The development of any product or service must follow a well-structured process and the ability of this course of action will decide the successful outcome. This is satisfied if the process designed matches the customer need.
Before we move forward let us begin with an example to provide you with a sign of relief that we can achieve at the right process with simple math.
Note – In this section do not bother about any technical terms just understand how to use the formula. Later you will find details.
USL = -15
LSL = -35
SD = 2,
Mean = -25
Cpu = Mean – LSL / 3 X SD
Cpl = USL – Mean / (3 X SD)
Cpk = Min (Cpu, Cpl)
Substitute the values in the formula
Cpu = (-15-(-25))/ (3*2) = -10/6 = -1.667
Cpl = (-25+35)/ (3*2) = 10/6 = 1.667
We know that Cpk is a minimum of [Cpu, Cpl] and hence a minimum of [-1.667, 1.667] is -1.667. Therefore the upper limit seems to suit best for this condition.
In the following section, you will find another example with a detailed explanation of each terminology used.
It refers to the arithmetical study of the natural process variability of the given responsibilities in consideration.
Cp – This is how it is represented. It denotes the capability of the process that can be achieved when perfectly centered between the lower and the upper limit.
Cpk – This is also used for calculating the ability of the process; it determines how close you are to the given target and how consistent you are around your average performance.
Another way to study the ability of the performance is by finding the Pp and the Ppk.
In this article, we will discuss Cp and Cpk is a process capability study.
Also, if you want to improve the process capability, then you need to apply the right design thinking which is discussed in DFSS (design for six sigma).
The Cp has 2 subdivisions
These can be calculated with the formula
Cpu = (Process mean - LSL)/ (3 * Standard deviation) where the LSL is the lower specification limit.
Cpl = (USL - Process Mean)/ (3 * Standard deviation) where the USL is the upper specification limit.
Now the term Cpk is only the value that is smallest of the above two, that is Cpu and Cpl.
Cpk is the smallest of the Cpu and Cpl. Let’s take an example
Example 2: - The training room temperature during the training must be kept between 18 degrees Celsius and 26 degrees Celsius. The process of maintaining this temperature has a standard deviation of 2 degrees Celsius. If the mean temperature is 21 degrees Celsius, find the PCI.
Here USL is 26 and LSL is 18 and the Standard deviation is 2, and the mean is 21.
Cpu= (26 - 21)/ (3 * 2) = 5/6 = 0.8334
Cpl = (21 - 18)/ (3 * 2) = 3/6 = 0.5
Cpk = Minimum of [ Cpu, Cpl]
That is Cpk = minimum of [0.8334, 0.5]
The process capability index Cpk is 0.5
As discussed in the process capability example in the above paragraph we need to find out the inconsistency in the process with the help of the upper and lower limits respectively.
The following can be seen from the analysis and process capability ratio:
6σ is a numerical study of deviations in the process. This is important because due to such variations the result of the product or service will also vary. Usually, that is the reason the customers provide the range (lower and upper) for any product that they can accept.
In a real sense, there is no perfect process and hence no perfect product as it is very difficult to meet perfection. That is why there are certain tolerances allowed. Thus to reduce the defects in the product the process must follow some criteria so that the products fall exactly or near the center of the sigma line defined by the upper and lower tolerance levels.
As 6σ is a statistical tool that determines sigma value and the process capability ratio and process capability analysis, you might be using this very often as a process champion at your organizations.
Now that you have a brief idea of the process capabilities and how to find the Cp and Cpk value using the formulae. To explore more on six sigma and its various tools we suggest you register for the online interactive six sigma green belt training with StarAgile. To register click on the link provided. Keep Learning!!!
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