Process Capability (Cp) Formula With Solved Examples

Process capability is a crucial part of Statistics. The information which is given into this method always has 1 or more characteristics that are utilized to give unique results. These characteristics are easily measurable and can be analyzed with the help of graphs. Process capability is commonly expressed in the form of Cpk, or Cp. The Cp formula shows how effectively a process can give results based on its specifications. Let us take a closer look at what Process capability is, how to measure it, the process capability formula, and other related terms to it. 

Also read: Isosceles Triangle Theorems

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What is Process Capability (Cp)?

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The word “process” can be defined as a specific combination of tools, methods, or even people, all of which come together to produce an output. This output can be easily calculated and should fulfill the requirements of the customer. For example, the drinks served at a bar have to have a temperature within the range of 10σ to 20σ. The process which keeps their temperature from fluctuating has a standard deviation of 2 degrees Celsius. In this case, Cp = 0.83

Owing to Statistics, the process capability of a process can be measured based on the specification which is generally known as the process capability index or the process performance index. The former is denoted by Cpk or Cpm while the latter is expressed as Ppk or even Ppm. 

Whatever the result is of this calculation is drawn in the form of a histogram. It can be easily observed from the process about how many parts will occur because of specification. There are usually two main parts of process capability. These are known as 

1. To measure the variability of the resultant output of a process, and 
2. Compare the gotten variability with a specification or product tolerance 

Also read: Chance and Probability

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Calculation of Process Capability

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The implementation of Cp is usually done in cases of statistical control. It basically describes the ability of the provider to deliver a product that is within the range of tolerance. Now, it is important to understand how to measure this whole process. Initially, one or two measurable quantities are taken into account. Each of them is capable enough to produce specific results. Where the output is in the form of a normal distribution, the process capability can be calculated with the help of mean and standard deviation. 

It should be seen to it that the process taken under consideration should be statistical control. If it isn’t, then the value of Cp would automatically become negligible. This is the reason common cause variation is preferred over special cause variation while measuring the process capability. After the process has given results, it needs to be studied carefully. Important data is taken from it.

In the Cp, the more the data is drawn, the more the chances are for the Cp to be accurate. A minimum of 17 data points is generally required to build up a conclusion. These points may be in relation to the materials, working conditions, people, and other tools. In this method, the mean and the standard deviation are also calculated. Where the distribution is normal, the process capability must witness a relationship between six standard deviations and the needed specification.

Also read: Empirical Probability Formula

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Process Capability Formula 

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Cp implies Process Capability. This process is used to find the measurable property of a process to the width of the specification. The resultant solution is expressed in the form of calculations or even histograms. It should be remembered that a value that is greater than 1.33 is considered to be a good process capability. Process Capability can be calculated using the following formula given below, 

Where, 

USL refers to the upper specification limit

LSL denotes the lower specification limit,

Σ implies standard deviation 

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Solved Examples

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Question: In a given case, if the USL is given as 40, LSL is 16, and the standard deviation is 2, calculate the value of process capability.

Solution: We know that

USL = 40

LSL = 16

Σ = 2

By formula we know that, 

Process capability = USL-LSL6 σ

Therefore, Cp = 40 - 166 2

Process capability =24/12

Process Capability is equal to 2. 

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Process Capability Ratio 

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Certain points must be remembered while calculating the process capability ratio. These are as follows, 

• When the output of Cp is equal to 1, it means it is a perfect process capability because of being centered perfectly. 
• When Cp is greater than 1, it means the process capability is compatible. It also denotes that the tolerance is greater than the process. 
• When the process becomes higher than tolerance, the Cp is called as incompatible.
• The process capability index or Cpk makes it a lot easier to calculate the close proximity of the Cp.
• When Cpk becomes negative, it should be taken care that the result of the process should not fall within the range expressed by the client, but outside it. 
• When the process capability index has a value of 3 and the process has 6σ¼ capacities, it indicates that the process is successful and commendable. The requirements have been achieved efficiently. 
• It should be noted that a minimum value of 1.33 of Cpk is required for satisfying the needs of customers. This sums up into exactly 4 σ¼ capacities. 

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Things to Remember 

• Process capability is that measurable aspect of a process to its specification. This is called the process performance index which is denoted by Ppk or process capability index which is written as Cpk. The outcome of the process is depicted in a histogram and some other calculations. 

• All the processes should fall under statistical control, else their value will be meaningless. It must be noted that at least 17 data points are needed to give a reasonable result of the whole process. The more the data, the more correct the result. 

• The processing capability or the Cp formula is measured with the help of an upper specification limit, a lower specification limit, and the standard deviation. After it is calculated, sufficient data must be taken from the result in order to make a conclusion. 

• A perfect process capability is one that has a value of 1. It is perfect as it is exactly located in the midpoint. Any Cp which is less than 1 is considered a failure and it couldn’t give the desired results. This poor process capability does not meet the satisfaction of customers. On the other hand, Cp lying between 1 and 1.33 is a good process.