The standard deviation is the variation from the "average or mean" for the type of equipment being tested and often can help you find the story behind the data. To assist in this we use the term normal distribution of data.

A normal distribution of data means that most of the examples in a set of data are close to the "average or mean" while relatively few results head to the outer extremes. This “average or mean” establishes what is considered “Normal” for that type of compartment and the extent of the variation away from this “average or mean” is deduced from the number of Standard Deviation amounts from this “average or mean” which permits warnings of increasing severity in accordance with the number of standard deviations.

If we are looking at the data set for a Pump drive and the wear metal we are considering is Iron (Fe), we need to look at the typical data that we have extracted from the analysis of all Pump Drives for Iron to establish the “average or mean” for iron in this type of compartment. Like most data, the outcome from the results will turn out being normally distributed. This means that the majority of Iron analysis results will be close to the “mean” while a smaller number of Iron results will be lower and higher than the “mean”. The amount by which these lower and higher results deviate from the “mean” fall into bands of multiples of the Standard Deviation with the highest number of Standard Deviations being the most critical.

Use Of Standard Deviation in Diagnostics

To assist in diagnoses of analysis data for wear we apply statistical analyses of the normalised wear values to determine whether or not the results are showing a variation from the “average" or "mean” results previously established for the type of compartment being tested.

The x-axis (the horizontal one) is the Iron, Copper or other wear metal values. And the y-axis (the vertical one) is the number of data points for each value on the x-axis... in other words, the number of pump drives that generate x amount of Iron.

Now, not all sets of data will have graphs that look this perfect. Some will have relatively flat curves others will be steep. Sometimes the mean will lean a little bit to one side or the other. However, all normally distributed data will have something like this same "bell curve" shape.

The standard deviation is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data. If you can imagine the centre of this target being the mean then all the shots taken around the centre are spread out in proportional groups 68% ended up in the middle 27% just out of centre and 1% on the extreme.

When the examples are tightly bunched together and the bell-shaped curve is steep, the standard deviation is small. When the examples are spread apart and the bell curve is relatively flat will mean you have a relatively large standard deviation.

One standard deviation away from the mean in either direction on the horizontal axis accounts for somewhere around 68 percent of Iron results in this group.

Two standard deviations away from the mean accounts for roughly 95 percent of Iron results.

Three standard deviations account for about 99 percent Iron results.

If this curve were flatter and more spread out, the standard deviation would have to be larger in order to account for those 68 percent or so Iron results. So that's why the standard deviation can tell you how spread out the results are in a set from the mean.

The computer will calculate the mean and three levels of standard deviation as shown in the table.

The analysis results are compared with the standard deviation benchmarks to determine the condition of the oil.

The following recommendations are made:

1. If the results are less than one (1) standard deviation, the outcome is analysed as being “Satisfactory”. For example, having an Iron result less than 273.9.

2. If the results are between one (1) and two (2) standard deviations, the oil is assessed as being “Slightly Elevated”. For example, having an Iron score between 273.9 and 387.2.

3. If the oil has a score exceeding two (2) standard deviations it is considered “Unsatisfactory” and some action will be required.