Don’t just move the average, understand the spread

Tim Akerman
Categories:   Data Analysis   Lean Six Sigma   Process Improvement   Quality   Six Sigma   Statistical Analysis  

Picture the scene; someone in your organisation comes up with a cost-saving idea. If we move the process mean to the lower limit, we can save £’000’s and still be in specification. The technical team doesn’t like it, but they can’t come up with a reason other than “it’ll cause problems”, the finance director loves the idea, and the production manager with one eye on costs says, well if we can save money and be in spec, what’s the problem?

Let me help you. 
In this scenario, the technical team may be right. If we assume that your process is in control and produces items with a normal distribution (remember that is the best case scenario!) logic dictates that half of your data is below the average value and half is above. That being the case, what you really want to know is how far from the average the distribution spreads. If the spread is large and you change process to the extreme where the average value sits right on the customer specification limit, half of everything you make will be out of spec. Can you afford a 50% failure rate? What will the impact be on your customers, your reputation, your workload (dealing with complaints). 

To work out how much we can move the process, we must first understand how much it varies, and we use a statistical value called the standard deviation to help us. Standard deviation is the average variation from the mean for a sample data set. To work it out, take 20 samples, measure them all 5 times then use a spreadsheet to work out the mean and standard deviation. If that is too much take 10 samples and measure 3 times. Keep in mind that the smaller sample size will give a larger standard deviation. Now take the mean and add 3 x standard deviation. This is the upper limit of your process spread. Subtract 3 x the standard deviation from the process mean to find the lower limit of your process spread. The difference between these two numbers is the spread of your process and will contain 99.7% of the results measured from the process output IF the process is in control and nothing changes.

If moving the mean takes the 3 standard deviation limits of your process outside of the specification, you will get complaints. It could be that the limits are already outside of the specification, in which case moving the average will make a bad situation worse.

It is possible to calculate the proportion of failures likely from a change of average, this done using z-score calculation. I’m not aiming to teach maths, so the important message is that the failure rate can be calculated.

This is the tip of the iceberg with understanding your process. If you don’t know that your process is stable and in control, the spread won’t help you because the process can jump erratically. To improve your process

1. Gain control, make sure the process is stable.

2. Eliminate errors and waste

3. Reduce variation

4. Monitor the process to make sure it stays that way.

The most significant and profitable gains are often from process stability, not from cost-cutting. All cost-cutting does is reduce the pain, think of cost-cutting as a painkiller when you have an infection. It makes it hurt less, but doesn’t stop the infection. You need to stop the infection to feel better.

Now do you want to hurt less or do you want to get better?