T T20-06 Control Chart (with Runs Tests) Purpose Allows the analyst create and analyze a "Control Chart". A visual analysis of the control time series with upper and lower confidence limits is shown along with the A/B and U/D "runs tests" for randomness. Inputs Observed Sample Statistics (range, means, proportions, or defects per unit) Control Chart Centerline, LCL, and UCL Outputs Control Chart Runs Tests

T Used in conjunction with control charts to test for randomness of observational data. The presence of patterns in the data or trends indicates that non-random (assignable) variation is present. A run is a sequence of observations with a certain characteristic. Two useful run tests:. Runs above and below the centerline data translated into A (above) and B (below). Runs up and down data translated into U (up) and D (down) Run Charts – Check For Randomness

T Counting Above/Below Runs (7 runs) Counting A/B Runs B1B1 A2A2 A2A2 A4A4 A6A6 A6A6 B3B3 B5B5 B5B5 B5B5 B7B7 If a value is equal to the centerline, the A/B rating is different from the last A/B rating.

T Counting Up/Down Runs (8 runs) Note: the first value does not receive a notation Counting U/D Runs U1U1 D6D6 U7U7 U7U7 U5U5 U3U3 U1U1 D4D4 D2D2 D8D8 If two values are equal, the U/D rating is different from the last U/D rating.

T Once the runs are counted they must be compared to the expected number of runs in a completely random series. The expected number of runs and the standard deviation of the expected number of runs are computed by the following formula: Expected Number of Runs

T Next, we compare the observed number of runs to the expected number of runs by calculating the following Standard Normal Z-statistic : Compare Observed Runs to Expected Runs

T For a degree of confidence of 99.7% (3 standard deviations), we compare the comparison to -3 standard deviations and + 3 standard deviations.. If either the Zab or Zud is.. < lower limit (-3) then we have too few runs (Out of Control).. Between the lower limit (-3) and upper limit (+3) then we have an acceptable number of runs (In Control).. > upper limit (+3) then we have too many runs (Out of Conrtrol) Too Few Runs Acceptable number Runs Too Many Runs Runs Test - In or Out of Control

T The observed means of 20 samples each containing 5 observations are shown here. The Centerline = , LCL = , and UCL = have been calculated Create the Control Chart and conduct the A/B, U/D Runs Tests for randomness. Example

T Input the Centerline, LCL, UCL, and Observed Values for the appropriate control chart in the light green cells.

T Input the Control Chart is automatically displayed showing the Centerline, LCL, UCL, and Observed Values

T Input the Sigma Level and the A/B and U/D Runs Tests are automatically calculated.