Car not fitting into the garage shed?

What would you do, if your car doesn’t fit into the garage shed? one would naturally go for a small car fitting into the garage shed.

Exactly is the same case, when the new process does not meet the process capability / specification. The process has to be designed accordingly to meet the specification. The process in the Pharmaceutical / vaccine industries for life saving drugs should consistently meet the product specification during the manufacture and till the end of the shelf life.

Process capability method may look like a jargon with complex statistical calculations, but these can be simplified to understand the basic principles.

Cp Cpk, Pp and Ppk are capability and performance indicators for the process. Is a process capable? Is the process acceptable? How is the process actually behaving vs how it theoretically could be behaving?

Ppk – Process performance.

Process performance, Ppk, indicates how the actual process performed over a period of time [long term]. It is an evaluation of how well a process performed.

They measure how close our process is running to its specification limits. They are calculated by applying suitable statistical methodologies. Software is designed / available for the evaluation of process capability and process performance.

Let us first understand the basics.

Standard deviation

Take an example of eight students in a particular class. The marks of a class of eight students are the following eight values.2,4,4,4,5,5,7,9. The mean [Average] is 5.

Calculate the deviations of each point data from the mean and square the result.

A large standard deviation indicates that the data points can spread far from the mean and a small standard deviation indicates that they are clustered closely around the mean.

Cp- Process capability

It is used to find the measurable property of a process to the width of the specification. Specifications are documents that describe values and accordingly products should be manufactured, defined, measured, or tested.

Cpk – Process capability index

Is the measure of process capability. It shows how closely a process is able to produce the output to its overall specifications. It decides how consistent we are to our average performance.

Example

Food served at a restaurant should be between 39°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 temperatures is 40.

USL [Upper Specification Limit] =49°C, LSL [Lower Specification Limit] =39°C, Standard Deviation =2°C, Mean = 40. Separate the above formula into two parts:

Pp-Process performance

The difference between C_p and P_p, as well as between C_pk and P_pk, results from the method of calculating standard deviation. The only difference lies in the denominator for the Upper and Lower statistics: Cpk is calculated using the WITHIN standard deviation, while Ppk uses the OVERALL standard deviation.

Example, there were 600 shafts made. 10 out of 100 were measured each hour for six hours. 60 data points were accumulated. There are six subgroups of 10 data points. Parts are made on one machine, by one operator, the same way on the same day. Cpk is calculated based on average standard deviation of sub groups [within] whereas Ppk is calculated based on overall standard deviation [Overall].

When the Cpk calculation is a high number then it is a good indication, the process is statistically in control. If the Cpk and Ppk calculations are very close or equal, then there is an even better indication that the process is statically in control. However, if the two calculations are considerably different, even though the Cpk value may be acceptable, this is an indication that the process is not in statistical control because there are more data points that have been evaluated in actual process conditions.

Note-The images given for representation in this blog are taken from Google Images. Many thanks for Google.