2009 5
1...1 2...3 2.1...3 2.2...3 3...10 3.1...10 3.1.1...10 3.1.2... 11 3.2...14 3.2.1...14 3.2.2...16 3.3...18 3.4...19 3.4.1...19 3.4.2...20 3.4.3...21 4...24 4.1...24 4.2...24 4.3 WinBUGS...25 4.4...28 4.4.1...28 4.4.2...28 4.4.3...28 4.4.4...28 5...35 5.1...35 5.2 D/G...36 5.2.1...36 5.2.2...36 5.2.3...38 5.2.4...40 6...44 7 ()...50 7.1 λ...50 i
7.2 pd...50 7.3 σ...52 7.3.1...52 7.3.2...52 7.3.3...52 7.3.4...65 7.3.5...66 7.4 µ...71 7.4.1...71 7.4.2...72 7.4.3...72 7.4.4...85 7.4.5 0 µ...89 7.4.6...94 8...95 8.1...95 8.2...98 8.2.1...98 8.2.2...99 8.3... 104 8.3.1... 104 8.3.2... 106 8.3.3...106 8.3.4... 119 9...122 9.1... 122 9.2... 123 9.3...129 9.3.1 Thinning... 129 9.3.2 µσthinning... 138 9.3.3... 138 10...139 10.1... 139 10.2... 140 10.3...143 11...144 ii
11.1... 144 11.2... 144 12 PSA...152 12.1... 152 12.2... 152 13...155...156 A PSA...157 A.1... 158 A.2... 160 A.3 3...161 A.4 PSA... 171 B...177 B.1 NUCIA... 177 B.2... 177 B.3 NUCIA... 180 C...185 D...187 E PSA...192 E.1 PSA... 193 E.2 PSA... 201 F PSA...202 iii
() iv
1 PSA 13 PSA PSA 18 PSA 2005 2008 PSA ( 2) 2 NUCIA [1] PSA 1982 1997 16 49 16 [2] [3] EF 2 NUCIA PSA NUCIA PSA 1
NUCIA PSA NUCIA PSA PSA PSA 2008 9 2009 3 A 2 3 4 3 5 3 6 5 2 7 / 8 9 10 11 12 13 2
2 2.1 NUCIA PSA ABWR 49 1982 2002 / PSA NUCIA NUCIA PSA XNUCIA Y NUCIA p Y Xp/ p X / (MCMC) 2-1 2.2 2-1 2-2 3
1, 1 2, 2 m, m 4 LogNorm( m, m ) 1 2 m Beta(,) p p 1 p 2 p m 1 X 1 Poisson( 1 T 1 Y 1 Bin(p 1, X 1 2 2 X 2 Poisson( 2 T 2 Y 2 Bin(p 2, X 2 m m X m Poisson( m T m Y m Bin(p m, X m i i p i i T i i X i i Y i i ( µ, σ ) LogNorm Poisson (,T ) λ ( α, β ) Beta Bin ( p, X ) 2-1
2-1 21 1/4 [h] 5 [] [1/h] 5% [1/h] [1/h] 95% [1/h] EF *6 5 19 1.3E+07 48.5 4.3E-06 2.8E-07 2.7E-06 1.2E-05 6.5 10 - - - 9.5E-05 4.0E-05 8.2E-05 1.9E-04 2.2 2 6.2E+07 5.4 1.3E-07 1.2E-09 3.5E-08 3.5E-07 17.3 24 7.7E+07 61.7 1.1E-06 2.3E-08 4.1E-07 3.2E-06 11.8 2 3.7E+07 5.2 2.6E-07 1.4E-09 5.8E-08 5.3E-07 19.2 1 1.8E+07 3.0 2.8E-07 2.9E-09 6.9E-08 7.9E-07 16.4 2 9.7E+06 5.1 7.7E-07 2.7E-09 1.8E-07 2.0E-06 27.3 1 3.1E+06 2.7 1.6E-06 5.2E-09 2.7E-07 3.9E-06 27.4 6 6.8E+06 15.7 4.1E-06 4.2E-09 3.2E-07 9.3E-06 47.3 8 7.5E+06 20.4 2.9E-06 3.7E-07 2.2E-06 6.9E-06 4.3 2 1.3E+05 5.9 4.5E-05 6.6E-06 