CPK Formula

Cpk Formula

The process capability index (cpk) is a metric for measuring process capability. The  CPK Formula demonstrates how closely a process can create output that meets its overall parameters. The CPK Formula determines how committed they are to achieving the average performance.

A person may execute with minimal variance, but he may be of a goal and near one of the specification limitations, indicating that Cpk will be low but Cp will be high.

The CPK Formula is  Cpk formula is:  Cpk=minUSL-mean3,mean-LSL3


standard deviation is σ 

the upper specification limit USL

the lower specification limit LSL

Cpk Formulas

The CPK Formula or process capacity index is an essential statistical instrument. It is used to assess a process’s ability to deliver the required output within the customer’s specified boundaries. In other words, The CPK Formula assesses the manufacturer’s capacity to provide a product within the tolerance range. It is also used to measure how close they are to a specific aim as well as the consistency of performance around the average. Students will cover the fundamentals of cpk as well as the CPK Formula with examples.

Concept of Cpk Formulas

Cp and Cpk are both used to measure Process Capability. In general, students may apply this when a process is statistically controlled. This is common with a mature process that will be around for a long time. The processing capacity will be determined by the sigma value from the Moving Range, Range, or Sigma control charts.

As a result, the process capability index, abbreviated as the CPK Formula, is used to assess process capability. The CPK Formula demonstrates how closely a process can deliver the desired output when compared to its overall requirements. The CPK Formula also determines the constancy of average performance.

Cpk provides us with the best-case scenario for the current procedure. The CPK Formula may also forecast future process performance, assuming consistency across time. Six Sigma requires us to characterise process quality in terms of sigma. This is because the CPK Formula allows us to easily discuss how competent different processes are using a similar mathematical model.

Important Points about Cpk

Cpk is a short-term process index that represents a process’s prospective capacity, providing it is examined and remains under control.

In Statistics, it is an option beside the z-score.

To assess process control, students can utilise time series and SPC charts. If the process is out of control, evaluating present performance is unlikely to reflect long-term performance.

The CPK Formula is the best a process can do when it is centred on its midway.

The “k” in the CPK Formula represents the quantity on which a distribution is centred. A properly centred process with the mean equal to the midpoint has a “k” value of 0.

The lowest and maximum values of “k” are 0.0 and 1.0, respectively. Cp = Cpk in a properly centred process.

A rough estimate for Cpk = Cp (1-k). Because the maximum value of k is 1.0, the value of Cpk will always be less than or equal to Cp.

The client must provide input on the lower specification limit (LSL) and upper specification limit (USL) (USL).

Process Capability Index

Cpk is a process capability index that determines how much a process is capable of producing. In contrast to Cp, Cpk does not presume that the process mean is centred between the stated limits. Many individuals use Process Capability as a method for estimating the production of a product they are producing. The CPK Formula assists manufacturers in estimating future production and managing resources to get the best outcomes. The process capacity index usually uses normal statistical analysis and data distribution as inputs. It is comparable to the mathematical words mean, average, and standard deviation. The CPK Formula differs in that it uses a control chart analysis to evaluate the statistical control of the system.

The Formula for Cpk

The CPK Formula is used to compute the process capability index (cpk), which is a measure of process capability. This number represents how closely a process can create output that meets its overall parameters. As a result, one can determine how consistent they are with their average performance. Any product or service must go through a well-structured development process. The ability of this line of action will determine success. The CPK Formula aids in validating the success of a procedure.

The CPK Formula is a useful statistical tool. The mathematical analysis of the inherent process variability of the provided responsibilities under evaluation is referred to as process capacity. The process capability index (cpk) is used to calculate the process’s capability.

The CPK Formula is:

Cpk formula is:  Cpk=minUSL-mean3,mean-LSL3

Solved Examples for Cpk Formulas

When food is brought to a client in a restaurant, it should be between 38^{\circ}C and 49^{\circ}C. The technique used to retain the food at the proper temperature has a process standard deviation of 2^{\circ}C and a mean value of 40. How can I find the process capability index?

USL (Upper Specification Limit) =49∘C

LSL (Lower Specification Limit) =39∘C

Standard Deviation =2∘C

Mean = 40

Cpk formula is:  Cpk=minUSL-mean3,mean-LSL3

= min(49−403×2, 40–393×2)

=min(96, 16)


= 0.166

Therefore, the process capability index i.e. Cpk is 0.166.

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FAQs (Frequently Asked Questions)

1. What are the advantages of utilising the Process Capability Index?

The industrial system is becoming increasingly wide and sophisticated as time passes. As a result, overseeing and supervising the manufacturing units has become a demanding endeavour. In such cases, one can apply Mathematics to help us. Mathematicians and economists have developed several logical and empirical formulae to aid management boards and quality analysts in their work. It is a very good approach for every investor to get an accurate estimate of potential gains. In the long run, the procedure can also aid in improved resource allocation and overall business management.

2. What is the most effective way to learn the Process Capability Index?

The Process Capability chapter is an essential element of the Statistical Studies curriculum. After the 10th board test, the books for the Commerce stream are accessible. The easiest method to approach this chapter is to first master all of the theories to understand the ideas and, if required, memorise the formulae. When you have completed all of the problems in the book, you are ready to consult the index for various factor values. You can also practise answering questions from other sources.

3. Where can I find all of the 'Process Capability Index' formulas?

‘Formulas’ are highly important in the Process Capability chapter for addressing problems and using the Process Capability Index. These formulas are stated only once in the chapter, along with an explanation and substance. The formulae may also be found on the Extramarks website. Hard copies can also be obtained by downloading and printing the PDF.

4. What is the meaning of the Cpk value?

If the Cp value equals the Cpk value, the process is running under borderline circumstances. The production capacity meets the design parameters for Six Sigma standards and is satisfactory.


If Cpk is less than zero, this indicates that the process mean has exceeded one of the specified restrictions.


If Cpk is larger than zero but less than one, the process mean is within specification limits but some of the manufacturing output has exceeded them.


If Cpk > 1, the process mean is precisely centred and within the specification limitations.

5. Is it necessary for students to fully understand “Process Capability” before learning about “Process Capability Index”?

‘Process Capability is the fundamental grasp of what the notion stands for and provides a thorough comprehension of its demand and application for what it is intended for. Before applying many ideas in the actual world, statistical data analysis and research are required. The ‘Process Capability Index’ was created as a result of this repetition of computations for the same variable value. It is a set of pre-prepared Process Capability values for various sets of situations that anyone may use and compare to eliminate the need for computations.