Six Sigma Pizza - Pie 23

So far..

We are trying to demystify the Six Sigma methodology for solving business problems. Six Sigma recommends the DMAIC method for solving recurring problems. In our story, we are supporting Ben, the owner of a Pizza restaurant to overcome their problems using Six Sigma.

We are in the final chapters of Measure Phase. We saw how to calculate process capability using DPMO method in the previous chapter. We discuss Cp-Cpk method in this chapter.

Now

The Cp-Cpk method

“Before we go to Cp-Cpk, let us refresh ourselves with Voice of Design. Can somebody explain VoD?” I asked.

Anand extended a helping hand this time.

“I prepared a diagram last time based on our discussions. Shall I use my laptop to project and show the image?” asked Anand and I invited him to do so.

He displayed a picture. 

“Voice of Design or VoD is the requirements of customers converted into the process language. VoD is also known as Specifications. In our case, the customers need of hot pizza, got translated into 'the temperature of pizza at the time of service should be 66° C ± 3° C'. Here, 66° C has become our target, the 3° C is called Tolerance. The Target minus Tolerance is called Lower Specification Limit, and ‘Target plus Tolerance is called Upper Specification Limit”.

“Wonderful Anand, Thank you” I thanked him. “Do you have any doubts?” I asked the audience while Anand was going back to the seat with his laptop. They said “no!”.

“Ok, then can somebody help me with Voice of Process?” I asked.

Voice of Process

“Voice of Process?” they wondered. 

“Kannan, I am afraid we have not discussed this earlier. Or, Have I missed the topic completely?” asked Ben.

“Ben, you are right. We haven’t discussed Voice of Process or VoP before. I am trying to see whether you can extrapolate the learning”.

The rustling and murmur represented their situation.

“Ok, I am giving you a clue. We have discussed the concept earlier, but not the name. That will have three lines, upper, middle and the lower, similar to VoD”.

Ravi raised his hand and said, “Sir, I think, it is the concept of control charts”. I appraised him by gently nodding my head with raised eyebrows encouraging him to continue.

“The data points we collected are plotted in a sequence with a centre line, upper and lower control limits. Since the data points are from our process, we can call this as Voice of Process. We have seen this as part of Descriptive Statistics as well”.

“Right, Ravi!” We can compare the control chart, with a histogram with control limits. 

I had a diagram, and I showed it.

All that we saw in descriptive statistics – the central tendency, dispersion and shape of data are collectively called as Voice of Process.

Process Capability

When we superimpose the Process Spread and Specification Spread, we get to know the number of defects the process may produce. This is how we calculate the Process Capability, mathematically as well.

Cp

Cp is the ratio of Specification Spread to Process Spread. We can mathematically depict as, 

“Let us take a simple example. Earlier we took an example of the punctual staff in your office and his office coming time. Now, let us imagine I got the data of his office coming time for the past three months. I wanted to see the Voice of Process.”

“His mean office coming time is 9.00 am, Standard Deviation is 5 minutes, and the shape of data is as shown in the picture.

So far, in this case, we have not considered the voice of design. Now, let me imagine that your office starts at 9.00 am. Your HR department has given a grace period till 9.15 am. People coming after 9.15 will be marked as ‘late’. Let us imagine that your housekeeping staff will allow you to get inside the office only from 8.45 am. Anybody coming before has to stand outside till they open the door. We arrive at the specification limits of 8.45 to 9.15 am.

Cp Calculation

"When we superimpose VoP & VoD we get - " I showed the image.

"Here, we are producing some defects on both sides. Let us calculate Cp".

“Wow, interesting!” said Anand. “What does 1 Cp mean?” he asked.

“Hold on for a while, Anand. We will interpret it in some time” I said. “Now, just imagine, you’ve got a new HR Manager who restricts the grace period to 10 minutes”. Now, our curve will look like this”, I showed the picture.

“Let us see what happens to Cp”, I said and started doing the calculation on the board.

“That’s quite simple and understandable” commented Ben. “When we make more defects, the Cp goes down. But, it will make more sense if it can say what we need to do to improve the process, like which side of the curve to look for.,” he said.

“That’s what a leader will look for, Ben. That is why we use the Cpk method”.

Cpk method

“The shortcoming of Cp is it does not tell us where the problem is,” I said. “Let us calculate Cp in a new scenario.

“Consider, your new HR manager had changed your office start time to 8.45 and was willing to give you 15 minutes grace time, and he ensures that the office will be ready and open from 8.30 am. Can you calculate Cp by yourself?” I asked. 

Some of them came out with answers, but many of them responded with confusion.  

Then I showed the picture on the screen. 

“What? Here we are making nearly 50% defects, but still, the Cp is 1” wondered Anand and many chorused with “that’s what”.

“I expected that!” said Ben.

"The problem with Cp is that it is not location-sensitive. It considers only the ranges. Cpk is called Process Capability Index - We can call as Corrected Process Capability. To make the metric location-sensitive, we introduce the mean into the formula. We split the entire range of Specification Spread and Process Spread with mean in the centre. Then we get Upper and Lower parts separately. The least among the two will be considered as Process Cpk.

I wrote,

Cpk also shows on which side are we making more defects.

"Kannan, Cpk makes more sense to me. But are we using both Cp and Cpk simultaneously? Or we use only Cpk and Cp remains as a theory?" Ben was high with his questions.

When to use Cp and When to use Cpk?

"I wanted to throw this question to conclude this session as a trump card, Ben. But you broke my dream. I share a rule of thumb on Cp and Cpk.

Cp is used for established processes where we know that the process is centred around the target specification. Cpk is useful for a new process when we are not sure about the process' centre.

As we had come to the end of the morning session, I wanted them to have a break here. Because they would understand the calculation of Z value with a gap from Cpk calculation. Secondly, I can utilise their drowsy post-lunch session in doing some exercises with Minitab.

I looked at them. They were still energetic and eager to calculate their process capability. But, I decided to go for a break

Next 

We will see the Z value calculation in the next chapter and also see how these three are interconvertible and how to convert them into a universal scale of Quality. In the coming chapters, we will start the Analyse Phase.