Cpk Calculation Excel

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Capability (Cp, Cpk) and Performance (Pp, PpK) indices are a means of comparing (among other things) if the data is made up of common versus special causes of variation. When a system behaves under common causes the data will be normally distributed. If this is the case then Cp=Pp and Cpk=Ppk (they won’t be exact but very close). Comment calculer le CP et CPK sur Excel ( une formule simple pour les gens qui ne se disposent pas du Minitab ) how to calculate CP and CPK with Excel. How to Determine Bin Intervals to Create a Histogram in Excel Bin intervals need to span enough distance to include the upper and lower spec limits and the min and max values. Using the data in the previous example, follow these steps to determine bin intervals for a histogram.

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Calculation

What is Ppk?

Our first two blogs in this process capability series answered two questions: What is process capability? – and - What is Cpk? This blog answers the next question: What is Ppk?

The answer is quite simple. Just to refresh your memory, Cpk is expressed as the following:

Cpk = Minimum (Cpu, Cpl)

Cpu=(USL-X)/3σ

Cosmic perspective 8th edition pdf. Cpl=(X-LSL)/3σ

where Cpu is the capability based on the upper specification limit (USL), Cpl is the capability based on the lower specification limit (LSL), X is the overall average, and σ is the estimated standard deviation from a range control chart. Cpk is the minimum of Cpu and Cpl.

Ppk is expressed as the following:

Ppk = Minimum (Ppu, Ppl)

Ppu=(USL-X)/3s

Ppl=(X-LSL)/3s

where Ppu is the capability based on the upper specification limit (USL), Ppl is the capability based on the lower specification limit (LSL), and s is the calculated standard deviation from all the data. Ppk is the minimum of Ppu and Ppl.

Look at the equations for Cpu and Ppu. What differences do you see? Now look at equations for Cpl and Ppl. What differences do you see?

The only difference is that Cpu and Cpl both use σ - the estimated standard deviation from a range control chart, while Ppu and Ppl both use s - the calculated standard deviation from all the data.

What does the difference mean? The easiest way to see this is through an example using an individuals control chart (X-mR). With an individuals control chart, the individual (X) value is plotted on the X chart. The range between consecutive points is plotted on the moving range (mR) chart. The average moving range is used to calculate the value of σ. And this value is used in the Cpk calculations.

Suppose the data are being collected hourly. Each moving range represents the “short-term” variation – the variation between consecutive hours. Cpk is sometimes referred to as the short-term capability – it represents what the process is capable of doing in the short-term – from hour to hour in this example.

HourXHourX
110611102
210412100
31041392
41061499
59915115
69216105
79917100
8931898
910919105
101052099

The figure below represents the moving range for the data given. The first X value is 106; the second X value is 104. So, the moving range between these two results is 2.

The average moving range for these data is 6.2. For a moving range between consecutive points, σ is calculated as the following:

σ = R/1.128 = 6.2/1.128= 5.50

This is the value that would be used in calculating Cpk.

For Ppk, the standard deviation of all the X values is calculated. Note that all the values are used at one time to determine the standard deviation. These values represent 20 hours (since there are 20 data points). This is a much longer time-frame than the between consecutive hours in the moving range chart. Because of this, Ppk is sometimes referred to as the long-term capability. In Excel, you can use the function STDEV to calculate the standard deviation. The result is:

s = 5.7

This is the value that would be used in calculating Ppk

The difference between Cpk and Ppk is simply in how you calculated the standard deviation. So, which is better to use: the short-term Cpk capability or the long-term Ppk capability? This will be the topic of our next blog.

Our SPC Knowledge Base has multiple publications on process capability if you would like more details.

The control chart above was made using SPC for Excel, a simple but powerful software for statistical analysis in the Excel environment.

Cp stands for process capability and Cpk stands for process capability index. Both are used for the measure of a potential capability of a process in short term. The higher the sigma level, the better the process is performing. You can learn how to calculate Cp and Cpk values using this tutorial. Learn to calculate the Process Capability (Cp) and Process Capability Index (Cpk) values using the steps and few examples given here.

CpkCpk Calculation Excel

Learn to Calculate Process Capability Index - Tutorial, Definition and Example

Process Capability (Cp) Definition:

Process capability is a technique to find out the measurable property of a process to a specification. Generally, the final solution of the process capability is specified either in the form of calculations or histograms

Process Capability Index (Cpk) Definition:

Process capability index (cpk) is the measure of process capability. It shows how closely a process is able to produce the output to its overall specifications.

Formula :

Where,

USL = Upper Specification Limit, LSL = Lower Specification Limit.

Example :

Food served at a restaurant should be between 38°C and 49°C when it is delivered to the customer. The process used to keep the food at the correct temperature has a process standard deviation of 2°C and the mean value for these temperature is 40. What is the process capability of the process?

Given,

Cpk Calculation Excel Format

USL (Upper Specification Limit) =49°C LSL (Lower Specification Limit) =39°C Standard Deviation =2°C Mean = 40

To Find,

Process Capability & Process Capability Index

Solution:
Process Capability :
Process Capability = (49 - 39) / (6 * 2)
= 10 / 12
= 0.833
Process Capability Index :
Solution 1
(USL-mean/ 3*std.Dev) = (49 - 40) / (3 * 2)
= 1.5
Solution 2
(mean-LSL/3*std.Dev) = (40 - 39) / (3 * 2)
= 0.166
Now, find the minimum value.
Process Capability Index = min (Solution 1, Solution 2)
= min (1.5 , 0.166)
= 0.166

Cp and Cpk are used in Six Sigma Quality Methods for analyzing the performance of the process carried out to deliver any product.

Related Tutorials:

How To Compute Cpk In Excel

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