3.3E-05 1.2E-04 4.3 - - - 2.6E-03 - - - 30.0 9 9.1E+08 23.5 4.8E-08 3.0E-11 2.7E-09 1.1E-07 60.0 0 9.1E+08 1.0 2.5E-09 7.2E-11 6.9E-10 6.4E-09 9.4 2 9.1E+08 5.2 9.7E-09 8.6E-11 2.4E-09 2.1E-08 15.8 0 9.1E+08 1.0 2.5E-09 7.2E-11 6.9E-10 6.4E-09 9.4 1 9.1E+08 3.0 4.1E-09 7.0E-11 1.5E-09 1.2E-08 13.3 0 3.4E+07 1.4 8.0E-08 4.1E-09 3.1E-08 2.4E-07 7.6 0 3.4E+07 1.4 8.0E-08 4.1E-09 3.1E-08 2.4E-07 7.6 0 3.4E+07 1.4 8.0E-08 4.1E-09 3.1E-08 2.4E-07 7.6 0 3.4E+07 1.4 8.0E-08 4.1E-09 3.1E-08 2.4E-07 7.6 0 3.4E+07 1.4 8.0E-08 4.1E-09 3.1E-08 2.4E-07 7.6 18 4.9E+08 45.9 1.1E-07 7.1E-09 6.8E-08 2.9E-07 6.3 3 4.9E+08 8.0 2.7E-08 5.4E-11 3.7E-09 7.4E-08 37.1 1 4.9E+08 2.9 1.0E-08 5.2E-11 1.9E-09 2.5E-08 21.8 1 4.9E+08 2.9 1.0E-08 5.2E-11 1.9E-09 2.5E-08 21.8 2 4.9E+08 5.8 2.0E-08 3.5E-11 2.2E-09 5.3E-08 39.1 12 1.0E+08 30.8 4.5E-07 4.0E-09 1.4E-07 1.2E-06 17.3 3 1.0E+08 7.7 1.1E-07 8.8E-10 3.6E-08 2.7E-07 17.6 0 1.0E+08 1.0 2.2E-08 5.7E-10 5.9E-09 5.8E-08 10.1 0 1.0E+08 1.0 2.2E-08 5.7E-10 5.9E-09 5.8E-08 10.1 0 1.0E+08 1.0 2.2E-08 5.7E-10 5.9E-09 5.8E-08 10.1 1 6.5E+08 3.0 7.1E-09 6.8E-11 1.9E-09 1.9E-08 16.8 4 6.5E+08 10.8 3.4E-08 7.1E-11 4.2E-09 8.4E-08 34.4 0 6.5E+08 0.9 2.8E-09 7.0E-11 8.1E-10 8.0E-09 10.7 1 6.5E+08 3.0 7.1E-09 6.8E-11 1.9E-09 1.9E-08 16.8 3 1.5E+09 7.6 8.3E-09 6.5E-11 2.5E-09 1.7E-08 16.4 4 1.5E+09 10.2 8.5E-09 3.3E-11 2.3E-09 2.4E-08 27.0 0 1.5E+09 0.9 1.7E-09 2.7E-11 3.5E-10 4.0E-09 12.2 1 1.5E+09 2.8 3.7E-09 2.5E-11 7.1E-10 7.6E-09 17.3 0 1.7E+08 1.2 1.4E-08 5.7E-10 4.9E-09 3.9E-08 8.3 0 1.7E+08 1.2 1.4E-08 5.7E-10 4.9E-09 3.9E-08 8.3 0 1.7E+08 1.2 1.4E-08 5.7E-10 4.9E-09 3.9E-08 8.3 0 1.7E+08 1.2 1.4E-08 5.7E-10 4.9E-09 3.9E-08 8.3 1 1.7E+08 2.8 2.2E-08 1.5E-10 5.1E-09 6.4E-08 20.8
2-1 21 2/4 [h] 5 [] [1/h] 5% [1/h] [1/h] 95% [1/h] EF *6 6 BWR 0 3.6E+07 0.6 5.6E-08 5.0E-10 8.1E-09 1.3E-07 15.8 0 3.6E+07 0.6 5.6E-08 5.0E-10 8.1E-09 1.3E-07 15.8 0 3.6E+07 0.6 5.6E-08 5.0E-10 8.1E-09 1.3E-07 15.8 0 3.6E+07 0.6 5.6E-08 5.0E-10 8.1E-09 1.3E-07 15.8 0 3.6E+07 0.6 5.6E-08 5.0E-10 8.1E-09 1.3E-07 15.8 (PWR) 0 2.2E+07 0.8 8.6E-08 1.3E-09 1.9E-08 2.8E-07 14.8 6 1.3E+09 15.2 1.6E-08 1.7E-10 6.3E-09 4.3E-08 16.1 7 1 1.3E+09 3.0 3.6E-09 2.1E-11 8.6E-10 9.8E-09 21.4 0 1.3E+09 1.2 2.1E-09 