1. Higher National Certificate in Engineering
Unit 36
LO2.1.1– Control Charts (Variable)

2. Learning Outcome 1.1
LO2.1: select and group sample data based on variable inspection and attributable inspection and calculate appropriate control chart limits

3. Developing Control Limits for Variable Data
To date we have produced a ‘run-chart’ and we’ve asked the question, is the process ‘good’ or ‘bad’ i.e. is it ‘in-control’ or ‘out-of-control’?
Shewhart’s genius was construct control limits on run-charts to enable to interpret whether a process is in or out of control.
Note the key point before we start is to satisfy yourself that only common cause variation is present – so firstly there is a need to eliminate special cause variation.

4. The use of X bar and R
It has been shown that for variable data the mean is given by…
x = x1 + x2 + x3 + … + xn n
And that the range…
R = largest x – smallest x
It is these are the values that are plotted on charts

5. Constructing Control Limits for Variable Data
Once we are happy that we have stability in our process – i.e. the process is exhibiting only common cause variation (this is generally established by producing a run chart by taking samples over a period of time – say about 20 or so samples), then we need to firstly determine the average of the averages: X-bar-bar and the average of the ranges of the samples R-bar.
Thus we construct two charts X-bar and R

6. X-bar-bar & R-bar
So to set up a chart, take 20 (minimum) random samples each of size, say 5-off at different time intervals.
Calculate x and R for each of the samples
Then calculate…
x = x1 + x2 + x3 + … + x20 20
R = R1 + R2 + R3 + …+ R20

7. Constructing Control Limits for Variable Data
Having calculated X-bar-bar and R-bar, we use this information together with constants which are given in a table – the constants we use being determined by our sample size – to calculate the control limits
Sample size A2 D3 D4 3
1.023
2.575 4
0.729
2.282 5
0.577
2.115 6
0.483
2.004 7
0.419
0.076
1.924

8. Constructing Control Limits for Variable Data
Upper Control Limitx (UCL) = x + A2 x R
Lower Control Limitx (LCL) = x - A2 x R
UCLR = D4 x R
LCLR = D3 x R

9. Control Limits
Exercise 1