A manufacturing process is designed to produce a product within a tolerance range specified by the customer. An index called the Cp value measures the capability of the process to meet these requirements. The ability of the process to manufacture products within the tolerance limits specified by the customer is known as its Cpk value.
How to Calculate Cp Ratio
The process capability of a manufacturing process is its ability to meet the design specifications for the product. The specifications have a target or nominal value and an allowance above and below the nominal value.
For example, consider the manufacture of water bottles. The target size is 25 ounces. The specifications require that the manufacturing process produce bottles ranging in size from an upper limit of 30 ounces to a lower limit of 20 ounces.
Actual manufacturing data shows that the process is producing bottles ranging from 32 ounces to 18 ounces. This range of production sizes represents a six deviation, or Six Sigma, spread and has a normal, bell-shaped, statistical distribution.
This manufacturing process is not capable of meeting the design specifications since a portion of the production is outside the upper and lower size limits.
Mathematically, this conclusion is calculated as follows:
Cp = Design specification width/Six deviations distance = (30 ounces-20 ounces)/(32 ounces - 18 ounces) = 10/14 = 0.71
A Cp less than one indicates that the manufacturing process is not capable of meeting the design specifications.
Note: Most manufacturing standards use a Six Sigma standard deviation spread because this figure represents 99.73 percent of production.
Cpk Calculation Formula
The Cp index is not sufficient by itself to analyze a process capability. What would happen if the nominal production output value shifts towards either the upper or lower limits and some of the production fall outside the design specifications? This is when a Cpk calculation is needed.
The Cpk formula takes the minimum results of the calculation in the shift of target output. The Cpk equation is:
Cpk = Minimum ((Upper specification limit - Nominal value)/3 Sigma spread or (Nominal value - Lower specification limit)/3 Sigma spread))
Using the above example of water bottles, suppose the mean shifts to the right to 27 ounces. The calculations for Cpk are as follows:
Cpk = Minimum ((30 - 27)/7 or (27 - 20)/7) = minimum of 3/7 or 7/7 = 0.43 or 1
In this case, the Cpk calculation is the lesser or 0.43. Since this value is less than one, this process is not acceptable because a large portion of the production falls outside the upper specification and is considered defective.
Interpretation of Cpk Value
If Cp equals Cpk, then the process is operating at borderline conditions. The production capability exactly falls within the design specifications for Six Sigma standards and is acceptable
If Cpk is less than zero, the process mean has gone beyond one of the specification limits.
If Cpk is greater than zero but less than one, the process mean is within the specification limits, but some part of the production output is outside the specification limits.
If Cpk is greater than one, the process mean is perfectly centered and is well within the specification limits.
In general, the higher the Cp and Cpk values, the higher the Sigma level. A Cpk greater than 1.33 is considered good and indicates a Sigma level 4. But a Cp or a Cpk greater than 3 implies that the specification limits are very loose and should be tightened.
The Cp ratio and the Cpk index are important metrics to use when evaluating the performance of a manufacturing process. Statistical sampling and continuous monitoring of the production process are essential to consistently producing a product that meets customers' demands.
James Woodruff has been a management consultant to more than 1,000 small businesses. As a senior management consultant and owner, he used his technical expertise to conduct an analysis of a company's operational, financial and business management issues. James has been writing business and finance related topics for National Funding, PocketSense, Bizfluent.com, FastCapital360, Kapitus, Smallbusiness.chron.com and e-commerce websites since 2007. He graduated from Georgia Tech with a Bachelor of Mechanical Engineering and received an MBA from Columbia University.