7.8E-11 6.8E-10 5.7E-09 8.6 1 1.3E+09 3.2 4.0E-09 7.4E-11 1.1E-09 1.1E-08 12.0 1 1.3E+09 3.2 4.0E-09 7.4E-11 1.1E-09 1.1E-08 12.0 / 1 3.4E+07 2.9 1.3E-07 1.2E-09 3.0E-08 3.3E-07 16.5 7 6.0E+07 18.1 6.0E-07 1.4E-09 9.6E-08 1.4E-06 31.2 8 - - - 8.9E-05 - - - 31.2 1 3.9E+08 3.1 1.1E-08 1.8E-10 3.5E-09 3.2E-08 13.3 0 3.9E+08 1.1 5.5E-09 2.3E-10 1.9E-09 1.7E-08 8.7 0 3.9E+08 1.1 5.5E-09 2.3E-10 1.9E-09 1.7E-08 8.7 0 3.9E+08 1.1 5.5E-09 2.3E-10 1.9E-09 1.7E-08 8.7 0 3.9E+08 1.1 5.5E-09 2.3E-10 1.9E-09 1.7E-08 8.7 *1 1 1.6E+08 3.1 2.6E-08 4.9E-10 8.1E-09 7.5E-08 12.3 7 0 1.6E+08 0.6 8.8E-09 7.1E-11 1.4E-09 2.5E-08 18.6 2 1.6E+08 6.0 7.1E-08 1.8E-10 9.0E-09 1.6E-07 29.3 0 6.5E+07 0.8 3.2E-08 4.8E-10 6.8E-09 7.5E-08 12.5 0 6.5E+07 0.8 3.2E-08 4.8E-10 6.8E-09 7.5E-08 12.5 0 5.4E+08 0.9 3.2E-09 6.7E-11 8.7E-10 9.9E-09 12.2 0 5.4E+08 0.9 3.2E-09 6.7E-11 8.7E-10 9.9E-09 12.2 0 5.4E+08 0.9 3.2E-09 6.7E-11 8.7E-10 9.9E-09 12.2 / 0 1.9E+08 0.9 9.9E-09 2.0E-10 2.6E-09 2.9E-08 12.0 () 0 1.9E+08 0.9 9.9E-09 2.0E-10 2.6E-09 2.9E-08 12.0 0 1.9E+08 0.9 9.9E-09 2.0E-10 2.6E-09 2.9E-08 12.0 / 0 2.4E+07 0.9 9.5E-08 1.4E-09 1.9E-08 2.4E-07 13.1 ( 0 2.4E+07 0.9 9.5E-08 1.4E-09 1.9E-08 2.4E-07 13.1 2 2.4E+07 5.3 2.8E-07 2.1E-09 9.5E-08 8.1E-07 19.5 (BWR) 0 4.4E+08 0.8 6.5E-09 6.3E-11 9.3E-10 1.2E-08 13.9 (PWR) 0 1.2E+08 0.8 1.6E-08 1.7E-10 3.1E-09 4.6E-08 16.3 PLR MG 13 5.1E+06 33.1 8.4E-06 5.2E-07 4.8E-06 2.0E-05 6.2 RPS,CRDM MG 0 1.3E+07 1.0 1.6E-07 4.0E-09 4.1E-08 4.5E-07 10.5 (PLR) 2 6.7E+05 5.4 3.4E-05 1.1E-07 4.4E-06 6.1E-05 23.6 1 1.9E+07 3.1 3.8E-07 3.0E-09 6.5E-08 7.2E-07 15.6
2-1 21 3/4 [h] 5 [] [1/h] 5% [1/h] [1/h] 95% [1/h] EF *6 7 9 7.1E+08 23.2 4.8E-08 2.2E-10 1.1E-08 1.4E-07 25.2 12 7.1E+08 30.6 4.7E-08 3.8E-09 3.3E-08 1.2E-07 5.5 1 7.1E+08 3.0 8.7E-09 5.6E-11 1.7E-09 1.8E-08 17.9 5 6.2E+07 12.9 2.6E-07 4.8E-09 1.3E-07 6.8E-07 11.9 0 3.4E+07 0.9 5.7E-08 1.6E-09 1.6E-08 1.6E-07 10.1 1 3.4E+07 3.0 1.3E-07 1.4E-09 3.6E-08 3.6E-07 16.0 *2 3 3.6E+08 7.8 3.1E-08 2.4E-10 1.0E-08 7.7E-08 17.9 *3 0 1.5E+10 0.9 1.3E-10 3.8E-12 3.7E-11 3.9E-10 10.2 1 1.5E+10 2.9 2.7E-10 3.0E-12 7.0E-11 7.8E-10 16.2 3 1.5E+10 7.6 7.6E-10 6.9E-12 2.5E-10 1.8E-09 16.0 *4 0 3.7E+09 0.9 6.6E-10 1.0E-11 1.3E-10 1.4E-09 11.7 0 3.7E+09 