Interpreting Process Capability

The following is an excerpt from The Quality Engineering Handbook by Thomas Pyzdek, © QA Publishing, LLC.

Perhaps the biggest drawback of using process capability indexes is that they take the analysis a step away from the data. The danger is that the analyst will lose sight of the purpose of the capability analysis, which is to improve quality. To the extent that capability indexes help accomplish this goal, they are worthwhile. To the extent that they distract from the goal, they are harmful. The quality engineer should continually refer to this principle when interpreting capability indexes.

CP
Historically, this is one of the first capability indexes used. The "natural tolerance" of the process is computed as 6s . The index simply makes a direct comparison of the process natural tolerance to the engineering requirements. Assuming the process distribution is normal and the process average is exactly centered between the engineering requirements, a CP index of 1 would give a "capable process." However, to allow a bit of room for process drift, the generally accepted minimum value for CP is 1.33. In general, the larger CP is, the better. The CP index has two major shortcomings. First, it cannot be used unless there are both upper and lower specifications. Second, it does not account for process centering. If the process average is not exactly centered relative to the engineering requirements, the CP index will give misleading results. In recent years, the CP index has largely been replaced by CPK (see below).

CR
The CR index is algebraically equivalent to the CP index. The index simply makes a direct comparison of the process to the engineering requirements. Assuming the process distribution is normal and the process average is exactly centered between the engineering requirements, a CR index of 100% would give a "capable process." However, to allow a bit of room for process drift, the generally accepted maximum value for CR is 75%. In general, the smaller CR is, the better. The CR index suffers from the same shortcomings as the CP index.

CM
The CM index is generally used to evaluate machine capability studies, rather than full-blown process capability studies. Since variation will increase when normal sources of process variation are added (e.g., tooling, fixtures, materials, etc.), CM uses a four sigma spread rather than a three sigma spread.

ZU
The ZU index measures the process location (central tendency) relative to its standard deviation and the upper requirement. If the distribution is normal, the value of ZU can be used to determine the percentage above the upper requirement by using Table 4 in the appendix of The Complete Guide to the CQM. The method is the same as described in Chapter III.B using the Z statistic, simply use ZU instead of using Z. In general, the bigger ZU is, the better. A value of at least +3 is required to assure that 0.1% or less defective will be produced. A value of +4 is generally desired to allow some room for process drift.

ZL
The ZL index measures the process location relative to its standard deviation and the lower requirement. If the distribution is normal, the value of ZL can be used to determine the percentage above the upper requirement by using Table 4 in the appendix of The Complete Guide to the CQM. The method is the same as described in III.B [of The Complete Guide to the CQM] using the Z transformation, except that you use -ZL instead of using Z. In general, the bigger ZL is, the better. A value of at least +3 is required to assure that 0.1% or less defective will be produced. A value of +4 is generally desired to allow some room for process drift.

ZMIN
The value of ZMIN is simply the smaller of the ZL or the ZU values. It is used in computing CPK.

CPK
The value of CPK is simply ZMIN divided by 3. Since the smallest value represents the nearest specification, the value of CPK tells you if the process is truly capable of meeting requirements. A CPK of at least +1 is required, and +1.33 is preferred. Note that CPK is closely related to CP, and that the difference between CPK and CP represents the potential gain to be had from centering the process.

CPM
A CPM of at least 1 is required, and 1.33 is preferred. CPM is closely related to CP. The difference represents the potential gain to be obtained by moving the process mean closer to the target. Unlike CPK, the target need not be the center of the specification range.

Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).