This article will explain what a process capability analysis is, how to measure the process capability and explain indexes of process capability.
Process Capability Analysis
In simple terms, process capability analysis explains the extent a six sigma process meets its specifications. For example, you are manufacturing and designing shafts (say 100 pieces) and you want the shaft diameter should be in between 20mm to 25mm. Now, after you are done with the manufacturing, you are seeing that only 85 shafts are meeting the requirement of 20 -25mm diameter. So your manufacturing process is capable of only producing 85% that meet standards.
In this way, if you want to quantify the capability of any statistical process, you have to go for process capability analysis and you will get process capability index Cp and Cpk.
Before addressing Cp and Cpk in detail, let’s keep it in mind that for any normally distributed process, 99.7% of all the output fall within ~+mn~ 3σ range with respect to the process mean. Or, 99.7% of output fall in the range of 6σ (where σ is standard deviation of the process).
Process Capability Index, Cp
This is the primary measurement of the process capability. Here, the ratio of the specification width or spread (USL-LSL) to the process width or spread (6σ) is measured. And if the value of the process capability index Cp is 1 then the process should produce 99.7 % good component.
Limitations of the Process Capability Index Cp
Cp works fine as long as the process mean coincides with the specification mean. But imagine a process like below:
If you calculate Cp for the above process, it be greater than 1, but you can see many of the outputs are actually falling below the LSL. This means that not all the outputs are acceptable, but you cannot tell it by seeing only the Cp. This limitation is overcome by the process capability index, Cpk.
Process Capability Index, Cpk
“Cpk “is being calculated considering the shift of the process mean and specification mean. The below formula is used for calculating Cpk:
k = abs (Specification mean – Process mean)/0.5*(USL-LSL)
Specification mean= (USL-LSL)/2
Process capability analysis is applied to check the capability of the process to produce acceptable outputs. Process capability index Cp does not consider the shift of the process mean to the specification mean, Cpk considers the shift.