0.9 6.6E-10 1.0E-11 1.3E-10 1.4E-09 11.7 *4 9 2 8.3E+09 5.3 1.0E-09 6.8E-12 2.7E-10 2.3E-09 18.5 0 8.3E+09 1.2 3.2E-10 1.2E-11 9.7E-11 8.5E-10 8.6 9 3 8.1E+09 7.9 1.5E-09 2.0E-12 1.9E-10 4.1E-09 45.4 9 4 8.1E+09 10.3 3.0E-09 4.4E-12 3.7E-10 5.2E-09 34.4 0 6.9E+08 1.4 4.7E-09 2.1E-10 1.7E-09 1.2E-08 7.8 0 6.9E+08 1.4 4.7E-09 2.1E-10 1.7E-09 1.2E-08 7.8 0 4.4E+08 1.2 5.8E-09 2.1E-10 1.9E-09 1.6E-08 8.7 / 3 4.4E+08 7.7 2.1E-08 2.8E-10 9.0E-09 6.0E-08 14.5 9 0 2.4E+08 0.5 6.6E-09 2.7E-11 6.4E-10 1.8E-08 25.7 ( 4 2.4E+08 10.6 9.2E-08 3.5E-10 2.0E-08 2.3E-07 25.4 0 1.3E+09 0.9 2.3E-09 2.6E-11 3.7E-10 4.1E-09 12.7 3 1.3E+09 7.9 9.5E-09 6.2E-11 2.6E-09 2.4E-08 19.6 3 2.4E+09 7.8 5.5E-09 3.7E-11 1.5E-09 1.2E-08 18.2 1 5.9E+08 3.0 7.6E-09 7.3E-11 1.8E-09 2.1E-08 16.8 / 4 5.9E+08 10.2 2.0E-08 3.6E-10 1.0E-08 5.5E-08 12.2 0 7.5E+08 1.0 2.9E-09 6.6E-11 7.5E-10 7.9E-09 10.9 / 8 7.5E+08 20.6 3.5E-08 1.1E-09 1.9E-08 8.2E-08 8.5 0 3.0E+08 1.1 1.4E-08 2.3E-10 2.2E-09 2.2E-08 9.9 / 2 3.0E+08 5.2 2.2E-08 2.2E-10 7.2E-09 6.0E-08 16.7 0 2.0E+09 0.9 1.1E-09 2.6E-11 2.9E-10 2.9E-09 10.6 / 5 2.0E+09 13.0 1.3E-08 4.8E-11 2.9E-09 2.7E-08 23.7
2-1 21 4/4 [h] 5 [] [1/h] 5% [1/h] [1/h] 95% [1/h] EF *6 8 0 5.6E+07 0.7 3.4E-08 5.7E-10 6.7E-09 8.5E-08 12.2 / 1 5.6E+07 2.9 7.3E-08 4.3E-10 1.7E-08 2.0E-07 21.8 0 3.6E+08 1.1 7.1E-09 2.1E-10 2.0E-09 1.9E-08 9.5 0 3.6E+08 1.1 7.1E-09 2.1E-10 2.0E-09 1.9E-08 9.5 1 9.9E+08 3.1 5.0E-09 6.7E-11 1.4E-09 1.3E-08 13.9 6 9.9E+08 15.6 2.0E-08 3.3E-11 2.3E-09 6.1E-08 43.0 1 7.1E+08 3.0 8.2E-09 8.0E-11 1.8E-09 1.7E-08 14.8 9 2 7.1E+08 5.3 9.0E-09 1.3E-11 1.1E-09 2.7E-08 44.9 0 3.4E+08 1.1 1.1E-08 2.0E-10 2.0E-09 1.9E-08 9.9 9 2 3.4E+08 5.4 2.5E-08 3.9E-11 2.8E-09 5.6E-08 37.9 3 2.2E+09 7.7 5.5E-09 4.5E-11 1.7E-09 1.2E-08 16.3 1 2.2E+09 3.1 3.1E-09 2.5E-11 6.0E-10 5.7E-09 15.1 2 3.5E+09 5.3 1.9E-09 3.0E-11 7.3E-10 5.4E-09 13.5 0 3.5E+09 1.2 1.1E-09 2.7E-11 2.4E-10 2.1E-09 8.8 0 4.3E+08 0.8 4.0E-09 6.7E-11 1.0E-09 1.2E-08 13.3 1 4.3E+08 2.8 1.4E-08 6.8E-11 2.1E-09 2.7E-08 20.1 8 - - - 3.1E-10 - - - 30.0 8 - - - 5.9E-10 - - - 30.0 8 - - - 2.1E-09 - - - 30.0 8 - - - 1.3E-08 - - - 30.0 8 - - - 3.1E-09 - - - 30.0 1. 2. 3. 4. 5.NUCIA() 6.EF 2 (= 7. µ-1.0-2.0-0.5 8. 9. WinBUGSµ-1.03-0.5 10.
