Cp - Cpk - Pp - Ppk

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The key metrics which report on process capability for continuous data are Cp and Cpk, Pp and Ppk.

Process Capability Indices - Cp


Purpose

To determine whether a process, given its natural short-term variation, has the potential capability to meet established customer requirements or specifications.

Cp is a ratio of the tolerance width to the short-term spread of the process. Cp does not consider the center of the process. It estimates the "instantaneous capability" of the process.


Anatomy

Process Capability

Cp is the short term level of performance.

Reference: Juran's Quality Control Handbook

Terminology

A. Process capability index: Indicates the short-term level of performance that a process can potentially achieve.

B. Tolerance width: Upper Specification Limit (USL) minus Lower Specification Limit (LSL).

C. Short-term process spread: Represents six times the short-term standard deviation (±3 sigma ST).

D. See below:

  • Cp < 1: The process output exceeds specifications. The process is incapable.
  • Cp = 1: The process barely meets specifications. There is a probability that at least 0.3% defects will be produced and even more if the process is not centered.
  • Cp > 1: The process output falls within specifications, but, defects might be produced if the process is not centered on the target value.
  • Cp = 2: Represents the short-term objective for process capability. Since Zst = 3 x Cp, we achieve 6 sigma when Cp = 2.

Major Considerations

Cp is used for continuous data and is based on several assumptions. Cp assumes that the process is statistically stable and that its data is approximately normally distributed.

If the distribution of the data is very skewed, the data should be transformed. Since Cp does not consider process centering, it should not be used alone to describe process performance. It should be used in conjunction with Cpk, which considers process centering.

Application Cookbook

1. To calculate Cp indices using Minitab, the following information is needed: Subgroup size, lower and upper specification limits and the method to estimate standard deviation.

2. In Minitab, use Stat > Quality tools > Capability Analysis

process capability study output example

Process Capability Study Minitab output example.

Process Capability Indices – Cpk


Purpose

To determine whether a process, given its short-term variation, meets established customer requirements or specifications. Cpk considers process centering.

It's the ratio of the distance measured between the process mean and the closest specification limit to half of the total process spread.

Anatomy

Cpk is the short term level of performance taking into account process centering.


Reference: Juran's Quality Control Handbook

Terminology

A. Process capability index: Indicates the level of performance that a process can achieve taking into account the location of the process mean. It is equal to the smaller of either Cpl or Cpu. When the process is centered, Cpu = Cpl = Cpk = Cp.

B. Process capability index (lower): Represents the distance between the lower tolerance and the mean divided by 3 sigma ST.

C. Process capability index (upper): Represents the distance between the upper tolerance and the mean divided by 3 sigma ST.

D. See below:

  • Cpk = Cp: The process mean is on target.
  • Cpk = 0: The process mean falls on one of the specification limits, therefore, 50% of the process output falls beyond the specification limits.
  • Cpk < -1: The process mean is completely out of the specification limits, therefore, 100% of the process output is out of specification limits.

Major Considerations

Cpk is used for continuous data and is based on several assumptions. Cpk assumes that the process is statistically stable and that its data is approximately normally distributed. Cpk assumes that data is approximately normally distributed.

If the distribution of the data is very skewed, we should transform the data. Cpk considers process centering and the short-term variation in the process. However, it should not be used alone to describe process capability. It should be used in conjunction with Cp, which is the short-term process capability index.

Application Cookbook

1. To calculate Cpk indices using Minitab, the following information is needed: Subgroup size, lower and upper specification limits and the method to estimate standard deviation.

2. In Minitab, use Stat > Quality Tools > Capability Analysis.

process capability study output example

Process Capability Study Minitab output example.

Process Capability Indices - Pp


Purpose

To determine whether a process, given its long-term variation, has the capability to meet established customer requirements or specifications.

Pp is a ratio of the tolerance width to the long-term spread of the process. Pp does not consider the center of the process.

Anatomy

process capability Pp

Pp is the long term level of performance.


Reference: Chrysler, Ford, General Motors, ASQC, and AIAG

Terminology

A. Process performance index: Indicates the long-term level of performance that a process can potentially achieve.

B. Tolerance width: Upper Specification Limit (USL) minus Lower Specification Limit (LSL)

C. Long-term process spread: Represents six times the long-term standard deviation (±3 sigma LT).

D. See below:

  • Pp < 1: The process variation exceeds specifications. Defects are being produced.
  • Pp = 1: The process barely meets specifications. There is a probability that at least 0.3%
    defects will be produced and even more if the process is not centered.
  • Pp = 1.5: Represents the long-term objective for process capability.

Major Considerations

Pp is used for continuous data and is based on several assumptions. It assumes that the process is statically stable and that its data is approximately normally distributed.

If the distribution of the data is very skewed, the data should be transformed. Since Pp does not consider process centering, it should not be used alone to describe process performance. It should be used in conjunction with Ppk, which considers process centering.

Application Cookbook

1. To calculate Pp indices using Minitab, the following information is needed: Subgroup size and lower and upper specification limits.

2. Stat > Quality tools > Capability Analysis.

process capability minitab example

Minitab output example.

Process Capability Indices – Ppk


Purpose

To determine whether a process, given its long-term variation, meets established customer requirements or specifications. Ppk considers the centering of the process.

Ppk is a ratio of the measured distance between the overall mean of the process and the closest specification limit to half of the total process spread.

Anatomy

process capability Ppk

Ppk is the short term level of performance taking into account process centering.

Reference: Chrysler, Ford, General Motors, ASQC, and AIAG

Terminology

A. Process performance index: Indicates the level of long-term performance that a process can achieve taking into account the location of the process mean. It is equal to the smaller of either Ppl or Ppu. When the process is centered, Ppu = Ppl = Ppk = Pp.

B. Process performance index (lower): Represents the distance between the lower tolerance and the mean long-term divided by 3 sigma LT.

C. Process performance index (upper): Represents the distance between the upper tolerance and the mean long-term divided by 3 sigma LT.

D. See below:

  • Ppk = Pp: The process mean is on target. Since ZLT = 3 x Ppk, we achieve 4.5 sigma LT when Ppk = 1.5.
  • Ppk = 0: The process mean falls on one of the specification limits. Therefore, 50% of the process output is out of the specification limits.
  • Ppk <- 1: The process mean falls completely out of the specification limits. Therefore 100% of the process output is out of the specification limits.

Major Considerations

Ppk is used for continuous data and is based on several assumptions. It assumes that the process is statistically stable and that its data is approximately normally distributed.

If the distribution of the data is very skewed, the data should be transformed (see Data Transformations tool). Using Ppk indices without the information provided by the Cp and Cpk indices may lead to the wrong interpretations of the capability of the process.

Application Cookbook

1. To calculate Ppk indices using Minitab, the following information is needed: Subgroup size and lower and upper specification limits.

2. Stat > Quality tools > Capability Analysis

process capability example

Process Capability Study Minitab output example.

Click here to learn how to perform a Process Capability Study.

From Cpk to Six Sigma Tools.

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