@MISC{Tuning_partiii, author = {Implementation And Tuning}, title = {Part III Tuning and Applications}, year = {} }

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Abstract

this paper, the mean (and not worst) delay is computed by assuming a stationary distribution for the decision function (x 2 ) t 0 \Gamma1jt 0 \Gamma1 just before the change time t 0 . To extend these results to lower values of ff, let us consider the limit case ff = 0. In this case, the filter equation (11.1.6) is in fact a cumulative sum for which we can use the formula giving the bounds for the ASN in sequential analysis discussed in subsection 4.3.2. For the comparison with the two-sided CUSUM algorithm, we need to know the lower bound for GMA and the upper bound for TGMA . It results from (4.3.74)-(4.3.75) that GMA max 0fflh 1 ae h 1 + ffl jj \Gamma 2h 1 jj + '(jj) jj OE(\Gammajj) \Gamma 1 Q(jj) oe where Q(jj) = OE(\Gammajj) e \Gamma2(h 1 +ffl)jj \Gamma OE(jj) OE(\Gammajj) e \Gamma2(h 1 +ffl)jj \Gamma OE(jj) e 2(h 1 \Gammaffl)jj TGMA h 2 1 + 1 + 4h 1 p 2 : The results of this comparison are presented in figure 11.1 for ff = 0:05 and in figure 11.2 for ff = 0, where the functions ( T ) and ( T ) are depicted for jj = 0:25; 0:5; 1; 2; and 4. They show that the two-sided CUSUM is more efficient in all cases except when ff = 0:05; jj = 0:25; 0:5 and T ! 10 3 . In these latter cases, the efficiency of the two-sided CUSUM and the GMA algorithms is approximately the same