Contents of Module

10.1 Simple Process Yield Metrics

10.2 Introduction to Process Capability

10.3 Basic Process Capability.

10.4 Z Scores

10.5 Sigma Shift

10.6 Off-Centre Distributions

10.7 Within capability and overall capability

10.8 Normality

10.9 Summary of Process Capability

10.10 Process Capability for Continuous Data

10.1 Simple Process Yield Metrics

Process Capability tells you how well your process meets the customer requirements, it’s that simple. In the Measure phase you would carry out an initial process capability study and then after you have gone through the Improve phase you could show your achievements and do a final process capability and compare.

Process Capability is a specific methodology for measuring your process defects in Six Sigma. You may also be aware of other measures such as process yield or Defects per Million Opportunities (DPMO).

10.1.1. Yield and DPMO example

Please calculate the yield and DPMO of a process where you have made a total of 625 parts of which 49 are defective.

The VOP is the width of the distribution delivered by the filling machine. Let’s say that we have measured the net weight from 200 samples. This is useful as bag weight also has the same units, grams, as the spec limits meaning that the units will cancel each other out when we calculate the Pp .  

Here is a histogram of our 200 data points. The curve of best fit for its normal distribution is also shown. If you remember back to the core statistics section we said that one of the characteristics of a normal distribution is that 99.73% of the data is within 3 StDevs of the mean.

92.16% may sound okay as a yield but it means that if you produce 1 million parts with that yield 78,400 parts will be defective out of that million.

Another term that you might hear is Rolling Yield. This is where the yield of a number of sub processes is combined by multiplying the individual yields together. For example, a process has three sub processes with yields YA , YB & YC , the rolling yield would be YA x YB x YC.   

10.2 Introduction to Process Capability

We are now going to focus on Process Capability and try to understand what the calculations actually mean in practical terms. Six Sigma is all about the customer and we call our customer requirements the Voice of the Customer (VOC). We call our process output the Voice of the Process (VOP). We should have in the Define phase determined which parameter we would be monitoring to establish our VOP. And also during the Define phase we would have looked at the needs of our customer and established the VOC. We select VOC and VOP to have the same units so that Process capability, Pp,  is a dimensionless number.

We are going to call  process capability, Pp .  You may have seen it called Cp in other texts but I believe that leads to an incorrect understanding of process capability so I am going to teach it correctly from the start.  Let’s go through a worked example and see how we calculate process capability. To help our understanding we are going to limit ourselves to normally distributed data or distributions where the underlying data is normally distributed in the Green Belt Edition.  We will have a more detailed discussion about that statement later in the module.

I am going to develop the explanation of  process capability calculations using an example of filling a bag with peanuts. This example will continue through the next couple of sections.

When you buy a 200g packet of peanuts the machine that filled the bag of peanuts works to a specification. The lower specification limit (LSL) is 200g, you should never have less than 200g nett weight of peanuts in your bag. But to save on cost the machine also has an upper specification limit (USL) of 220g. VOC is described as 220-200=20g or USL-LSL. This is also called the tolerance width or just tolerance. It is the difference/distance between the USL and LSL.

Or we could say that our process delivers 99.73%  of  its’s population in 6 Stdevs ( 3 from each side of the mean). This means that VOP is the StDev delivered by the process multiplied by 6.  When the distribution is not normally distributed it gets much harder to calculate the VOP. The Green Belt edition of this book only considers normally distributed processes. If you are told that your process is not normally distributed then please consult a knowledgeable Black Belt.

Let’s have a look at our process capability equation and substitute our data from the peanut filling machine.

I like to think of process capability as a ratio of widths, it is the width of the spec limits divided by the width of the process delivery.

A higher value of  process capability is better as this means that the process width is small and easily fits within the specification limits. It’s good to have a safety margin. If VOC and VOP are equal , then Pp =1, then your process fits exactly within your spec limits and you have no room for error. But if we are hyper technical that is not true because if VOC=VOP=6σ, then only 99.73% of the process is within the specification limits and 0.27% will still be rejects.  

While we are thinking of widths, we can also determine the distance from our mean to the USL (or LSL). If we think of this distance in units of StDev we can also get a measure of the capability of our process. This number is expressed in units of StDevs and is called the Z score.

Again, the higher the Z score the more capable the process. There is also another metric called the Z Bench score. This is the distance in units of StDev from the mean to a line that marks all process defects as drawn under the normal curve. All process defects means collecting the defects under both tails and then adding them together.

Let’s say that we have done an improvement project on the peanut filling machine and we have reduced the fill weight StDev from 3 to 1.667, a good improvement. What’s our process capability now?

Our Z score would be 6 as the mean is six StDev’s away from either spec limit. This is actually now a Six Sigma process and this is where the name for Six Sigma originates. It’s the aspirational target of having a process where the mean is 6 sigma’s away from the nearest specification limit. You may have heard that a Six Sigma process only produces 3.4 defects per million opportunity and has a Yield of  99.99966%.

There are tables available that will tell you what your DPMO or Yield% will be for a particular process capability or Z score.

10.5 Sigma shift

f you look at the table again and look at the Yield% for a Z score of 3 you might get a little confused. The Yield% stated in the table is 93.3% but I have previously said that 99.73% of all data under a normal curve lies within 3 StDev’s of the mean. Is 93.3% a mistake in the table? Personally, I don’t like the Sigma shift concept but it is not a mistake. What is happening is that a 1.5σ shift is applied to the defects to account for the long term deterioration of process capability. If you see the DPMO of a 6σ process reported as 3.4 you will now know that a 1.5σ shift has been applied to that data. The actual number of defects generated by a 6σ process, in the short term, is actually only 0.002 DPMO.

Like it or not, this reporting convention exists and it does install a safety margin that becomes more important at lower Z scores.

10.3 Basic Process Capability

10.4 Z Scores

Next PageNext Page

Free Sample  

Process Capability chapter from Sigma Statistics using Minitab 17, Green Belt Edition.

It does not include 10.11 Process Capability for Attribute data.