============================================================================== x x x CLASS 6/75 for STAT 3616 x x x ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 7 by TRIAL # 9 ) = 23.36 % <==> 1 / 4 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 6 and The Current # of Sequential TRIALS = JMAX = 8 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 23 <==> 100 * ( 8 Choose 6 ) * ( PP(L) ** 7 ) * ( QQ(L) ** 2 )) (PP,QQ,PROB) ==> .75000E+00 .25000E+00 .23360E+00 ==> PROB = 23.36 % ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 9 by TRIAL # 151 ) = .77 % <==> 1 / 131 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 8 and The Current # of Sequential TRIALS = JMAX = 150 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 1 <==> 100 * ( 150 Choose 8 ) * ( PP(L) ** 9 ) * ( QQ(L) ** 142 )) (PP,QQ,PROB) ==> .53333E-01 .94667E+00 .76512E-02 ==> PROB = .77 % ============================================================================== [ IALPHA,MDEV,JTC,MTC,IDELTA ] <====> 16 131 8 19 1 ============================================================================== SUMMARY of 1-EVENT FREQ. COUNTS with TEST FREQ. INTERVAL [ 3 ... 6 ] ============================================================================== Requested MINIMUM # SUCCESSFUL STAR EVENT Indices = 2 # Successful INDICES over 150 STAR EVENTS = 8 Total # of STAR EVENTS = 150 PP(E) = Occ. FREQ. PROBABILITY = 5.33 % QQ(E) = 1 - PP(E) = 94.67 % PROB % = Pr( EVENT E is [*]-Qualified ) <=====> .77 % Expected Frequency Cadence = 1 / k = 1 / 19 KTC = Cumulative Intersection Sum in Right Tail = 2 IDELTA /NCT /IRATIO /NKTC /MTC-1 = 1 / 1 / 19 / 0 / 18 / ============================================================================== where 1 ====> OCCURRENCE of a Specified EVENT and 0 ====> NON-OCCURRENCE of a Specified EVENT ============================================================================== Last 150 [*]-Qualifying Frequencies <====> 1 1 1 1 0 0 0 0 0 1 1 0 3 0 1 1 0 0 1 2 4 1 0 1 0 1 2 1 1 0 0 5 0 1 0 5 1 1 1 0 2 2 0 0 0 1 1 2 2 2 0 0 2 0 2 1 0 0 1 0 3 2 1 0 1 3 0 0 0 1 0 0 0 1 1 0 0 0 1 2 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 2 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 3 1 1 2 0 0 1 0 0 0 0 2 0 0 2 3 0 0 2 0 0 0 0 0 0 1 0 1 0 0 0 2 0 2 150 Last [*]-Qual. Indices for EVENT: 8 8 15 35 68 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ============================================================================== PROB_MIN = .01 <=====> The Selected LOWER BOUND for PPP ... where II = 8 .GE. 2 = MINII and [ JYY , TTMAX ] <====> [ 0 , 151 ] ============================================================================== 8 <==> II Impacted STAR EVENT Indices vs. Events with KCT = 19 ===> 13 21 32 36 61 66 117 132 8 Corresponding BINARY SUCCESS-FAILURE Indices ====> PPP % = 23.36 % 1 1 1 1 0 1 0 1 Pr( The Next PPP BINARY SUCCESS Will Occur by Trial # 151 ) = 23.36 % ============================================================================== There exist : 6 [ 1 ]"s and 2 [ 0 ]"s in 8 Trials ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 7 by TRIAL # 9 ) = 23.36 % <==> 1 / 4 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 6 and The Current # of Sequential TRIALS = JMAX = 8 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 23 <==> 100 * ( 8 Choose 6 ) * ( PP(L) ** 7 ) * ( QQ(L) ** 2 )) (PP,QQ,PROB) ==> .75000E+00 .25000E+00 .23360E+00 ==> PROB = 23.36 % ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 9 by TRIAL # 151 ) = .77 % <==> 1 / 131 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 8 and The Current # of Sequential TRIALS = JMAX = 150 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 1 <==> 100 * ( 150 Choose 8 ) * ( PP(L) ** 9 ) * ( QQ(L) ** 142 )) (PP,QQ,PROB) ==> .53333E-01 .94667E+00 .76512E-02 ==> PROB = .77 % ============================================================================== [ IALPHA,MDEV,JTC,MTC,IDELTA ] <====> 16 131 8 19 1 ============================================================================== SUMMARY of 1-EVENT FREQ. COUNTS with TEST FREQ. INTERVAL [ 3 ... 