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## Quick reference

### Normal Variation

All processes experience normal random variation. This is often modeled with a bell-shaped curve and can be described with statistical data parameters including the mean, median, range and standard deviation.

### When to use

When initiating an SPC analysis. You will need to determine the pattern of variation. Once the variation has become normal variation, you can begin to control the process.

### Instructions

Normal variation is represented with the Bell-Shaped curve which is a symmetrical distribution that has a high center peak and with upper and lower edges that approach zero. This is also referred to as a Gaussian distribution, named after Carl Gauss the father of the science of statistics.

This normal curve is a mathematical representation of the effect of random distribution. Because it is a predictable size and shape, the random variation is predictable. A predictable process can be controlled with statistical process control. If the variation was not random variation, the process would not be predictable and therefore it could not be controlled.

This predictable shape and size can be expressed with a set of commonly used statistical measures. We will use these measures throughout our discussion of SPC.

- Mean – this is the average value of all the items in the data set.

- Median – if all the values in the data set are ordered from smallest to largest, this is the value of the middle point.

- Range – this is the span from the smallest value to the largest value in the data set.

- Standard Deviation – this is a statistical measure of the typical spread of the data. It starts with the difference of each value from the mean value, which is called a deviation. It then squares those deviations, determines the average of those and then takes the square root of that number.

The standard deviation for a normal curve can be used to predict the percentage of values in the data set that will fall within a span. Of most significance to us in SPC is the span from minus 3 standard deviation to plus 3 standard deviations. This span will contain 99.73% of all the data values in the data set. This range was used by Walter Shewhart when first developing SPC control charts.

### Hints & tips

- When your data set for a process parameter is represented by a normal distribution, you know you are dealing with random variation. This type of process is an ideal candidate for statistical process control.
- You will be using the mean, median, range and standard deviation a lot in SPC. Make sure you thoroughly understand what they are and how to calculate them.

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