## 5.29 - Statistical Process Control

Statistical Process Control (SPC) is a method that gives confidence each part or component is within tolerance, without having to measure every piece. It is associated the concept of controlling the process and not the product. It is form of feed forward control.

If we measure the diameter of every component coming of a machine we could get the flowing results:- (Note: Frequency = Rate of occurrence of a particular dimension)

This type of diagram is called a frequency distribution. The bell shape of the curve is very common in practical situations.

 If the tolerance band of the dimension on the component is wider than the bell shaped frequency curve, can confidently predict that all of the components will be within tolerance. We can then say that the machining process is capable of achieving the accuracy required.  However, if the frequency curve is wider than the tolerance band we can say that the machine is not capable of achieving the accuracy required.

We can predict the shape and position of the bell shaped curve by measuring a small number or sample of components and calculating the sample average and range.

 Sample Average X̄ = Sum of measurements for all components in sample Number of components in the sample Sample Average R = Largest measurement - Smallest measurement

For example, if a sample of 4 components are measured and found to be 9.5, 9.7, 9.2, and 9.4 mm.

 Then: X̄ = 9.5 + 9.7 + 9.2 + 9.4 = 9.45mm 4 and R = 9.7 - 9.2 = 0.50mm

These values can be plotted on control charts

### Average Control Chart The Average Control Chart indicates when a process is under control (i.e. where the plots are not heading outside the limits). If all the plots on the chart are within the action limits we can be confident that all components are within tolerance.

If a sample goes outside the warning limits the machine should be reset.

### Range Control Chart The Range Control Chart is used to give an indication of machine capability and any readings outside the action limits require corrective action.

To apply SPC properly, operators must trained and provided with:

• A means of calculating X̄ and R
• Standard graph sheets
• A list of recommendations for follow-up action.