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Capability Analysis
An important technique used to determine how well a process meets a set of specification limits is called a process capability analysis. A capability analysis is based on a sample of data taken from a process and usually produces:
1. An estimate of the DPMO (defects per million opportunities).
2. One or more capability indices.
3. An estimate of the Sigma Quality Level at which the process operates.
STATGRAPHICS provides capability analyses for the following cases:
1. Measurement data for uncorrelated variables. This is appropriate for variables that operate independently of one another and for which it is sufficient to make separate capability statements about each. The analysis may be based on the Gaussian distribution or any of 25 other probability distributions.
2. Measurement data for correlated variables. This is used for variables that tend to move together and which must be considered simultaneously in order to make a proper statement about the capability of the process.
3. Attribute data that occur in the form of counts or proportions. The analysis may be based on either a binomial or hypergeometric distribution.
4. Attribute data that occur in the form of rates. The analysis may be based on either a Poisson or negative binomial distribution.
Capability Analysis for Uncorrelated Measurements
Traditionally, process capability analysis has been based on the assumption that each variable that characterizes a product or service behaves independently. In such cases, it is sufficient to make separate capability statements about each. Unless the defect rate is high, so that there is a significant chance that more than one variable will be out of spec at the same time, the overall capability can be calculated from the sum of the defect rates of each response.
For such data, STATGRAPHICS calculates the DPMO and capability indices for each variable separately. Any of 26 probability distributions may be used. A typical capability plot is shown below:
Capability Analysis for Correlated Measurements
When the variables that characterize a process are correlated, separately estimating the capability of each may give a badly distorted picture of how well the process is performing. In such cases, it is necessary to estimate the joint probability that one or more variables will be out of spec. This requires fitting a multivariate probability distribution, an example of which is shown below:
Capability Analysis for Counts or Proportions
When examination of an item or event results in a PASS or FAIL rather than a measurement, the capability analysis must be based on a discrete distribution. For very large lots, the relevant distribution is the binomial. For small lots or cases of limited opportunities for failure, the hypergeometric distribution must be used:
When the relevant measure of performance is a rate, then the capability analysis is based on: a Poisson distribution if failures occur randomly; a negative binomial distribution if failures tend to occur in clumps.
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