# Statistical process control

## Introduction to SPC

### SPC chart introduction for non-mathematicians.

All processes vary and the the aim of SPC is to minimize this variation. Variation is expressed as 'sample standard deviations' (SD) and SD is a mathematical term, based on probability theory. Click the links to download copies of a Capability Study Template and Statistical Process Control Chart.

Consider the process of driving a car along a dry, straight, level road; look at your hands on the steering wheel - they move as you make slight adjustments. Why are the adjustments necessary? Because the road is not totally flat, there's some play in car's suspension, etc.

If you draw a graph of the movements you will have a 'normal distribution curve'. In a normal distribution, most of the time your hands are in the middle. (In the secret language of SPC the 'middle' is called the 'average' or 'mean' or 'x-bar')

But sometimes your hands are a little to the left, at other times they're a little to the right, and on rare occasions they're on the extreme left or extreme right.

### SPC Application

Using the sample standard deviation (SD), you can then calculate and chart the usual extremes of a process under a given set of conditions. This variation is 'normal' and we cannot reduce the variation without making fundamental changes to the process (e.g. going on an advanced drivers course, buying sports suspension, etc.)

Because of the properties of the normal distribution it is usual in SPC or quality control applications to multiply the standard deviation by three and then add that to and take it away from the average which gives a confidence level which encompasses 99.73% of the observations or 'population'.

For example:

average = 20

1 SD = 1.3

3 SD = 3.9

average + 3 SD = 23.9

average - 3 SD = 16.1

therefore 99.73% of all that we see will be between 16.1 and 23.9

#### Back in the car...

A child runs out in front of you and you swerve to avoid him. The chart now shows a blip which is outside the normal curve. This indicates that something unusual has happened.

In SPC applications it is often useful to recognize what is normal and what is non-normal. This case is clearly non-normal. In some situations also helps to know when things happen. Therefore, an SPC control charts also has a time axis.

### SPC Control Charts

We can then apply these concepts in an SPC chart for monitoring customer complaints.

Having collected the basic information we can then add the average and +/- 3 SD markers.

What we are saying is:

1. Given the normal variation of the process we will always have a level of complaints. There is nothing we can do without making fundamental changes to the process.

2. As long as the individual plots are between the red lines then the process is exhibiting normal variation.

3. BUT clearly something unusual (non-normal) happened in March - we had far more complaints than usual. We need to investigate and find out why.

4. THIS IS THE CLEVER BIT - February's low result is equally unusual. We need to find why it happened and build that in to the process. Do it often enough and the average line will go down, and eventually become zero.

To help the investigation, use appropriate problem solving tools.

### The problem with traditional SPC

Most SPC control chart techniques are based around the +/- 3 SD method, which covers 99.73% of a population. 99.73% sounds good until you realize that this means that 0.27% are not accounted for, there is 1/4 percent chance of something slipping through the net.

If you are trying to control critical processes or very high volume (e.g. aerospace, building nuclear reactors, making silicone chips, etc.) then you will get it wrong once in every 370 attempts.

Such critical industries tend to use Six Sigma (+/- 6 SD) methods as it gives a 99.9997% (3 in a million failures) confidence level. Three in a million sounds much better than one in three hundred and seventy.

To learn more, we recommend reading the articles from SPC Press & Statistical Process Controls, INC