6 ] ============================================================================== Requested MINIMUM # SUCCESSFUL STAR EVENT Indices = 2 # Successful INDICES over 150 STAR EVENTS = 8 Total # of STAR EVENTS = 150 PP(E) = Occ. FREQ. PROBABILITY = 5.33 % QQ(E) = 1 - PP(E) = 94.67 % PROB % = Pr( EVENT E is [*]-Qualified ) <=====> .77 % Expected Frequency Cadence = 1 / k = 1 / 19 KTC = Cumulative Intersection Sum in Right Tail = 2 IDELTA /NCT /IRATIO /NKTC /MTC-1 = 1 / 2 / 19 / 0 / 18 / ============================================================================== where 1 ====> OCCURRENCE of a Specified EVENT and 0 ====> NON-OCCURRENCE of a Specified EVENT ============================================================================== Last 150 [*]-Qualifying Frequencies <====> 1 1 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 0 1 2 3 0 0 0 1 0 3 0 0 0 0 3 0 1 0 5 0 0 0 0 1 0 0 0 0 0 1 3 4 2 0 1 2 0 1 0 0 0 1 0 2 2 0 0 0 2 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 3 1 1 2 0 1 1 0 0 0 0 0 1 1 2 3 1 0 2 0 0 0 0 0 0 0 0 0 0 1 0 2 0 0 150 Last [*]-Qual. Indices for EVENT: 8 42 51 64 68 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ============================================================================== PROB_MIN = .01 <=====> The Selected LOWER BOUND for PPP ... where II = 8 .GE. 2 = MINII and [ JYY , TTMAX ] <====> [ 0 , 151 ] ============================================================================== 8 <==> II Impacted STAR EVENT Indices vs. Events with KCT = 19 ===> 21 27 32 36 48 49 117 132 8 Corresponding BINARY SUCCESS-FAILURE Indices ====> PPP % = 23.36 % 0 1 1 1 1 1 0 1 Pr( The Next PPP BINARY SUCCESS Will Occur by Trial # 151 ) = 23.36 % ============================================================================== There exist : 6 [ 1 ]"s and 2 [ 0 ]"s in 8 Trials ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 4 by TRIAL # 4 ) = 100.00 % <==> 1 / 1 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 3 and The Current # of Sequential TRIALS = JMAX = 3 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 100 <==> 100 * ( 3 Choose 3 ) * ( PP(L) ** 4 ) * ( QQ(L) ** 0 )) (PP,QQ,PROB) ==> .10000E+01 .00000E+00 .10000E+01 ==> PROB =100.00 % ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 4 by TRIAL # 151 ) = .45 % <==> 1 / 221 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 3 and The Current # of Sequential TRIALS = JMAX = 150 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 0 <==> 100 * ( 150 Choose 3 ) * ( PP(L) ** 4 ) * ( QQ(L) ** 147 )) (PP,QQ,PROB) ==> .20000E-01 .98000E+00 .45263E-02 ==> PROB = .45 % ============================================================================== [ IALPHA,MDEV,JTC,MTC,IDELTA ] <====> 16 48 3 102 0 ============================================================================== SUMMARY of 1-EVENT FREQ. COUNTS with TEST FREQ. INTERVAL [ 3 ... 6 ] ============================================================================== Requested MINIMUM # SUCCESSFUL STAR EVENT Indices = 2 # Successful INDICES over 150 STAR EVENTS = 3 Total # of STAR EVENTS = 150 PP(E) = Occ. FREQ. PROBABILITY = 2.00 % QQ(E) = 1 - PP(E) = 98.00 % PROB % = Pr( EVENT E is [*]-Qualified ) <=====> .45 % Expected Frequency Cadence = 1 / k = 1 / 50 KTC = Cumulative Intersection Sum in Right Tail = 2 IDELTA /NCT /IRATIO /NKTC /MTC-1 = 0 / 3 / 50 / 0 / 101 / ============================================================================== where 1 ====> OCCURRENCE of a Specified EVENT and 0 ====> NON-OCCURRENCE of a Specified EVENT ============================================================================== Last 150 [*]-Qualifying Frequencies <====> 1 1 1 0 0 0 0 0 0 1 1 0 2 0 1 1 0 0 1 1 2 1 0 1 1 1 2 0 1 0 0 3 0 2 0 3 1 1 1 0 1 1 0 0 0 0 1 2 3 1 0 1 1 0 2 0 0 0 2 0 1 1 0 0 1 2 0 0 0 1 0 1 0 1 2 0 0 0 2 2 0 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 2 2 1 1 0 1 1 0 0 0 0 1 0 1 1 2 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 2 150 Last [*]-Qual. Indices for EVENT: 8 15 51 64 68 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ============================================================================== PROB_MIN = .01 <=====> The Selected LOWER BOUND for PPP ... where II = 3 .GE. 2 = MINII and [ JYY , TTMAX ] <====> [ -52 , 99 ] ============================================================================== 3 <==> II Impacted STAR EVENT Indices vs. Events with KCT = 50 ===> 32 36 49 3 Corresponding BINARY SUCCESS-FAILURE Indices ====> PPP % = 100.00 % 1 1 1 Pr( The Next PPP BINARY SUCCESS Will Occur by Trial # 99 ) = 100.00 % ============================================================================== There exist : 3 [ 1 ]"s and 0 [ 0 ]"s in 3 Trials ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 8 by TRIAL # 9 ) = 34.36 % <==> 1 / 3 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 7 and The Current # of Sequential TRIALS = JMAX = 8 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 34 <==> 100 * ( 8 Choose 