Tool 147: Process Capability Ratios

AKA

Capability Indices

Classification

Analyzing/Trending (AT)

Tool description

Process capability ratios are calculated to determine the process variation that comes from natural or special causes. These ratios, also called C_p and C_pk Indices, relate the process variability to the design specification (tolerance) that reflects the customer's expectation or requirements. C_p is listed to characterize the capability, and C_pk is used to measure actual process performance.

Typical application

• To estimate how well the process meets customer requirements.

• To monitor and measure product quality.

• To verify process variability to design specifications.

• To promote communications among design engineering, suppliers, and manufacturing.

Problem-solving phase

→	Select and define problem or opportunity
→	Identify and analyze causes or potential change
	Develop and plan possible solutions or change
	Implement and evaluate solution or change
→	Measure and report solution or change results
	Recognize and reward team efforts

Typically used by

	Research/statistics
	Creativity/innovation
1	Engineering
	Project management
2	Manufacturing
	Marketing/sales
	Administration/documentation
	Servicing/support
3	Customer/quality metrics
4	Change management

links to other tools

before

• Standard Deviation

• Sampling Methods

• Descriptive Statistics

• Normal Probability Distribution

• Control Chart

after

• Variance Analysis

• Process Flowchart

• Process Analysis

• Activity analysis

• Basili Data Collection Method

Notes and key points

• Definitions of process capability ratios:

  • _Cp: A measure of ideal or potential process capability. The C_p index reflects the best ability of a process to perform within lower and upper design specification limits (LSL ⃡ USL).

  • C_pk: A measure of actual or located process performance. The C_pk index reflects the actual, located process mean relative to the design target value.

  • CPU: Upper process capability

  • CPL: Lower process capability

  • μ or : Process average

  • Equations for calculating C_p and C_pk:

    

  • Process capability:

    

Step-by-step procedure

• STEP 1 A team is formed with the goal of reduced process variability.

• STEP 2 Through the data collection process, process data such as specific product specifications tolerances, control charts, samples of measurements, and historical data calculations, are acquired. See example Fax Paper Extension Wire Measurements.

• STEP 3 Sample data are organized and summarized using descriptive statistics. A recommendation is made to read some background tools contained in this book:

  • Descriptive statistics (tool 66)

  • Normal probability distribution (tool 119)

  • Standard deviation (tool 184)

• STEP 4 Using process means and standard deviations, the C_p capability ratios can be calculated and compared.

  Note

  Measurement in this example is centimeters (cm).

• STEP 5 An action plan is developed on the basis of the actual process performance results calculated. Required activities usually require reduction of process variations or recentering of the process within the specifications.

Example of tool application

Fax Paper Extension Wire Measurements

C_p—Process capability and variability