Capability analysis measures the ability of a process to meet specifications when the process is in statistical control.
A process must be in control before attempting to assess the capability. An out-of-control process is unpredictable and not capable of been characterized by a probability distribution.
Most process capability indices assume a normally distributed quality characteristic. If the distribution is non-normal, it may be possible to transform the data to be normally distributed. The process mean and process sigma define the normal distribution.
If the process is stable over time, the estimates of short-term sigma and long-term sigma are very similar. They are both estimates of the same parameter, although statistically speaking the long-term sigma is a slightly more efficient estimator.
However, if there are any changes in the process mean over time, the estimate of long-term sigma is greater than that of short-term sigma. The larger the difference between the values of long-term and short-term indices, the more opportunity there is to improve the process by eliminating drift, shifts and other sources of variation.
Capability ratios (Cp/Pp) describe the variability of a process relative to the specification limits.
A capability ratio is a unit-less value describing the ratio of process distribution spread to specification limits spread. A value of less than 1 is unacceptable, with values greater than 1.33 (1.25 for one-sided specification limits) widely accepted as the minimum acceptable value, and values greater than 1.50 (1.45 for one-sided specification limits) for critical parameters (Montgomery, 2012). The higher the value, the more capable the process of meeting specifications. A value of 2 or higher is required to achieve Six Sigma capability which is defined as the process mean not closer than six standard deviations from the nearest specification limit.
All of the indices assume a normally distributed process quality characteristic with the parameters specified by the process mean and sigma. The process sigma is either the short-term or long-term sigma estimate.
Indices computed using the short-term sigma estimate are called Cp indices (Cp, Cpl, Cpu, Cpk, Cpm). While those using long-term sigma estimate are called Pp indices (Pp, Ppl, Ppu, Ppk, Ppm). If the Cp indices are much smaller than the Pp indices, it indicates that there are improvements you could make by eliminating shifts and drifts in the process mean.
| Index | Purpose |
|---|---|
| Cp/Pp | Estimates the capability of a process if the process mean were to be centered between the specification limits. Note: If the process mean is not centered between the specification limits the value is only the potential capability, and you should not report it as the capability of the process.
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| Cpl/Ppl | Estimates the capability of a process to meet the lower specification limit. Defined as how close the process mean is to the lower specification limit. |
| Cpu/Ppu | Estimates the capability of a process to meet the upper specification limit. Defined as how close the process mean is to the upper specification limit. |
| Cpk/Ppk | Estimates the capability of a process, considering that the process mean may not be centered between the specification limits. Defined as the lesser of Cpl and Cpu. Note: If Cpk is equal to Cp, then the process is centered at the midpoint of the specification limits. The magnitude of Cpk relative to Cp is a measure of how off center the process is and the potential improvement possible by centering the process.
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| Cpm/Ppm | Estimates the capability of a process, and is dependent on the deviation of the process mean from the target. Note: Cpm increases as the process mean moves towards the target. Cpm, Cpk, and Cp all coincide when the target is the center of the specification limits and the process mean is centered.
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Z benchmark describes the sigma capability of a process.
Z benchmark indices are an alternative to Cp and Pp indices. They are the definition of the sigma capability of a Six Sigma process.
All of the indices assume a normally distributed process quality characteristic with the parameters specified by the process mean and sigma. The process sigma is either the short-term or long-term sigma estimate.
| Index | Description |
|---|---|
| < LSL | The number of sigma units from the process mean to the lower specification limit. |
| > USL | The number of sigma units from the process mean to the upper specification limit. |
| < SL > | The number of sigma units from the process to mean to the point if all nonconforming units are put in one tail of the distribution. |
Z shift is the difference between the short-term and long-term indices. The larger the Z shift, the more scope there is to improve the process by eliminating shifts and drifts in the process mean. Some industries define the sigma capability of a process as the long-term Z benchmark + a 1.5 Z shift. Meaning a process with a long-term Z benchmark of 4.5 is quoted as a Six Sigma process. It is best to avoid such rules and directly measure the short-term and long-term Z benchmark capability.
Nonconforming units describe the number of nonconforming units a process produces, expressed in parts per million.
The number of nonconforming units is an alternative to traditional Cp and Pp indices. They are easily understandable by end-users.
| Index | Description |
|---|---|
| < LSL | The number of nonconforming units that are less than the lower specification limit. |
| > USL | Thr number of nonconforming units that are greater than the upper specification limit. |
| < SL > | The total number of nonconforming units that are outside the specification limits. |
Plot a process capability histogram and compute indices to determine if a process can meet specifications.