7 ) * ( PP(L) ** 8 ) * ( QQ(L) ** 1 )) (PP,QQ,PROB) ==> .87500E+00 .12500E+00 .34361E+00 ==> PROB = 34.36 % ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 9 by TRIAL # 151 ) = .77 % <==> 1 / 131 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 8 and The Current # of Sequential TRIALS = JMAX = 150 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 1 <==> 100 * ( 150 Choose 8 ) * ( PP(L) ** 9 ) * ( QQ(L) ** 142 )) (PP,QQ,PROB) ==> .53333E-01 .94667E+00 .76512E-02 ==> PROB = .77 % ============================================================================== [ IALPHA,MDEV,JTC,MTC,IDELTA ] <====> 16 131 8 19 1 ============================================================================== SUMMARY of 1-EVENT FREQ. COUNTS with TEST FREQ. INTERVAL [ 3 ... 6 ] ============================================================================== Requested MINIMUM # SUCCESSFUL STAR EVENT Indices = 2 # Successful INDICES over 150 STAR EVENTS = 8 Total # of STAR EVENTS = 150 PP(E) = Occ. FREQ. PROBABILITY = 5.33 % QQ(E) = 1 - PP(E) = 94.67 % PROB % = Pr( EVENT E is [*]-Qualified ) <=====> .77 % Expected Frequency Cadence = 1 / k = 1 / 19 KTC = Cumulative Intersection Sum in Right Tail = 2 IDELTA /NCT /IRATIO /NKTC /MTC-1 = 1 / 4 / 19 / 0 / 18 / ============================================================================== where 1 ====> OCCURRENCE of a Specified EVENT and 0 ====> NON-OCCURRENCE of a Specified EVENT ============================================================================== Last 150 [*]-Qualifying Frequencies <====> 1 1 1 0 0 0 0 0 0 1 1 0 3 0 1 1 0 0 1 2 3 1 0 1 1 1 2 0 1 0 0 4 0 1 0 5 1 1 1 0 1 1 0 0 0 0 0 2 3 2 0 1 2 0 2 0 0 0 1 0 2 2 0 0 1 3 0 0 0 1 0 0 0 1 1 0 0 0 1 2 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 0 1 2 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 3 1 1 2 0 0 1 0 0 0 0 1 0 1 2 3 0 0 2 0 0 0 0 0 0 1 0 1 0 0 0 2 0 2 150 Last [*]-Qual. Indices for EVENT: 8 8 15 64 68 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ============================================================================== PROB_MIN = .01 <=====> The Selected LOWER BOUND for PPP ... where II = 8 .GE. 2 = MINII and [ JYY , TTMAX ] <====> [ 0 , 151 ] ============================================================================== 8 <==> II Impacted STAR EVENT Indices vs. Events with KCT = 19 ===> 13 21 32 36 49 66 117 132 8 Corresponding BINARY SUCCESS-FAILURE Indices ====> PPP % = 34.36 % 1 1 1 1 1 1 0 1 Pr( The Next PPP BINARY SUCCESS Will Occur by Trial # 151 ) = 34.36 % ============================================================================== There exist : 7 [ 1 ]"s and 1 [ 0 ]"s in 8 Trials ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 3 by TRIAL # 3 ) = 100.00 % <==> 1 / 1 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 2 and The Current # of Sequential TRIALS = JMAX = 2 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 100 <==> 100 * ( 2 Choose 2 ) * ( PP(L) ** 3 ) * ( QQ(L) ** 0 )) (PP,QQ,PROB) ==> .10000E+01 .00000E+00 .10000E+01 ==> PROB =100.00 % ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 3 by TRIAL # 151 ) = .36 % <==> 1 / 275 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 2 and The Current # of Sequential TRIALS = JMAX = 150 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 0 <==> 100 * ( 150 Choose 2 ) * ( PP(L) ** 3 ) * ( QQ(L) ** 148 )) (PP,QQ,PROB) ==> .13333E-01 .98667E+00 .36332E-02 ==> PROB = .36 % ============================================================================== [ IALPHA,MDEV,JTC,MTC,IDELTA ] <====> 24 48 2 102 0 ============================================================================== SUMMARY of 1-EVENT FREQ. COUNTS with TEST FREQ. INTERVAL [ 3 ... 6 ] ============================================================================== Requested MINIMUM # SUCCESSFUL STAR EVENT Indices = 2 # Successful INDICES over 150 STAR EVENTS = 2 Total # of STAR EVENTS = 150 PP(E) = Occ. FREQ. PROBABILITY = 1.33 % QQ(E) = 1 - PP(E) = 98.67 % PROB % = Pr( EVENT E is [*]-Qualified ) <=====> .36 % Expected Frequency Cadence = 1 / k = 1 / 75 KTC = Cumulative Intersection Sum in Right Tail = 2 IDELTA /NCT /IRATIO /NKTC /MTC-1 = 0 / 5 / 75 / 0 / 101 / ============================================================================== where 1 ====> OCCURRENCE of a Specified EVENT and 0 ====> NON-OCCURRENCE of a Specified EVENT ============================================================================== Last 150 [*]-Qualifying Frequencies <====> 0 0 1 1 0 0 0 1 0 0 1 0 2 0 0 0 0 0 1 1 2 0 