2-2 21 5% 95% EF *2 *1 [1/d] [1/d] [1/d] [1/d] 9 DG 19 42332 49.0 1.5E-03 5.8E-05 7.7E-04 4.4E-03 8.7 3 143096 7.8 8.0E-05 7.3E-07 2.6E-05 2.1E-04 16.9 6 11776 15.5 1.6E-03 2.1E-06 1.7E-04 5.2E-03 49.6 2 271 6.1 2.3E-02 3.2E-03 1.6E-02 6.1E-02 4.3 1 50481 3.2 1.1E-04 1.4E-06 2.7E-05 2.6E-04 13.8 7 490002 18.0 4.7E-05 4.8E-08 4.4E-06 1.3E-04 51.7 1 490513 2.9 9.7E-06 6.4E-08 1.9E-06 2.5E-05 19.8 1 153155 3.6 4.2E-05 1.7E-06 1.5E-05 1.0E-04 7.7 6 154627 16.2 3.2E-04 4.3E-07 2.6E-05 7.4E-04 41.4 5 132460 12.8 1.4E-04 2.5E-06 6.0E-05 3.4E-04 11.6 0 132365 1.1 1.9E-05 5.8E-07 5.7E-06 5.5E-05 9.7 0 259336 1.1 9.7E-06 2.1E-07 2.4E-06 2.5E-05 10.8 1 252416 3.3 2.2E-05 5.6E-07 6.6E-06 5.5E-05 9.9 1 41714 3.1 1.2E-04 1.2E-06 2.9E-05 3.3E-04 16.3 1 41378 3.4 1.4E-04 4.3E-06 4.8E-05 3.5E-04 9.0 0 1315 0.7 1.4E-03 1.4E-05 2.4E-04 4.0E-03 17.1 0 1179 0.7 1.5E-03 1.4E-05 2.6E-04 4.3E-03 17.7 0 8323 0.8 2.7E-04 3.9E-06 5.3E-05 6.8E-04 13.3 0 8165 0.8 2.9E-04 4.1E-06 5.6E-05 7.0E-04 13.2 3 307782 7.8 3.4E-05 8.3E-07 1.4E-05 8.7E-05 10.3 1 230491 3.1 2.2E-05 1.7E-07 5.1E-06 5.4E-05 17.7 3 230325 7.8 4.8E-05 3.7E-07 1.6E-05 1.2E-04 18.1 1 185281 3.0 2.5E-05 2.0E-07 5.9E-06 6.8E-05 18.4 0 185949 0.9 1.1E-05 2.0E-07 2.5E-06 2.8E-05 11.9 1.NUCIA() 2.EF 2 (=
3 2.1 2-1 3.1 ipsanuciap i PSAX i Y i Bin(p i,x i ) f i ( p, X ) Y ~ Bin yi xi yi ( y ; x, p ) = C p ( 1 p ) i i i i x i i y i i i (3.1) X i i Yi i pi i NUCIA PSA p i 3.1.1 a) (10 ) [3] 144 214 2.5 b) (16 ) [2] 201 312 2.5 10
3.1.2 p i p i p i Beta( α, β ) p i α β p i Z W V p i Beta( α, β ) 3-1 [2][3] 3-1 p i Z/W Beta( α, β ) Wp i W W=Vp i 0.4 Beta( α, β ) Beta ( 4, 6) Beta( 4, 6) (W) 10 (Z) 4 3-1 Beta ( 4,6) 0.022 Beta(4,6) 3-1 16 W(=V)=513Z=201 Jeffreys 0.4 W 11
Beta(4,6) X i Y i directed graph 3-2 3-1 p i Beta ( 4,6) 12
p i X i Y i i p i i X i i Y i i α,β i ( p X ) Y ~ Bin, i i 3-2 13
3.2 3.2.1 a) it i X i λ i X i ~ Poisson( λ T ) ( λiti ) f ( xi; λi, Ti ) = exp( λiti ) x! i i (3.2) i xi b) λ i µσ lnλ i 1 1 2 f ( λi ) = exp (ln λ ) 2 i µ σλ 2π 2σ (3.3) i < i 0 λ < < µ < σ > 0 c) µσ (a µ,b µ )(a σ,b σ ), 1 f ( µ ) = aµ µ bµ (3.4) bµ aµ 1 f ( σ ) = aσ σ bσ (3.5) b a σ σ d) 3-3 14
b a a b i T i i X i i λ i i X i i T i i µ,σ- a,b X i ~ Poisson ( λ T ) i i 3-3 15
3.2.2 a) id i ix i pd i X f i ~ Bin ( pd, D ) i i xi Di xi ( x ; pd, D ) = C pd ( 1 pd ) i i i Di Xi i i (3.6) b) pd i NUREG/CR-6823 [4] µσlogit(p) 2 1 1 logit( pdi ) µ ( ) = exp σ π ( ) f pd (3.7) i 2 pd 2 σ i 1 pdi logit( pd i ) = ln[ pd /( 1 pd )] < µ < σ > 0 i i c) µσ (3-4),(3-5) d) 3-4 16
a b a b c i pd i D i X i i pd i i X i i D i i µ,σ- a,b pd = logit 1 ( c) = e /(1 + e i i ( pd D ) X ~ Bin, i i c i c i ) 3-4 17
3.3 3.1 3.2 3-5 a b a b p i T i i i X i Y i i p i i X i i Y i i λ i i T i i µ,σ- a,b α,β 3-5 18
3.4 3.4.1 µ σ E ( x) = ( b + a) / 2 2 Var( x) = ( b a) /12 a µ µ = E( µ ) b = E( µ ) + 3Var( µ ) 3Var( µ ) (3.8) a σ σ = E( σ ) b = E( σ ) + 3Var( σ ) 3Var( σ ) (3.9) µσ λ max λ min 90 E(σ)E(µ) [6] E( σ ) = ln( λ E( µ ) = ln λ max / λmin ) / 3. 29 max 1.645E( σ ) = ln λ max λ λ min λ max min (3.10) Var(µ)Var(µ) 10 5 Var(σ)(3.9)σa σ b σ a σ σ>0 σ(0.1,3)a σ =0.1, b σ =3 (EF)1.2 < EF < 139 19
