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The process capability index, or process capability ratio, is a statistical measure of
process capability The process capability is a measurable property of a process to the specification, expressed as a process capability index (e.g., Cpk or Cpm) or as a process performance index (e.g., Ppk or Ppm). The output of this measurement is often illustra ...
: the ability of an engineering
process A process is a series or set of activities that interact to produce a result; it may occur once-only or be recurrent or periodic. Things called a process include: Business and management *Business process, activities that produce a specific se ...
to produce an output within
specification A specification often refers to a set of documented requirements to be satisfied by a material, design, product, or service. A specification is often a type of technical standard. There are different types of technical or engineering specificati ...
limits. The concept of process capability only holds meaning for processes that are in a state of statistical control. This means it cannot account for deviations which are not expected, such as misaligned, damaged, or worn equipment. Process capability indices measure how much "natural variation" a process experiences relative to its specification limits, and allows different processes to be compared to how well an organization controls them. Somewhat counterintuitively, higher index values indicate better performance, with zero indicating high deviation.


Example for non-specialists

A company produces axles with nominal diameter 20 mm on a lathe. As no axle can be made to ''exactly'' 20 mm, the designer specifies the maximum admissible deviations (called tolerances or specification limits). For instance, the requirement could be that axles need to be between 19.9 and 20.2 mm. The process capability index is a measure for how likely it is that a produced axle satisfies this requirement. The index pertains to statistical (natural) variations only. These are variations that naturally occur without a specific cause. Errors not addressed include operator errors, or play in the lathe's mechanisms resulting in a wrong or unpredictable tool position. If errors of the latter kinds occur, the process is not in a state of statistical control. When this is the case, the process capability index is meaningless.


Introduction

If the upper and lower
specification A specification often refers to a set of documented requirements to be satisfied by a material, design, product, or service. A specification is often a type of technical standard. There are different types of technical or engineering specificati ...
limits of the process are USL and LSL, the target process mean is T, the estimated mean of the process is \hat and the estimated variability of the process (expressed as a
standard deviation In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
) is \hat, then commonly accepted process capability indices include: \hat is estimated using the
sample standard deviation In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
.


Recommended values

Process capability indices are constructed to express more desirable capability with increasingly higher values. Values near or below zero indicate processes operating off target (\hat far from T) or with high variation. Fixing values for minimum "acceptable" process capability targets is a matter of personal opinion, and what consensus exists varies by industry, facility, and the process under consideration. For example, in the automotive industry, the
Automotive Industry Action Group The Automotive Industry Action Group'' (AIAG) is a not-for-profit association founded in 1982 and based in Southfield, Michigan. It was originally created to develop recommendations and a framework for the improvement of quality in the North Amer ...
sets forth guidelines in the Production Part Approval Process, 4th edition for recommended Cpk minimum values for critical-to-quality process characteristics. However, these criteria are debatable and several processes may not be evaluated for capability just because they have not properly been assessed. Since the process capability is a function of the specification, the Process Capability Index is only as good as the specification. For instance, if the specification came from an engineering guideline without considering the function and criticality of the part, a discussion around process capability is useless, and would have more benefits if focused on what are the real risks of having a part borderline out of specification. The loss function of Taguchi better illustrates this concept. At least one academic expert recommends the following: However where a process produces a characteristic with a capability index greater than 2.5, the unnecessary precision may be expensive.


Relationship to measures of process fallout

The mapping from process capability indices, such as Cpk, to measures of process fallout is straightforward. Process fallout quantifies how many defects a process produces and is measured by DPMO or PPM. Process yield is the complement of process fallout and is approximately equal to the area under the
probability density function In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can ...
\Phi(\sigma) = \frac \int_^\sigma e^ \, dt if the process output is approximately normally distributed. In the short term ("short sigma"), the relationships are: In the long term, processes can shift or drift significantly (most
control chart Control charts is a graph used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. (ISO 7870-1) The hourly status is arranged on the graph, and the occurrence of abnormalit ...
s are only sensitive to changes of 1.5σ or greater in process output). If there was a 1.5 sigma shift 1.5σ off of target in the processes (see Six Sigma), it would then produce these relationships: Because processes can shift or drift significantly long term, each process would have a unique sigma shift value, thus process capability indices are less applicable as they require statistical control.


Example

Consider a quality characteristic with target of 100.00 μm and upper and lower specification limits of 106.00 μm and 94.00 μm respectively. If, after carefully monitoring the process for a while, it appears that the process is in control and producing output predictably (as depicted in the
run chart A run chart, also known as a run-sequence plot is a graph that displays observed data in a time sequence. Often, the data displayed represent some aspect of the output or performance of a manufacturing or other business process. It is therefore ...
below), we can meaningfully estimate its mean and standard deviation. If \hat and \hat are estimated to be 98.94 μm and 1.03 μm, respectively, then The fact that the process is running off-center (about 1σ below its target) is reflected in the markedly different values for Cp, Cpk, Cpm, and Cpkm.


See also

*
Process (engineering) In engineering, a process is a series of interrelated tasks that, together, transform inputs into a given output. These tasks may be carried out by people, nature or machines using various resources; an engineering process must be considered in t ...
*
Process capability The process capability is a measurable property of a process to the specification, expressed as a process capability index (e.g., Cpk or Cpm) or as a process performance index (e.g., Ppk or Ppm). The output of this measurement is often illustra ...
*
Process performance index In process improvement efforts, the process performance index is an estimate of the process capability of a process during its initial set-up, ''before'' it has been brought into a state of statistical control. Formally, if the upper and lower spe ...


References

{{DEFAULTSORT:Process Capability Index Index numbers Quality control