0 1 1 1 2 1 1 0 0 3 0 1 0 2 1 0 1 0 1 1 0 0 0 1 2 2 3 1 0 1 1 0 0 1 0 0 2 0 2 1 1 0 1 1 0 0 1 1 0 1 0 1 2 0 0 0 1 2 0 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 2 0 1 0 1 0 0 0 0 0 2 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 2 150 Last [*]-Qual. Indices for EVENT: 15 35 42 51 64 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ============================================================================== PROB_MIN = .01 <=====> The Selected LOWER BOUND for PPP ... where II = 2 .GE. 2 = MINII and [ JYY , TTMAX ] <====> [ -27 , 124 ] ============================================================================== 2 <==> II Impacted STAR EVENT Indices vs. Events with KCT = 75 ===> 32 49 2 Corresponding BINARY SUCCESS-FAILURE Indices ====> PPP % = 100.00 % 1 1 Pr( The Next PPP BINARY SUCCESS Will Occur by Trial # 124 ) = 100.00 % ============================================================================== There exist : 2 [ 1 ]"s and 0 [ 0 ]"s in 2 Trials ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 5 by TRIAL # 5 ) = 100.00 % <==> 1 / 1 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 4 and The Current # of Sequential TRIALS = JMAX = 4 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 100 <==> 100 * ( 4 Choose 4 ) * ( PP(L) ** 5 ) * ( QQ(L) ** 0 )) (PP,QQ,PROB) ==> .10000E+01 .00000E+00 .10000E+01 ==> PROB =100.00 % ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 5 by TRIAL # 151 ) = .53 % <==> 1 / 189 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 4 and The Current # of Sequential TRIALS = JMAX = 150 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 1 <==> 100 * ( 150 Choose 4 ) * ( PP(L) ** 5 ) * ( QQ(L) ** 146 )) (PP,QQ,PROB) ==> .26667E-01 .97333E+00 .52806E-02 ==> PROB = .53 % ============================================================================== [ IALPHA,MDEV,JTC,MTC,IDELTA ] <====> 12 48 4 102 1 ============================================================================== SUMMARY of 1-EVENT FREQ. COUNTS with TEST FREQ. INTERVAL [ 3 ... 6 ] ============================================================================== Requested MINIMUM # SUCCESSFUL STAR EVENT Indices = 2 # Successful INDICES over 150 STAR EVENTS = 4 Total # of STAR EVENTS = 150 PP(E) = Occ. FREQ. PROBABILITY = 2.67 % QQ(E) = 1 - PP(E) = 97.33 % PROB % = Pr( EVENT E is [*]-Qualified ) <=====> .53 % Expected Frequency Cadence = 1 / k = 1 / 38 KTC = Cumulative Intersection Sum in Right Tail = 2 IDELTA /NCT /IRATIO /NKTC /MTC-1 = 1 / 6 / 38 / 0 / 101 / ============================================================================== where 1 ====> OCCURRENCE of a Specified EVENT and 0 ====> NON-OCCURRENCE of a Specified EVENT ============================================================================== Last 150 [*]-Qualifying Frequencies <====> 1 1 1 1 0 0 0 0 0 0 1 0 2 0 0 0 0 0 0 1 3 0 0 1 1 1 2 1 1 0 0 4 0 1 0 3 1 0 1 0 2 1 0 0 0 1 2 2 3 1 0 1 1 0 1 1 0 0 2 0 2 1 1 0 1 1 0 0 0 1 0 1 0 1 2 0 0 0 1 2 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 2 2 1 1 0 1 1 0 0 0 0 2 0 1 1 2 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 2 150 Last [*]-Qual. Indices for EVENT: 15 35 51 64 68 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ============================================================================== PROB_MIN = .01 <=====> The Selected LOWER BOUND for PPP ... where II = 4 .GE. 2 = MINII and [ JYY , TTMAX ] <====> [ -64 , 87 ] ============================================================================== 4 <==> II Impacted STAR EVENT Indices vs. Events with KCT = 38 ===> 21 32 36 49 4 Corresponding BINARY SUCCESS-FAILURE Indices ====> PPP % = 100.00 % 1 1 1 1 Pr( The Next PPP BINARY SUCCESS Will Occur by Trial # 87 ) = 100.00 % ============================================================================== There exist : 4 [ 1 ]"s and 0 [ 0 ]"s in 4 Trials ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 8 by TRIAL # 9 ) = 34.36 % <==> 1 / 3 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 7 and The Current # of Sequential TRIALS = JMAX = 8 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 34 <==> 100 * ( 8 Choose 7 ) * ( PP(L) ** 8 ) * ( QQ(L) ** 1 )) (PP,QQ,PROB) ==> .87500E+00 .12500E+00 .34361E+00 ==> PROB = 34.36 % ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 9 by TRIAL # 151 ) = .77 % <==> 1 / 131 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 8 and The Current # of Sequential TRIALS = JMAX = 150 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 1 <==> 100 * ( 150 Choose 8 ) * ( PP(L) ** 9 ) * ( QQ(L) ** 142 )) (PP,QQ,PROB) ==> .53333E-01 .94667E+00 .76512E-02 ==> PROB = .77 % ============================================================================== [ IALPHA,MDEV,JTC,MTC,IDELTA ] <====> 16 131 8 19 1 ============================================================================== SUMMARY of 1-EVENT FREQ. COUNTS with TEST FREQ. INTERVAL [ 3 ... 