The Psychology of Quality and More

# Understanding variation

The Quality Toolbook > Variation > Understanding variation

The continuously variable nature of the universe is at the heart of the science of statistics, and at first glance can look very complex, particularly if approached from a mathematical viewpoint. This can lead to it being ignored, which is a pity, as even a simple appreciation of it can result in a reduction in haphazard attempts to control it, with a consequent saving in wasted time and degraded performance.

## What is variation?

When a process is executed repeatedly, its outputs are seldom identical. For example, when a gun is successively fired at a target, as in Fig. 1, the bullets will not all pass through the same hole.

Fig. 1. Variation in targeted results

This lack of repeatability is caused by the variation or variability in the process. If these causes are understood, then this can lead to the development of solutions to reduce the variation in the process and result in more consistent products which require less inspection and testing, have less rejection and failure, cost less to build, have more satisfied customers and are more profitable.

## Causes of variation

Variation in process output is caused by variations within the process. These may be one or more of:

1. Differing actions within the process.
2. Differing effects within the process.
3. Differing inputs to the process.

As an example for each of these conditions, the variation in the placement of the bullet holes in the target may be affected by:

1. The gun being held or used differently.
2. Wear in the hammer mechanism causing the shell to be struck differently.
3. The bullets being of slightly differing shape or weight.

Thus, even if the first point is eliminated by putting the gun in a clamp and firing it remotely, the bullets will still not all hit the target in the identical position.

The reasons why variation occurs can be divided into two important classes, known as common and special causes of variation. These are discussed further below.

## Common causes of variation

Within any process there are many variable factors, as indicated above, each of which may vary a small amount and in a predictable way, but when taken together result in a degree of randomness in the output, as indicated in the figure below. These seemingly uncontrollable factors are called common causes of variation.

Common causes of variation can seldom be eliminated by 'tampering' with the process. For example, consider the effect of simple adjustments to the clamped gun, as in the figure below.

Fig. 2. Tampering

1. The first hole is to the left of center, so the clamp is rotated a little to the right.
2. If the clamp had been left alone, the second bullet would have gone a little to the right of center, but as it has been moved right, the bullet now goes further to the right. As a reaction to this, the clamp is rotated somewhat more to the left.
3. The third bullet tends towards the left anyway, so the result is a hole even further to the left.

It can be seen from this that it would have been better not to tinker with the clamp, and that the score would be more likely to improve if the whole system were understood first and then fundamental improvements made, such as building a better gun or making better bullets.

## Special causes of variation

Special causes of variation are unusual occurrences which come from outside the normal common causes, for example where a shot goes outside the main grouping, due to someone tripping over the gunner as the gun is fired, as below:

Fig. 3. Special and common causes of variation

Special causes can thus be addressed as individual cases, finding the cause for each occurrence outside the normal grouping and preventing it from recurring. This may be contrasted with the way that common causes must be addressed through the overall process.

The way that causes are addressed in a process improvement project is usually first to recognize and eliminate special causes, and then to find ways of improving the overall process in order to reduce common causes of variation.

## Static and dynamic variation

The distribution of measurements as described above takes no account of time or sequence, as it is not important which measurement came first or last. This is static variation.

If the order in which measurements are made is known, then significant trends may be detected, which may be useful for catching a problem before it becomes serious. This is dynamic variation.

For example, if the gunner is initially accurate, but becomes less so as his arm tires, then this may not be detected from the final positioning of holes on the target - it could only be seen by plotting the positioning of the holes across time.

Dynamic variation is commonly measured using the Control Chart.

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