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

The warning limits mentioned in the rules for Shewhart Control charts are the one sigma and two sigma warning limits.

The data shown in the figure has symmetric upper and lower control limits with respect to the center line (or mean). The rules that depend on the use of warning limits are Rule Nos. 2,3 and 10. In this particular data we can observe the following with respect to these rules:

Rule 2: Two out of three consecutive points outside the two sigma warning limits but inside the control limits

We might hit this rule for the consecutive points at instants 18,19,20 depending on the warning limit and calculation of sigma.

Rule 3: Four of Five consecutive points beyond the one sigma warning limits.

  We might hit this rule for the consecutive points at instants 16,17,18,19,20 depending on the warning limit and calculation of sigma.

Rule 10: One or more points near a warning or control limit.

The possibility of hitting this rule in particular can be high considering that we will be adding four warning limits +/- one sigma and +/- two sigma. The points that can violate this rule might be at instants 2,3,5,6,8,11,12,16,17,18,19 and 20.

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