6 ] ============================================================================== Requested MINIMUM # SUCCESSFUL STAR EVENT Indices = 2 # Successful INDICES over 150 STAR EVENTS = 8 Total # of STAR EVENTS = 150 PP(E) = Occ. FREQ. PROBABILITY = 5.33 % QQ(E) = 1 - PP(E) = 94.67 % PROB % = Pr( EVENT E is [*]-Qualified ) <=====> .77 % Expected Frequency Cadence = 1 / k = 1 / 19 KTC = Cumulative Intersection Sum in Right Tail = 2 IDELTA /NCT /IRATIO /NKTC /MTC-1 = 1 / 7 / 19 / 0 / 18 / ============================================================================== where 1 ====> OCCURRENCE of a Specified EVENT and 0 ====> NON-OCCURRENCE of a Specified EVENT ============================================================================== Last 150 [*]-Qualifying Frequencies <====> 1 1 1 1 0 0 0 0 0 0 1 0 3 0 0 0 0 0 0 2 4 0 0 1 1 1 2 1 1 0 0 5 0 0 0 5 1 0 1 0 2 1 0 0 0 1 1 2 3 2 0 1 2 0 1 1 0 0 1 0 3 2 1 0 1 2 0 0 0 1 0 0 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 2 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 3 1 1 2 0 0 1 0 0 0 0 2 0 1 2 3 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 150 Last [*]-Qual. Indices for EVENT: 8 15 35 64 68 8 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ============================================================================== PROB_MIN = .01 <=====> The Selected LOWER BOUND for PPP ... where II = 8 .GE. 2 = MINII and [ JYY , TTMAX ] <====> [ 0 , 151 ] ============================================================================== 8 <==> II Impacted STAR EVENT Indices vs. Events with KCT = 19 ===> 13 21 32 36 49 61 117 132 8 Corresponding BINARY SUCCESS-FAILURE Indices ====> PPP % = 34.36 % 1 1 1 1 1 1 0 1 Pr( The Next PPP BINARY SUCCESS Will Occur by Trial # 151 ) = 34.36 % ============================================================================== There exist : 7 [ 1 ]"s and 1 [ 0 ]"s in 8 Trials ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 4 by TRIAL # 4 ) = 100.00 % <==> 1 / 1 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 3 and The Current # of Sequential TRIALS = JMAX = 3 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 100 <==> 100 * ( 3 Choose 3 ) * ( PP(L) ** 4 ) * ( QQ(L) ** 0 )) (PP,QQ,PROB) ==> .10000E+01 .00000E+00 .10000E+01 ==> PROB =100.00 % ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 4 by TRIAL # 151 ) = .45 % <==> 1 / 221 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 3 and The Current # of Sequential TRIALS = JMAX = 150 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 0 <==> 100 * ( 150 Choose 3 ) * ( PP(L) ** 4 ) * ( QQ(L) ** 147 )) (PP,QQ,PROB) ==> .20000E-01 .98000E+00 .45263E-02 ==> PROB = .45 % ============================================================================== [ IALPHA,MDEV,JTC,MTC,IDELTA ] <====> 11 35 3 115 0 ============================================================================== SUMMARY of 1-EVENT FREQ. COUNTS with TEST FREQ. INTERVAL [ 3 ... 6 ] ============================================================================== Requested MINIMUM # SUCCESSFUL STAR EVENT Indices = 2 # Successful INDICES over 150 STAR EVENTS = 3 Total # of STAR EVENTS = 150 PP(E) = Occ. FREQ. PROBABILITY = 2.00 % QQ(E) = 1 - PP(E) = 98.00 % PROB % = Pr( EVENT E is [*]-Qualified ) <=====> .45 % Expected Frequency Cadence = 1 / k = 1 / 50 KTC = Cumulative Intersection Sum in Right Tail = 2 IDELTA /NCT /IRATIO /NKTC /MTC-1 = 0 / 8 / 50 / 0 / 114 / ============================================================================== where 1 ====> OCCURRENCE of a Specified EVENT and 0 ====> NON-OCCURRENCE of a Specified EVENT ============================================================================== Last 150 [*]-Qualifying Frequencies <====> 1 1 1 1 0 0 0 1 0 0 1 0 2 0 0 0 0 0 1 1 3 0 0 1 0 1 2 1 1 0 0 4 0 1 0 3 1 0 1 0 2 1 0 0 0 1 2 2 2 1 0 0 1 0 1 1 0 0 2 0 2 1 1 0 1 1 0 0 1 1 0 1 0 1 2 0 0 0 1 2 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 2 2 1 1 0 1 1 0 0 0 0 2 1 0 1 2 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 2 150 Last [*]-Qual. Indices for EVENT: 15 35 42 51 68 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ============================================================================== PROB_MIN = .01 <=====> The Selected LOWER BOUND for PPP ... where II = 3 .GE. 2 = MINII and [ JYY , TTMAX ] <====> [ -65 , 86 ] ============================================================================== 3 <==> II Impacted STAR EVENT Indices vs. Events with KCT = 50 ===> 21 32 36 3 Corresponding BINARY SUCCESS-FAILURE Indices ====> PPP % = 100.00 % 1 1 1 Pr( The Next PPP BINARY SUCCESS Will Occur by Trial # 86 ) = 100.00 % ============================================================================== There exist : 3 [ 1 ]"s and 0 [ 0 ]"s in 3 Trials ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 4 by TRIAL # 4 ) = 100.00 % <==> 1 / 1 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 3 and The Current # of Sequential TRIALS = JMAX = 3 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 100 <==> 100 * ( 3 Choose 3 ) * ( PP(L) ** 4 ) * ( QQ(L) ** 0 )) (PP,QQ,PROB) ==> .10000E+01 .00000E+00 .10000E+01 ==> PROB =100.00 % ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 4 by TRIAL # 151 ) = .45 % <==> 1 / 221 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 3 and The Current # of Sequential TRIALS = JMAX = 150 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 0 <==> 100 * ( 150 Choose 3 ) * ( PP(L) ** 4 ) * ( QQ(L) ** 147 )) (PP,QQ,PROB) ==> .20000E-01 .98000E+00 .45263E-02 ==> PROB = .45 % ============================================================================== [ IALPHA,MDEV,JTC,MTC,IDELTA ] <====> 13 40 3 110 0 ============================================================================== SUMMARY of 1-EVENT FREQ. COUNTS with TEST FREQ. INTERVAL [ 3 ... 6 ] ============================================================================== Requested MINIMUM # SUCCESSFUL STAR EVENT Indices = 2 # Successful INDICES over 150 STAR EVENTS = 3 Total # of STAR EVENTS = 150 PP(E) = Occ. FREQ. PROBABILITY = 2.00 % QQ(E) = 1 - PP(E) = 98.00 % PROB % = Pr( EVENT E is [*]-Qualified ) <=====> .45 % Expected Frequency Cadence = 1 / k = 1 / 50 KTC = Cumulative Intersection Sum in Right Tail = 2 IDELTA /NCT /IRATIO /NKTC /MTC-1 = 0 / 9 / 50 / 0 / 109 / ============================================================================== where 1 ====> OCCURRENCE of a Specified EVENT and 0 ====> NON-OCCURRENCE of a Specified EVENT ============================================================================== Last 150 [*]-Qualifying Frequencies <====> 2 2 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 3 0 0 1 1 1 1 1 1 0 0 4 0 1 0 2 1 0 1 0 3 1 0 0 0 1 2 1 2 0 0 1 0 0 2 1 0 0 2 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 2 0 0 0 1 2 0 0 0 0 1 1 0 0 2 1 0 0 1 0 0 0 0 2 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 2 2 2 0 0 1 2 0 0 0 0 2 0 1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 2 150 Last [*]-Qual. Indices for EVENT: 35 51 64 68 68 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ============================================================================== PROB_MIN = .01 <=====> The Selected LOWER BOUND for PPP ... where II = 3 .GE. 2 = MINII and [ JYY , TTMAX ] <====> [ -60 , 91 ] ============================================================================== 3 <==> II Impacted STAR EVENT Indices vs. Events with KCT = 50 ===> 21 32 41 3 Corresponding BINARY SUCCESS-FAILURE Indices ====> PPP % = 100.00 % 1 1 1 Pr( The Next PPP BINARY SUCCESS Will Occur by Trial # 91 ) = 100.00 % ============================================================================== There exist : 3 [ 1 ]"s and 0 [ 0 ]"s in 3 Trials ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 4 by TRIAL # 4 ) = 100.00 % <==> 1 / 1 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 3 and The Current # of Sequential TRIALS = JMAX = 3 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 100 <==> 100 * ( 3 Choose 3 ) * ( PP(L) ** 4 ) * ( QQ(L) ** 0 )) (PP,QQ,PROB) ==> .10000E+01 .00000E+00 .10000E+01 ==> PROB =100.00 % ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 4 by TRIAL # 151 ) = .45 % <==> 1 / 221 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 3 and The Current # of Sequential TRIALS = JMAX = 150 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 0 <==> 100 * ( 150 Choose 3 ) * ( PP(L) ** 4 ) * ( QQ(L) ** 147 )) (PP,QQ,PROB) ==> .20000E-01 .98000E+00 .45263E-02 ==> PROB = .45 % ============================================================================== [ IALPHA,MDEV,JTC,MTC,IDELTA ] <====> 11 35 3 115 0 ============================================================================== SUMMARY of 1-EVENT FREQ. COUNTS with TEST FREQ. INTERVAL [ 3 ... 