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

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

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.

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

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

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

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

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

Control Limits Exercise 1