Measure – Capability Analysis


Process Capability Analysis

A capable process meets customer requirements 100% of the time. Customer requirements are defined using an upper specification limit (USL) and a lower specification limit (LSL). Think of these specification limits as goal posts.

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Not Capable
Capable
Not Capable to Centered & Capable
histogram1
Cp < 1, Cpk <1
histogram2
Cp >= 1, Cpk >= 1
histogram-compare

Process capability analysis determines how well the output of a stable process meets these specifications using the following metrics:

Cp and Cpk
Process Capability Metrics

  • Cp measures how well the data would fit within the spec limits (USL, LSL)
  • Cpk measures how centered the data is between the spec limits.

Use Cp Cpk  when you have a sample, not the population, and are testing the potential capability of a process to meet customer needs.

Cp and Cpk use Sigma estimator.

Pp and Ppk
Process Performance Metrics

  • Pp measures how well the data would fit within the spec limits (USL, LSL)
  • Ppk measures how centered the data is between the spec limits.

Use Pp Ppk when you have the total population and are testing the performance of a system to meet customer needs.

Pp, Ppk use standard deviation.

Cp vs Cpk Examples

Fits But Is Not Centered

not-centered

Process improvement goal is to make changes that will move the output closer to the target without increasing variation.

Centered But Does Not Fit

centered

Process improvement goal is to reduce variation so that the process fits between the spec limits.

 

Capability Analysis Metrics Rules of Thumb

Cp>1 Process is capable (product will fit between the customer’s upper and lower specification limits if the process is centered).

Cpk>1 Process is capable and centered between the LSL and USL.

If Cp=Cpk the process is centered at the midpoint of the specification limits.

If Cp>Cpk the process is off-center.

Cp and Cpk should be close in value to Pp and Ppk.

If Cp and Cpk are much greater than Pp or Ppk (33% greater), your process may not be stable enough to conduct a capability analysis. Use control charts to evaluate the stability of your process.

 

Capability Suite of Six Charts Created Using the QI Macros

capability-suite

The Capability Suite Six Charts:

These are the same six charts included in Minitab’s Capability Sixpack™

  • X Chart (XmR for individual data, Xbar for 2+ samples) to evaluate stability.
  • Range or Standard Dev Chart (R for n<5; S for n<4) to evaluate stability.
  • Values Plot of individual data points.
  • Histogram with Cp, Cpk, Pp, Ppk to evaluate capability.
  • Probability Plot for analysis of normality of the data.
  • Capability Plot of within and overall variation vs specification limits.

One Sided Spec Limits
If you need to perform a one tailed capability analysis, just delete the formula in either the USL or LSL field.

Cp and Cpk Calculation Mistakes to Avoid

Most people try to calculate Cp as the upper spec limit minus the lower spec limit divided by six times the standard deviation:

Cp = (USL-LSL)/6*Stdev
However, this is actually the formula for process performance (Pp).

The QI Macros Cp Cpk template uses the correct formula which estimates the standard deviation from the average of the ranges divided by a constant (Rbar/d2).

Cp = (USL-LSL)/6*Rbar/d2
The same is true for Cpk.

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