6 ] ============================================================================== Requested MINIMUM # SUCCESSFUL STAR EVENT Indices = 2 # Successful INDICES over 150 STAR EVENTS = 3 Total # of STAR EVENTS = 150 PP(E) = Occ. FREQ. PROBABILITY = 2.00 % QQ(E) = 1 - PP(E) = 98.00 % PROB % = Pr( EVENT E is [*]-Qualified ) <=====> .45 % Expected Frequency Cadence = 1 / k = 1 / 50 KTC = Cumulative Intersection Sum in Right Tail = 2 IDELTA /NCT /IRATIO /NKTC /MTC-1 = 0 / 10 / 50 / 0 / 114 / ============================================================================== where 1 ====> OCCURRENCE of a Specified EVENT and 0 ====> NON-OCCURRENCE of a Specified EVENT ============================================================================== Last 150 [*]-Qualifying Frequencies <====> 1 1 1 2 0 0 0 0 0 0 1 0 2 1 0 0 0 0 0 1 3 0 0 1 1 1 1 1 1 0 0 4 0 0 0 3 1 0 1 0 2 1 0 0 0 1 1 1 2 1 0 1 1 0 1 1 0 0 1 1 2 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 0 0 2 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 2 1 1 1 0 0 1 0 0 0 0 2 0 1 1 2 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 2 0 2 150 Last [*]-Qual. Indices for EVENT: 15 35 64 68 69 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ============================================================================== PROB_MIN = .01 <=====> The Selected LOWER BOUND for PPP ... where II = 3 .GE. 2 = MINII and [ JYY , TTMAX ] <====> [ -65 , 86 ] ============================================================================== 3 <==> II Impacted STAR EVENT Indices vs. Events with KCT = 50 ===> 21 32 36 3 Corresponding BINARY SUCCESS-FAILURE Indices ====> PPP % = 100.00 % 1 1 1 Pr( The Next PPP BINARY SUCCESS Will Occur by Trial # 86 ) = 100.00 % ============================================================================== There exist : 3 [ 1 ]"s and 0 [ 0 ]"s in 3 Trials ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 5 by TRIAL # 5 ) = 100.00 % <==> 1 / 1 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 4 and The Current # of Sequential TRIALS = JMAX = 4 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 100 <==> 100 * ( 4 Choose 4 ) * ( PP(L) ** 5 ) * ( QQ(L) ** 0 )) (PP,QQ,PROB) ==> .10000E+01 .00000E+00 .10000E+01 ==> PROB =100.00 % ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 5 by TRIAL # 151 ) = .53 % <==> 1 / 189 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 4 and The Current # of Sequential TRIALS = JMAX = 150 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 1 <==> 100 * ( 150 Choose 4 ) * ( PP(L) ** 5 ) * ( QQ(L) ** 146 )) (PP,QQ,PROB) ==> .26667E-01 .97333E+00 .52806E-02 ==> PROB = .53 % ============================================================================== [ IALPHA,MDEV,JTC,MTC,IDELTA ] <====> 10 40 4 110 1 ============================================================================== SUMMARY of 1-EVENT FREQ. COUNTS with TEST FREQ. INTERVAL [ 3 ... 6 ] ============================================================================== Requested MINIMUM # SUCCESSFUL STAR EVENT Indices = 2 # Successful INDICES over 150 STAR EVENTS = 4 Total # of STAR EVENTS = 150 PP(E) = Occ. FREQ. PROBABILITY = 2.67 % QQ(E) = 1 - PP(E) = 97.33 % PROB % = Pr( EVENT E is [*]-Qualified ) <=====> .53 % Expected Frequency Cadence = 1 / k = 1 / 38 KTC = Cumulative Intersection Sum in Right Tail = 2 IDELTA /NCT /IRATIO /NKTC /MTC-1 = 1 / 11 / 38 / 0 / 109 / ============================================================================== where 1 ====> OCCURRENCE of a Specified EVENT and 0 ====> NON-OCCURRENCE of a Specified EVENT ============================================================================== Last 150 [*]-Qualifying Frequencies <====> 2 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 3 0 0 0 1 0 2 1 0 0 0 3 0 1 0 3 0 1 0 0 3 1 0 0 0 2 2 2 2 2 1 0 2 1 1 1 0 1 1 0 2 1 2 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 2 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 2 1 1 0 0 0 0 0 0 0 2 1 2 2 0 1 1 0 1 0 0 1 1 0 1 2 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 150 Last [*]-Qual. Indices for EVENT: 9 35 42 51 68 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ============================================================================== PROB_MIN = .01 <=====> The Selected LOWER BOUND for PPP ... where II = 4 .GE. 2 = MINII and [ JYY , TTMAX ] <====> [ -72 , 79 ] ============================================================================== 4 <==> II Impacted STAR EVENT