of exceeding the

upper control limit. (Here X indicates the random count for the week.) On the other hand, if the mean is just slightly higher, say [[mu].sub.t] = 6.5, then the

upper control limit is 14.63, leaving a probability of

This was tried both ways, and the

upper control limit tended to be quite wide when the limits were based on the [chi square] limits.

The points are erratic; two points are significantly above the

upper control limits, and a few points are on or below the lower control limits.

For example, the lab manager noticed the control chart for ML had peaked above the

upper control limit. This told him something had changed, and that this change was adversely affecting the product.

Therefore, in case I, the control chart for this case also has an

upper control limit equal to an appropriate percentile of chi-square distribution.

2) Calculate the

upper control limit, UCL and the lower control limit, LCL of the arithmetic average surface roughness [R.sub.a] and the surface roughness [R.sub.z], which are used in the I-MR charts.

t + 1] = the

upper control limit in time period t + 1; [LCL.sub.t + 1] = the lower control limit in time period t + 1; [z.sub.t] = the center line (Eq.

The probability

upper control limit is compared with the 3-sigma

upper control limit of 50.

At Point 3 on the chart, the deviation of the dimension was out of the established parameter (above the

upper control limit (UCL) for the dimension).

Then, to keep [Alpha] unchanged, we try to relax the

upper control limit at the same time.

1, they are marked [UCL.sub.X], [LCL.sub.X] for

upper control limit and lower control limit for X and [UCL.sub.R], for

upper control limit for R.

They are added to make both the probabilities below the lower control limit -3 and above the

upper control limit 3 closer to (0.27 per cent)/2 = 0.135 per cent.