Property Control Charts

Control charts were originally developed in the 1920s as a quality assurance tool for the control of manufactured products. Although there are many types of control charts, the most common in a quality assessment program is a property control chart in which we record single measurements.

A property control chart is a sequence of points, each representing a single determination of the property we are monitoring,. To construct the control chart, we analyze a minimum of 7–15 samples while the system is under statistical control. The center line (CL) of the control chart is the average of these n samples. Boundary lines around the center line are determined by the standard deviation, S, of the n points, with the upper and lower warning limits (UWL and LWL) and the upper and lower control limits (UCL and LCL) are given by the following equations

UWL = CL + 2S LWL = CL – 2S UCL = CL + 2S LCL = CL – 2S

An example of a property control chart is illustrated here.

Figure15.3

The position of the data points relative to the boundary lines determines whether the analysis is in statistical control, based on a set of rules:

  1. An analysis is no longer under statistical control if any single point exceeds either the UCL or the LCL.
  2. An analysis is no longer under statistical control if two out of three consecutive points are between the UWL and the UCL or between the LWL and the LCL.
  3. An analysis is no longer under statistical control if seven consecutive results fall completely above or completely below the center line.
  4. An analysis is no longer under statistical control if six consecutive results increase or decrease in value.
  5. An analysis is no longer under statistical control if 14 consecutive alternate up and down in value.
  6. An analysis is no longer under statistical control if there is any obvious nonrandom patter to the results.

The first two rules are based on the assumption that results are normally distributed; if true, then only 0.26% of results will fall outside of the UCL or the LCL, and only 5% of results will fall outside of the UWL or the LWL. The remaining four rules are based on the expectation that the distribution of results is random and that the presence of an pattern in the data indicates that the analysis is no longer under statistical control.

The illustration below provides three examples of control charts in which the results show an analysis that has fallen out of statistical control. The highlighted areas show violations of: (a) rule 3; (b) rule 4; and (c) rule 5.

Figure15.6

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