Western Electric Rules Some definitions Run: A control chart may indicate an out

Question

Western Electric Rules Some definitions Run: A control chart may indicate an out-of-control condition when one or more points fall beyond the control limits or when the plotted points exhibit some nonrandom pattern of behavior. In general run is defined as a sequence of observations of the same type. Sensitizing Rules for Shewhart ControLCharts: 1- One or more points outside of the control limits. 2- Two of three consecutive points outside the two-sigma warning limits but still inside the control limits. 3- Four of five consecutive points beyond the one-sigma limits. 4- A run of eight consecutive points on one side of the center line. 5- Six points in a row steady increasing or decreasing. 6- Fifteen points in a row in zone C (both above and below the center line) 7- Fourteen points in a row alternating up and down. 8- Eight points in a row on both sides of the center line with none in zone C. 9- An unusual or nonrandom pattern in the data. 10- One or more points near a warning or control limit.

Explanation / Answer

As per the western electric rules:

1.      One or more points outside the control limits:

None of the points are outside the UCL and LCL

2.      Two of three consecutive points outside the two sigma warning limits, but still inside the control limits

UCL = Centre line + 3 * sigma. If we divide the region between center line and UCL into 3 parts, the top most part will represent the > 2 sigma limit and < UCL

Similarly

LCL = Centre Line + 3 * sigma. Thus if we divide the region between center line and LCL into 3 parts, the lowest region will represent the > 2 sigma limit and < LCL

There are no such points

3.      Four of five consecutive points outside the one sigma limits

This means 4 consecutive points should cross the first line either on the upperside of center line or on the bottom side of the center line

The last 4 consecutive points seem to lie outside the one sigma limit below the center line ( although one of them is just on the border of the one sigma limit ).

4.      A run of 8 consecutive points on one side of the center line

No such 8 consecutive points exist.

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