interval, so it is a measure of how the process is actually performing.
Pp is a capability index calculated as follows:
Given the measurements for the whole process, the shape and scale parameters are estimated (if not specified by the user).
Given the lower specification limit (LSL) and the upper specification limit (USL), two probabilities are calculated:
· p1 is the probability that a randomly-selected measurement from the Weibull distribution is less than LSL
· p2 is the probability that a randomly-selected measurement from the Weibull distribution is greater than USL
Let Z1 = p1*100 th percentile, and Z2 = p2*100 th percentile of the standard normal distribution.
Then, Pp equals (Z2-Z1) / 6.
Ppk is another capability index. It equals the minimum of PPL and PPU.
PPL is a capability index defined as the ratio of the interval formed by the process mean and LSL to the one-sided spread of the process (represented by three times the overall standard deviation).
PPU is a capability index defined as the ratio of the interval formed by the process mean and USL to the one-sided spread of the process (represented by three times the overall standard deviation).
Cm is the ratio between the distance from to the target value M and half the range of the tolerance interval.
A good reference web site is:
Home page of the NIST Engineering Statistics Handbook
http://www.itl.nist.gov/div898/handbook/
Process Capability section:
http://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm
9/22/2006
Cp/Cpk are capability indices that only apply to stable processes. The data must be free of special cause variation, and should be normally distributed. This is usually demonstrated by a control chart that is in statistical control (no out of control rules violations). Cp is a measure of how good the process could be if only common cause variation was present and the mean of the process was targeted at the nominal of the specification. Cpk includes the effect of targeting, and will always be less than or equal to Cp.
Pp/Ppk are performance indices. Stability is not a requirement for Pp/Ppk. Both common cause variation and special cause variation are included in the Pp/Ppk calculation.
Note, when sampling, common cause variation is from the within subgroup variation, and the special cause is between subgroup variation.
The formulas for Cp and Pp are essentially identical, as are the formulas for Ppk and Cpk. The only difference is how the standard deviation is calculated. For Cp and Cpk, the standard deviation is estimated by R-bar/d2 from a stable process. For Pp and Ppk, the standard deviation formulais used (SQRT of the sum of squares of xi - Xbar/n-1).
Pp/Ppk, because it can be used on data that is non-normal and unstable, is not a predictive indice. It can describe a finite set of data, but will not give any prediction in the future output of the process.
Cp/Cpk, because it is established from data that is stable (an in-control process where only common cause variation is present) is a predictive indice. You can expect the process to continue to run at the same capability until a process change occurs. It is important to continue sampling and utilizing control charts to identify when such a change has occurred.
Cm/Cmk are indices that were created by Q-Das, Inc. (a statistical software and process control software company) to differentiate between machine capability and process capability. There is no fundamental difference between these indices and Cp/Cpk. I would not recommend using them as they are not recognized outside of companies that do not use their software (although Q-Das methodology has been adopted by the VDA - the German equivalent of the AIAG).