00035 Í241034634b4e2dd3fb05e21831301a

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Moinau

A summary of chosen tests parameters:

lead CUSUM 2nd CUSUM SPRT EWMA GCC

hj = 2.8

^ = 3.5

a = .05 p = .10 a = .2 k = 1.5

k = 3

The tests, with the chosen parameters, provide for a satisfactory run length distinction between confirming correct detections and false alarms.

Data Reauirements

Unlike typical statistical testing methods that look at only one data element (the actual reading), this system reÄ…uires three elements. The system examines the test values at the initial firing, the test values five observations past the firing, and the number of test firings during the five additional runs. Instead of using a single point estimate to make a decision, the system has two point estimates, and data on what happened during the interval between the two readings. Also, comparing the two point estimates allows for making a determination on the correctness of the firing.

Even with the additional observations, on average the system should outperform a single CUSUM test. From the Average Run Length (ARL) table (Table 1), hj = 2.8 should detect a two-times acceptable shift in an average of

12.9    observations. The additional five observations will increase this to an average of 17.9 runs to detect. In comparison, for h^ = 4.2 the ARL should be

19.9    runs. The = 4.2 is a popular choice among CUSUM enthusiasts, siÅ„ce it offers good detection sensitivity yet also offers good protection against false alarms. On average, the system will be able to provide detection information 2.0 observations sooner than h_t = 4.2.

Rule Descriptions

Examining the three data elements, rules were developed which would exploit the information that distinguished between actual detections and false alarms. Rulesets were developed to look specifically at the values at the fifth additional observation, at the number of firings during the extra time span, and at the differences in the test values between the initial and additional readings.

Each signal, with the accompanying three data elements, is passed through a series of fllters of rules. Each signal passes through Ruleset 1, and may be classified as either a detection, false alarm, or may pass through unclassified. If unclassified, the signal goes through Ruleset 2. If still