Indices vs. Events with KCT = 38 ===> 21 32 36 41 4 Corresponding BINARY SUCCESS-FAILURE Indices ====> PPP % = 100.00 % 1 1 1 1 Pr( The Next PPP BINARY SUCCESS Will Occur by Trial # 79 ) = 100.00 % ============================================================================== There exist : 4 [ 1 ]"s and 0 [ 0 ]"s in 4 Trials ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 5 by TRIAL # 5 ) = 100.00 % <==> 1 / 1 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 4 and The Current # of Sequential TRIALS = JMAX = 4 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 100 <==> 100 * ( 4 Choose 4 ) * ( PP(L) ** 5 ) * ( QQ(L) ** 0 )) (PP,QQ,PROB) ==> .10000E+01 .00000E+00 .10000E+01 ==> PROB =100.00 % ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 5 by TRIAL # 151 ) = .53 % <==> 1 / 189 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 4 and The Current # of Sequential TRIALS = JMAX = 150 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 1 <==> 100 * ( 150 Choose 4 ) * ( PP(L) ** 5 ) * ( QQ(L) ** 146 )) (PP,QQ,PROB) ==> .26667E-01 .97333E+00 .52806E-02 ==> PROB = .53 % ============================================================================== [ IALPHA,MDEV,JTC,MTC,IDELTA ] <====> 12 48 4 102 1 ============================================================================== SUMMARY of 1-EVENT FREQ. COUNTS with TEST FREQ. INTERVAL [ 3 ... 6 ] ============================================================================== Requested MINIMUM # SUCCESSFUL STAR EVENT Indices = 2 # Successful INDICES over 150 STAR EVENTS = 4 Total # of STAR EVENTS = 150 PP(E) = Occ. FREQ. PROBABILITY = 2.67 % QQ(E) = 1 - PP(E) = 97.33 % PROB % = Pr( EVENT E is [*]-Qualified ) <=====> .53 % Expected Frequency Cadence = 1 / k = 1 / 38 KTC = Cumulative Intersection Sum in Right Tail = 2 IDELTA /NCT /IRATIO /NKTC /MTC-1 = 1 / 12 / 38 / 0 / 101 / ============================================================================== where 1 ====> OCCURRENCE of a Specified EVENT and 0 ====> NON-OCCURRENCE of a Specified EVENT ============================================================================== Last 150 [*]-Qualifying Frequencies <====> 1 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 3 0 0 0 1 0 2 1 0 0 0 3 0 1 0 3 0 0 0 0 2 1 0 0 0 1 2 2 3 1 0 1 1 0 1 1 0 0 1 0 2 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2 1 1 1 0 1 1 0 0 0 0 1 1 1 1 2 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 150 Last [*]-Qual. Indices for EVENT: 35 42 51 64 68 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ============================================================================== PROB_MIN = .01 <=====> The Selected LOWER BOUND for PPP ... where II = 4 .GE. 2 = MINII and [ JYY , TTMAX ] <====> [ -64 , 87 ] ============================================================================== 4 <==> II Impacted STAR EVENT Indices vs. Events with KCT = 38 ===> 21 32 36 49 4 Corresponding BINARY SUCCESS-FAILURE Indices ====> PPP % = 100.00 % 1 1 1 1 Pr( The Next PPP BINARY SUCCESS Will Occur by Trial # 87 ) = 100.00 % ============================================================================== There exist : 4 [ 1 ]"s and 0 [ 0 ]"s in 4 Trials ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 7 by TRIAL # 8 ) = 33.99 % <==> 1 / 3 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 6 and The Current # of Sequential TRIALS = JMAX = 7 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 34 <==> 100 * ( 7 Choose 6 ) * ( PP(L) ** 7 ) * ( QQ(L) ** 1 )) (PP,QQ,PROB) ==> .85714E+00 .14286E+00 .33992E+00 ==> PROB = 33.99 % ============================================================================== ============================================================================== Utilizing a NEGATIVE-BINOMIAL PROBABILITY DISTRIBUTION ============================================================================== Pr( E has SUCCESS # 8 by TRIAL # 151 ) = .71 % <==> 1 / 140 (apr.) ============================================================================== Characterizing this NEGATIVE-BINOMIAL Distribution ... The Current # of SUCCESSES = M0 = 7 and The Current # of Sequential TRIALS = JMAX = 150 IDELTA = 100 * Pr ( EVENT E is [*]-Qualified ) = 1 <==> 100 * ( 150 Choose 7 ) * ( PP(L) ** 8 ) * ( QQ(L) ** 143 )) (PP,QQ,PROB) ==> .46667E-01 .95333E+00 .71214E-02 ==> PROB = .71 % ============================================================================== [ IALPHA,MDEV,JTC,MTC,IDELTA ] <====> 18 131 7 19 1 ==============================================================================