Process Capability Indices Cp Cpk

Process Capability and its benefit

Process Capability and its benefits

Brief guide on Concept of Capability Indices – Cp, Cpk, Pp, and Ppk

To get FREE Excel Sheet for calculation of process capability indices – Cp, Cpk, Pp, and Ppk, refer end section of the page.

What is Process Capability?

Process capability means the ability of the process to achieve desired results that meets the customer specification and statistical limits in a consistent manner. Process capability is defined based on the historical performance of the process. Process capability is one of the tools of Statistical Process Control (SPC).

In the fewest possible words – process capability indicates how efficiently a process can perform its intended purpose.




Why is process capability important?

The business owner or process owner always wishes that the product that produces should give maximum benefit, consistency, less rejection, maximum yield, fewer stoppages, and less viability.

Monitoring process capability allows to understand and evaluate the manufacturing process performance. Based on the process is evaluation, process should be fine-tuned to meet the customer requirement. Capability Indices (Cp, Cpk, Pp, and Ppk) will help to understand the process behavior to enhance product quality, cut down scrap, improve product process consistency, reduce the cost of production and the loss of cost because of poor quality.

When process capability was first introduced? – 1956
How and where? – In Statistical Quality Control Handbook
Who has published this book? – Western Electric Company
Definition of process capability – When extraneous effects are eliminated and process works naturally, performance in that scenario is called as process capability.
Process capability can be determined by plotting variables on a control chart.

Majorly used indices to measure process capability and performance are as follows:
Pp: Process Performance
Ppk: Process Performance index
Cp: Process Capability
Cpk: Process Capability index
Reference: ASTM E2281

When we talk about statistics, it is assumed that the data population is normally distributed. Variability of the process can be observed as either short-term or long-term.

Cp and Cpk are measured using short-term standard deviation or variability.
Pp and Ppk are measured using long-term standard deviation or variability.

Process Capability/ Process Potential Index – Cp

Cp accounts only for spread or variation of the process

Process Capability formula
Process Capability graph

Process capability index or Centering Index – Cpk

Cpk accounts only for spread and location of the process

Process Capability Index formula
Process Capability Index Graph

Tips for Cp and Cpk

Cpk will be always ≤ Cp
When process is perfectly centered, the value of Cpk and Cp are the same.
Cp represents the maximum likely value for Cpk
Cp requires 2 specification limits
Cpk can be calculated using single as well as both side specification limits

Formula for Cp and Cpk calculation

Process Capability formulas

LSL: Lower specification limit
USL: Upper specification limit
Mean: Average of all the data
Sigma (σ): estimated inherent variability


Process Performance – Pp

Pp is a measure of the overall process capability.
It is a ratio of Specification spread and overall process variation. The overall variation is based on overall standard deviation.

Process performance index – Ppk

Ppk is the measure of the overall process capability by estimating process location and the process spread. It is a ratio of (process mean – closest specification limit) and overall standard deviation.

Formula for Pp and Ppk calculation:

Process Performance formulas

USL: upper specification limit
LSL: lower specification limit
Mean: grand average of all the data
SD: overall variability


Summary of difference between Cp and Cpk vs Pp and Ppk

Cp and Cpk Pp and Ppk
This is process capability metrics This is process performance metrics
Cp is the capability index Pp is the performance index
Cp and Cpk use Sigma estimator Pp, Ppk use standard deviation
Cp and Cpk calculates for sample, not the entire population Pp and Ppk calculates the entire population
Cp and Cpk can be used to calculate when process is existing and under statistical control Pp and Ppk can be used to calculate when process is new or process is not under statistical control
Measure for short term Measure for long term
Cpk represents the potential process capability (how well a given process could perform when all special causes have been eliminated) Ppk addresses how the process has performed without the demonstration of the process to be stable
Forecast future batch failure rate Does not forecast future batch failure rate

Interpretation of process capability in relation to sigma level and capability rating

Cpk Value Sigma Value Schematic representation Area under normal distribution curve (%) Capability Rating*
0.333 1 1-sigma-graph 68.27 Terrible
0.667 2 2-sigma-graph 95.45 Poor
1.000 3 3-sigma-graph 99.73 Marginally capable
1.333 4 4-sigma-graph 99.99364 Capable
1.667 5 5-sigma-graph 99.99994 Good
2.000 6 6-sigma-graph 100 Excellent
*Bothe, D. R., Measuring Process Capability, Cedarburg, W.I., Landmark Publishing Inc., 2001
Reference: Presentation on Use Process Capability to Ensure Product Quality
Lawrence X. Yu, Ph.D., Director (acting), Office of Pharmaceutical Science, CDER, FDA


The process capability index considers not only the process mean and variability but also considers the specification. The measurement gives a quantitative measure of the process performance and the applicability is cross sectors.

To measure the process performance, no additional testing is required since historically generated data can be used to do the data analysis.

Process Capability Indices, Cp, Cpk, Pp, and Ppk are simple yet powerful indicators that provide a perspective of the process and will enable manufacturers to ensure product quality and process robustness.

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