In many industries, the moment the word Process Capability is discussed, the immediate thing that comes to most people's mind is Cpk. This is a Statistical Jargon that is linked to Process Capability. But to a common man, Cpk value does not make any sense. When we say the Cpk of the process is 1.22, what meaning does it convey to a common man. Nothing!!. Let me explain with an analogy. If all the media and newspapers start reporting the ambient temperature in our places in Fahrenheit, it will not make sense to anybody. Like there are different units to measure and report temperature, there are different units for Process capability. We should talk in a language that is understandable to most people. Since our upbringing is to visualize the temperature in Centigrade, we have to measure and report the temperature in centigrade. Similarly there are 2 units for Process capability, one is mostly commonly used and hardly visualized and understood which is Cpk, and the other one is Rejection ppm, which is easily visualized and understood but rarely used for reporting Process Capability.
So, how to report Process Capability in Rejection ppm and make everybody understand. Fortunately there is a simple and power tool for doing this called
This can be done in Excel easily. Since this blog is only about how to report Process capability in Rejection ppm, let us not go into the detail of how to collect the data. We can use the same data collected for reporting Cpk.
The following 2 inputs are required for simulation
1) Average of the entire data
2) Standard Deviation (Sigma).
Use the following function in Excel in the CELL A1. Type =NORMINV(RAND(),Average value, Sigma)
For a Process, let us say the Average value is 20.1 and Sigma is 0.05, type of function as shown in the picture
Drag the cell to 10,00,000 rows (1 Million). Now we have virtually produced and inspected 1 Million Parts.
Now to find out how many rejections we have got in this 1 million parts, use the following function in excel
For the above data, let us say, USL is 20.20 and LSL is 20.18. Type the function as shown in the picture
The process will make a rejection of 22,809 ppm (2.2%) above USL and 0 ppm (0% below) LSL. This indicates that the process mean is shifted towards the USL side, which can be corrected in further production through setting. Now we can again simulate and see if we set the mean to the Target value which in this case is 20,then how much will be our rejection ppm. For this just change the average value to target value in the =NORMINV(......) function. The picture below shows the rejection if the process is set to the target
The Total rejection from the process will be 72 ppm.
Now you see this is a super easy way to find out the Process capability. This process will produce 72 parts out of spec in a production qty of 10,00,000. Now, can we say this process is Capable. The cut off value for the PPM is 100. If the Total Rejection (Both USL and LSL combined) is < 100 PPM, the process is capable. Hence, this process is capable, but we have to ensure the mean setting to the target in future production.
Monte-Carlo simulation method of predicting the rejection ppm helps in visualizing what is process capability and can be explained to any common man.
So, let us not make things complicated by using unnecessary Statistics and Calculations.