What is the meaning of "k" in Cpk and Ppk? And Cpk vs. Ppk

antoine.dias

Quite Involved in Discussions
#11
Re: Cp vs. Cpk - What is the difference - A visual animation

Marc said:
  • Cmk – Machine capability
  • Cpk – Process capability index
  • Cpm – Targeted capability index
  • Ppk – Performance capability index
  • Ppk – Preliminary process capability index (had to use it for Ford in
    the start up of new projects)

Are Cpk & Ppk acronyms? If so, what do they actually mean or represent?

From a link:

Can anyone summarize when to use Cpk vs. Ppk - And why?
Cpk is used as a capability index using the variation in the sample with the formula of R(bar)/d2.
Ppk is used as a performance index using the standard variation formula calculated over the set of measured individual measurements (not the variation in the sample)

Best regards,

Antoine
 
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sushant_kulkarni

Involved In Discussions
#12
Re: What is the differents between cp and cpk?

Process range. First, it is customary to establish the ± 3 sigma limits around the nominal specifications. Actually, the sigma limits should be the same as the ones used to bring the process under control using Shewhart control charts (see Quality Control). These limits denote the range of the process (i.e., process range). If we use the ± 3 sigma limits then, based on the normal distribution, we can estimate that approximately 99% of all piston rings fall within these limits.

Specification limits LSL, USL. Usually, engineering requirements dictate a range of acceptable values. In our example, it may have been determined that acceptable values for the piston ring diameters would be 74.0 ± .02 millimeters. Thus, the lower specification limit (LSL) for our process is 74.0 - 0.02 = 73.98; the upper specification limit (USL) is 74.0 + 0.02 = 74.02. The difference between USL and LSL is called the specification range.

Potential capability (Cp). This is the simplest and most straightforward indicator of process capability. It is defined as the ratio of the specification range to the process range; using ± 3 sigma limits we can express this index as:

Cp = (USL-LSL)/(6*Sigma)

Put into words, this ratio expresses the proportion of the range of the normal curve that falls within the engineering specification limits (provided that the mean is on target, that is, that the process is centered, see below).

Bhote (1988) reports that prior to the widespread use of statistical quality control techniques (prior to 1980), the normal quality of US manufacturing processes was approximately Cp = .67. This means that the two 33/2 percent tail areas of the normal curve fall outside specification limits. As of 1988, only about 30% of US processes are at or below this level of quality (see Bhote, 1988, p. 51). Ideally, of course, we would like this index to be greater than 1, that is, we would like to achieve a process capability so that no (or almost no) items fall outside specification limits. Interestingly, in the early 1980's the Japanese manufacturing industry adopted as their standard Cp = 1.33! The process capability required to manufacture high-tech products is usually even higher than this; Minolta has established a Cp index of 2.0 as their minimum standard (Bhote, 1988, p. 53), and as the standard for its suppliers. Note that high process capability usually implies lower, not higher costs, taking into account the costs due to poor quality. We will return to this point shortly.

Capability ratio (Cr). This index is equivalent to Cp; specifically, it is computed as 1/Cp (the inverse of Cp).

Lower/upper potential capability: Cpl, Cpu. A major shortcoming of the Cp (and Cr) index is that it may yield erroneous information if the process is not on target, that is, if it is not centered. We can express non-centering via the following quantities. First, upper and lower potential capability indices can be computed to reflect the deviation of the observed process mean from the LSL and USL.. Assuming ± 3 sigma limits as the process range, we compute:

Cpl = (Mean - LSL)/3*Sigma
and
Cpu = (USL - Mean)/3*Sigma

Obviously, if these values are not identical to each other, then the process is not centered.

Non-centering correction (K). We can correct Cp for the effects of non-centering. Specifically, we can compute:

K=abs(D - Mean)/(1/2*(USL - LSL))

where

D = (USL+LSL)/2.

This correction factor expresses the non-centering (target specification minus mean) relative to the specification range.

Demonstrated excellence (Cpk). Finally, we can adjust Cp for the effect of non-centering by computing:

Cpk = (1-k)*Cp :)

If the process is perfectly centered, then k is equal to zero, and Cpk is equal to Cp. However, as the process drifts from the target specification, k increases and Cpk becomes smaller than Cp.
 
A

artichoke

#13
Re: What is the differents between cp and cpk?

If we use the ± 3 sigma limits then, based on the normal distribution, we can estimate that approximately 99% of all piston rings fall within these limits.
Control limits are not probability limits. They do not give a probability of events falling outside limits.

Potential capability (Cp). This is the simplest and most straightforward indicator of process capability.
"Capability" means the capability of a process to meet specifications. This can only occur if a process is in statistical control. Capability indexes do not in themselves provide this information. A process that is out of control may fail to meet specifications, not matter where spec limits have been set.

Put into words, this ratio expresses the proportion of the range of the normal curve that falls within the engineering specification limits
We never know the true distribution of data. There is no justification for assuming normality.

Interestingly, in the early 1980's the Japanese manufacturing industry adopted as their standard Cp = 1.33!
There is no problem with this for well controlled processes.

If the process is perfectly centered, then k is equal to zero, and Cpk is equal to Cp. However, as the process drifts from the target specification, k increases and Cpk becomes smaller than Cp.
It is possible to have Cpk less than 1.0 and still have all data within spec. Capability ratios can be quite misleading. They should always be used in conjunction with control charts and histograms. Those looking for numbers to present to management might better consider MSD, Mean Square Deviation About Target. This gives a measure of how a stable process is performing relative to "on target with minimum variance".
 
D

dknox4

#14
Cp = the ratio of the process spread to the specification tolerence.

Cpk = the lowest ratio of the above when the process spread is centered on the specification mid-point.

Cpk is always lower or, at best equal, to the Cp because of the centering. Rarely does the mean of the process fall exactly on the mean of the spec.
 

Stijloor

Staff member
Super Moderator
#15
The origins of k actually go back to the 1970s in Japan. The Japanese are credited with developing the the Cp, Cpl, Cpu, Cpk, and k indexes of process capability.

So what is k? It is an index of process centering, defined as follows, where M is the middle of the tolerance, mu is the process average, USL is the upper spec limit, and LSL is the lower spec limit:

k = |M - mu| / [(USL - LSL) / 2]

k is then used as follows to compute Cpk.

Cpk = Cp (1 - k)

When the process average is centered at the middle of the tolerance, M = mu, and therefore, M - mu = 0. With k = 0, Cpk will equal Cp.

Cpk = Cp (1 - 0) = Cp

If the process average is centered anywhere else, then the absolute value of the quantity M - mu is greater than zero, making k also greater than 0. Suppose k is 0.30 for a process. Then the Cpk index for this process is only 70% of the Cp index.

Cpk =Cp (1 - 0.30) = 0.70Cp

So in one way, k measures how much potential capability is lost due to poor centering. In the above example, Cpk could be increased by 30% if we could center mu at M.
 
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