Attribute Charts

There are four main types of attribute chart which differ in the type of data which they are used to record. Before listing the charts it will be useful to provide a couple of definitions:

Defects are errors in the output of a process, for example:

• bubbles in paintwork
• typing errors in a document
• flaws in a length of material

Defectives are items which, because of the presence of one or more defects are considered faulty and unfit for use. Examples include:

• lightbulbs which don't work
• bad copies from a photocopier
• bearings outside the specified tolerance limits

For a given sample, the number of defective items cannot be larger than the sample size. However, the number of defects found within the sample is potentially infinite.

The four main attribute charts are:

• Number Defective (np-Chart): this chart monitors the number of defective items in each sample, where the sample size is constant. This chart is sometimes called an f-Chart ('f' for faulty).
• Proportion Defective (p-Chart): this chart is similar to the np-Chart but instead of recording the number of defective items, the p-Chart records the proportion of defective items in a sample (the number of defective items divided by the sample size). This means it can be used with samples of varying size. Theoretically, the control limits should be recalculated each time the sample size changes. However, in practice this is tiresome and is not really necessary, so long as the sample size does not vary from the average by more than ±20%.
• Number of Defects (c-Chart): this chart is used to record the number of defects found in each sample, where the sample size is constant.
• Number of Defects per Unit (u-Chart): this is similar to the c-Chart, but is used for samples of varying size. In order to be able to compare samples of different sizes, this chart records the average number of defects per unit in the sample (calculated by dividing the number of defects by the sample size). As with the p-Chart, the same control limits may be used so long as the sample size does not vary from the average by more than ±20%.

In addition the XmR chart can be used as a generic 'catch-all' chart for any attribute data. It is not as sensitive as the more specific charts, but means you don't have to try and decide which is the appropriate chart for a given situation. If in doubt, the XmR chart will give more reliable results than the wrong type of attribute chart.

In this course we will only be looking in detail at the u-Chart.