00049 Êb10896ff0f5787f3cbee8d106ea4ee

48

Molnau

lags slightly behind the baseline at the beginning, siÅ„ce it cannot reach a decision until the 36th point. The system quickly overtakes the baseline and produces a sizable detection advantage over the rest of the observation rangÄ™. Not until the end of the rangÄ™ does the baseline approach the total number of correct classifications.

The table in FigurÄ™ 12 summarizes the comparison of the two cumulative values. At the end of the flrst observation bÅ‚ock, which the system cannot fire, the baseline produces only four correct decisions. By the end of the second bÅ‚ock or 40th observation, the system has accumulated 33 morÄ™ correct decisions than the baseline, or 5.3% of the total readings. Up to the 45th and 50th observations, the system compiles about a 13% detection advantage. After the 55th reading, the system has amassed 101 morÄ™ correct detections than the baseline~an improvement of 16.4% of the total runs madÄ™. The system remains ahead of the baseline until the end of the detection rangÄ™.

As with the shift case, all misses are counted to have fired one observation past the last point in the detection rangÄ™. Here, all misses are given an arbitrary count of 81. With this, the system took an average of 52.86 readings to make a correct decision. This compares to 57.66 observations for the baseline. The system therefore reaches a correct decision an average of 4.80 readings sooner than the baseline. The time reÄ…uired to achieve this number of readings in a process producing in the defects per million rangÄ™ is large, therefore this large time differential is important.

Nuli Case

As shown in FigurÄ™ 10, the system and the baseline methods produced the same results for the in-control scenario. Both tests produced seventy incorrect detection classifications for the one thousand simulated runs, giving a 93% success ratÄ™. The problem of using a morÄ™ sensitive procedurÄ™ is the almost geometrie inerease in false alarm notifications. Therefore equaling the baseline's success ratÄ™, while still offering the faster detection, is important.

Discussion and Conclusions

The results of the research show that the system performed very well when measured against the baseline method--a CUSUM procedurÄ™ with an 1^ value of 4.2. The system outperformed the baseline handily in speed of detection. At some points, the system would have correctly classified the equivalent of over 10% of the total received signals before the baseline. Also, the system performed as well as the baseline in accuracy. The system provided a composite performance over the test scenarios of 95.02% success, compared to