a µ µ = E( µ ) b = E( µ ) + 3Var( µ ) 3Var( µ ) (3.11) E ( µ ) = ln λ λ Var ( µ ) = 10 max min a σ b σ = 0.1 = 3 (3.12) 3.4.2 a µ b µ (3.8) pd max /(1 pdmax) E( σ ) = ( m n) /3.29= ln / 3.29 pdmin /(1 pdmin ) pd max pdmin E( µ ) = m 1.645E( σ ) = ln 1 pd max 1 pdmin (3.13) m = logit( pd ) = ln( pd /(1 pd )) n = logit( pd max min ) = ln( pd max min /(1 pd pd min pd max max min )) Var(µ) 10 a σ =0.1, b σ =3 a µ µ = E( µ ) b = E( µ ) + 3Var( µ ) 3Var( µ ) (3.14) E ( µ ) pd x pd 1 pdmax 1 pd = ma ln min min 20
Var ( µ ) = 10 aσ = 0.1 bσ = 3 (3.15) 3.4.3 3.4.13.4.2 a) Y i Max( λi,mle) 0.5 p i p EXP,i Max(λi,MLE) i=my m X m = Ym / pexp, m X m λ max Beta( α, β ) α /( α + β ) Beta 4,6 ( ) p = E( Beta(4,6)) = 4 /(4 + 6) = 0. 4 ( 3.16) EXP, i m λ max λ max = Ym /( 0.4 T m ) = λm, MLE 2.5 (3.17) Y m m T m m λ m m,mle 21
b) Y i Min(λ i,mle ) 0.5 Min(λ i,mle )λ min λ min = Min( λ i, ) (3.18) MLE c) 1) µ f µ ) = b µ 1 a ( µ µ aµ µ b (3.19) i) a µ b µ = ln λ λ max = ln λ λ min max min + 30 30 λmax = Max( λ i, MLE) 2.5 ( i = 1,2, L, n) λ = Min( λ ( i = 1,2, L, n) min i,mle) λ : i i,mle ii) a µ b µ pd = ln pd 1 pd max = ln pd 1 pd max max max = Max( pd i, MLE pd 1 pd min min 30 pd min 30 1 pd min ) 2.5 ( i = 1,2, L, n) max + pd min = Min( pd i, MLE) ( i = 1,2, L, n) 22
pd, i MLE : i 2) σ f 1 a ( σ ) = aσ σ bσ bσ σ a 0.1, b = 3 (3.20) σ = σ 23
4 3 4.1 1982 2002 21 49 21 WinBUGS Ver.1.4.1 [5] 26 0 19 0 4-1 D/G 3.0E-7 [/h] 3.4E-11 [/h] 4.5E-4 [/d] 1.9E-6 [/d] 4.2 (3.19)(3.20) 4-2 D/G 4-2 a µ b µ a σ b σ 1.9E+1 8.5E+0 0.1 3 2.5E+1 1.4E+1 0.1 3 1.2E+1 9.9E-1 0.1 3 1.4E+1 3.0E+0 0.1 3 24
4.3 WinBUGS WinBUGS [5] 4-1~ 4-4 WinBUGS / 4-1~ 4-4 50 [6] =1hr =1 =0 25
model { for(i in 1:N){ lambda[i] ~ dlnorm(mu,tau) nu[i] <- lambda[i]*t[i] x[i] ~ dpois(nu[i]) p[i] ~ dbeta(alpha,beta) y[i] ~ dbin(p[i],x[i]) } mu ~ dunif(amu,bmu) sigma ~ dunif(asigma,bsigma) tau <- 1/(sigma*sigma) total <- sum(x[1:n-1]) } list( # ******************************************* # set evidences # ******************************************** # hours list : last data is dummy t=c( 1710086,1831102,1758330,1959216,1930446, 1950872,2170215,2137584,1757776,1801792, 1968928,1269940,968142,868784,1375752, 1842320,1869238,1553524,1129040,1163536, 1796970,816102,2218480,1518048,1942080, 1966425,1794367,1531802,1961328,2154870, 2629386,2198368,2084288,1782534,1748188, 1893165,1762657,1232868,1082788,2296020, 2569380,1014045,651150,2340934,2182970, 2574429,2638825,1011472,2252507,1), # events list : last data is dummy y=c( 1,3,0,3,0,1,3,1,1,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,3,3,0,0,0,0,2,1,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0), # ******************************************* # set paramters # ******************************************** # data