Western Electric rules are applied to a control chart of a g

Western Electric rules are applied to a control chart of a given quality characteristic. The probabilities to decide based on these rules are 0.001, 0.002, 0.001, 0.003 respectively.

(a) Compute ARL of this process.

(b) Is it wise to adopt more sensitisng rules? Elaborate.

Solution

(a) ARL = 1 / 0.007 =142.857......

(b)
Warning limits on control charts are limits that are inside the control limits. When warning limits are used, control limits are referred to as action limits. Warning limits, say at 2-sigma, can be used to increase chart sensitivity and to signal process changes more quickly than the 3-sigma action limits.   The Western Electric rule, which addresses this type of shift is to consider a process to be out of control if 2 of 3 plot points are between 2 sigma and 3 sigma of the chart centerline.Warning limits on control charts are limits that are inside the control limits. When warning limits are used, control limits are referred to as action limits. Warning limits, say at 2-sigma, can be used to increase chart sensitivity and to signal process changes more quickly than the 3-sigma action limits.   The Western Electric rule, which addresses this type of shift is to consider a process to be out of control if 2 of 3 plot points are between 2 sigma and 3 sigma of the chart centerline...
So, it is good to use this rule!!but, further rules which can deduce the ARL more i.e decreasing the false alarm!will be wise!