Process Capability Formula

CP means or stands for Process capability. That said the CP calculation formula is used to determine the measurable property of a process to the width of the specification. The ultimate solution of the process capability is usually manifested either in the form of calculations or histograms. The formula to calculate CP is as below:-

CP = (USL–LSL)/6×σ

Where,

USL = the upper specification limit

LSL = the lower specification limit and

σ = the standard deviation.


What is Process Capability Ratio?

Process capability is used to identify the inconsistency in the process using the upper and lower limits respectively. Elements stated below can be observed from the evaluation and process capability ratio:

  • If the value of CP is equivalent to 1, the process is perfectly centered i.e. (CP = 1 is a perfect process)

  • When CP is greater than one, it suggests tolerance> the process. This validates that the process seems to be able to do this. (CP> 1 is process compatible)

  • If the process length is higher than the tolerance, the process variation is within the range of tolerance, making the process incapable.

  • CPk makes it feasible to compute the closeness of the performance of the process to the condition set upon by permitting for the natural inconsistency of the process.

  • If the value of CPk is negative, you are required to ensure that the process you inherited leads to an outcome that is not within the range mentioned by the client and is completely outside. There is a separate CPk calculation formula.

  • The CPk of 3 suggests that the output is outstanding and the process has 6σ capacities and that is what we require to achieve.

  • We require a CPk of minimum 1.33, which is 4σs, in order to satisfy most customers.

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Solved Examples

Example: Find out CP whose USL, LSL and σ are 12, 7 and 4 respectively?

Solution:

From the above cp equation, it is given that

USL = 12

LSL = 7

σ = 4

Now using the process capability ratio formula, which is as below;

CP = (USL − LSL) 6σ

CP = (12 − 7)6 × 4

CP = 0.208333

FAQs (Frequently Asked Questions)

Q1. What is the Cpk Formula?

Answer: Cpk stands for process capability index which is the measure of process capability. It displays how intricately a process is capable of producing the output to its overall specifications. It also judges the level of consistency in our average performance. The cpk calculation formula is:-

Cpk = min(USL−mean/3σ,mean−LSL/3σ)

Where,

USL = the upper specification limit,

LSL = the lower specification limit.

σ = standard deviation

Q2. What is the Cp and Cpk Formula?

Answer: An ideally centered process will consist of Cp = Cpk. Both Cpk and Ppk are associated with the standard deviation and centering of the process about the centre point to the permissible tolerance specifications. An approximation for Cpk = Cp (1-k). And since the maximum value for k equals to 1.0, then the value for Cpk will be always equal to or less than Cp. Similar to Ppk, the Cpk capability index is only a function of the mean of the data and standard deviation, not a nominal (target) value that may be historical or given by the customer.

Q3. Why Do We Divide by 3 to Find the Value of Cpk?

Answer: With respect to the origin of the 3-sigma limits, it was an idea introduced by Walter Shewhart's. Since in a normal distribution 99.73% of the population falls within ± 3 sigmas of the mean, he regarded it as a rational point to put the limits.