collection probability parameters alpha=4, beta=6, # hyper parameters for failure rates amu=-1.9e+1, bmu=-8.5, asigma=0.1, bsigma=3, # the number fo plants N=50 ) #************************************************* # initial value for keep away compile error #************************************************* list( x=c( 2,4,1,4,1,2,4,2,2,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,4,4,1,1,1,1,3,2,2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1) ) 4-1 BUGS model { for(i in 1:N){ lambda[i] ~ dlnorm(mu,tau) nu[i] <- lambda[i]*t[i] x[i] ~ dpois(nu[i]) p[i] ~ dbeta(alpha,beta) y[i] ~ dbin(p[i],x[i]) } mu ~ dunif(amu,bmu) sigma ~ dunif(asigma,bsigma) tau <- 1/(sigma*sigma) total <- sum(x[1:n-1]) } list( # ******************************************* # set evidences # ******************************************** # hours list : last data is dummy t=c( 347391756,294415043,282714345,315013944,310388139, 383903740,398596155,368065245,302667055,310246060, 339024790,249906050,190516515,170964280,270728340, 259191395,300546767,305711330,194406575,200346355, 288927105,160597215,394334820,298730160,382173600, 372834180,247305993,211118358,287211969,280492245, 392654976,369325824,350160384,368573184,361471488, 380904798,409207602,265771116,233418156,316445580, 354121020,204025854,131011380,370142976,345166080, 354816891,363692175,169927296,357792954,1), # events list : last data is dummy y=c( 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0), # ******************************************* # set paramters # ******************************************** # data collection probability parameters alpha=4, beta=6, # hyper parameters for failure rates amu=-2.5e+1, bmu=-1.4e+1, asigma=0.1, bsigma=3, # the number fo plants N=50 ) #************************************************* # initial value for keep away compile error #************************************************* list( x=c( 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1) ) 4-2 BUGS 26
model { for(i in 1:N){ m[i] ~ dnorm(mu,tau) p[i] <- exp(m[i])/(1+exp(m[i])) x[i] ~ dbin(p[i],n[i]) pd[i] ~ dbeta(alpha,beta) y[i] ~ dbin(pd[i],x[i]) } mu ~ dunif(amu,bmu) sigma ~ dunif(asigma,bsigma) tau <- 1/(sigma*sigma) total <- sum(x[1:n-1]) } list( # ******************************************* # set evidences # ******************************************** # demands list : last data is dummy n=c( 595,628,601,672,663,723,755,695,573,584, 638,474,359,324,508,419,477,554,346,414, 456,280,542,354,697,513,298,258,1015,1178, 1429,1358,1300,1149,1125,1612,1730,1120,984,1786, 1997,535,343,2038,1928,1944,1998,556,806, 1), # events list : last data is dummy y=c( 0,0,0,0,0,0,2,1,0,0, 2, 0,0,0,1,0,1,0,0,1, 0,0,0,0,0,2,0,0,0,0, 0, 0,0,1,0,2,0,0,3,0, 1,0,0,0,0,1,0,0,1,0), # ******************************************* # set paramters # ******************************************** # data collection probability parameters alpha=4, beta=6, # hyper parameters for failure rates amu=-1.2e+1, bmu=-9.9e-1, asigma=0.1, bsigma=3, # the number fo plants N=50) #************************************************* # initial value for keep away compile error #************************************************* list( x=c( 1,1,1,1,1,1,3,2,1,1, 3,1,1,1,2,1,2,1,1,2, 1,1,1,1,1,3,1,1,1,1, 1,1,1,2,1,3,1,1,4,1, 2,1,1,1,1,2,1,1,2,1) ) 4-3 D/G BUGS model { for(i in 1:N){ m[i] ~ dnorm(mu,tau) p[i] <- exp(m[i])/(1+exp(m[i])) x[i] ~ dbin(p[i],n[i]) pd[i] ~ dbeta(alpha,beta) y[i] ~ dbin(pd[i],x[i]) } mu ~ dunif(amu,bmu) sigma ~ dunif(asigma,bsigma) tau <- 1/(sigma*sigma) total <- sum(x[1:n-1]) } list( # ******************************************* # set evidences # ******************************************** # demands list : last data is dummy n=c( 5153,7310,7002,7819,7714,9043,9429,8686,7156,7300, 7976,5911,4489,4048,6354,10658,12219,6042,3785,3065, 7355,2483,9709,7953,6548,3174,1376,1202,2964,3122, 5432,5162,4941,3207,3098,5108,5462,3507,3080, 3621, 4037,2133,1358,3452,3254,4355,4498,2022,4560,1), # events list : last data is dummy y=c( 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0, 0,0,0,0,0,0,0,0,0,0), # ******************************************* # set paramters # ******************************************** # data collection probability parameters alpha=4, beta=6, # hyper parameters for failure rates amu=-1.4e+1, bmu=-3.0, asigma=0.1, bsigma=3, # the number fo plants N=50) #************************************************* # initial value for keep away compile error #************************************************* list( x=c( 1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1, 1,1,1,1,1,1,1,1,1,1) ) 4-4 BUGS 27
4.4 4.4.1 5% ) 4-1 1 4-3 [7] 4-3 26 2 0 6 19 D/G 3 0 4 7 5 4.4.2 WinBUGSMC error 5% NUREG/CR-6823 [4] 9 10 4.4.3 4-4~ 4-7 / 4-5 4.4.4 2 0.4 10 4 )MC error5% 28
2 3 / 29
4-4 30 2 MCMC 3 MCMC
4-5 31 2 MCMC 3 MCMC
4-6 D/G 32 2 MCMC 3 MCMC
4-7 33 2 MCMC 3 MCMC
0.04 0.03 0.02 0.01 0.0 total sample: 100000 33 50 100 150 0.6 0.4 0.2 0.0 total sample: 100000-1 10 20 0.06 0.04 0.02 0.0 total sample: 100000 21 50 100 D/G 0.6 0.4 0.2 0.0 total sample: 100000-1 10 20 4-5 34
5 3 5.1 16 [2] 5-1 16 16 EF 30 (5.1) 5-1 16 [2] / / median mean T T = median = median T B 2 exp( σ / 2) = median T 1 ln EFT exp 2 1.645 2 (5.1) medianb median T mean T EF T 30 35
5.2 D/G 5.2.1 16 [2] D/G 21 1982 2002 5.2.2 NUCIA21 D/G 19 5-2 D/G 11 8 5-2 D/G 5-2 16 D/G 5-3 36
5-3 D/G 37
3 30 2 5-3 Plant 36Plant41 2 / 30 / 5-4 5-5 5-4 D/G (NUCIA21 ) ( ) ( 2) () 0.5h 33103 33090 13 9 4 2.0h 9230 9224 6 2 4 42333 42314 19 11 8 5-5 D/G No. [h] 1 15 4.17E-03 2 20 5.56E-03 3 1 1.67E-02 4 1 1.67E-02 5 2 3.33E-02 6 3 5.00E-02 7 10 1.67E-01 8 11 1.83E-01 9 26 4.33E-01 10 1 4 1.07E+00 11 1 50 1.83E+00 30 2 5.2.3 f(t;θ) θ ( ) ( ) T F T; θ = T f t; θ dt (5.2) T R( T; θ ) 1 F( T;θ ) 0 = (5.3) L(θ) 38
l ( ) = f ( t ) L ;θ m θ i F( Tj; ) R( Tk ; θ ) i= 1 j = 1 n θ (5.4) k = 1 t i l T j m T k n 5-1 T LC T RC f F R ν ν () t = νλt 1 exp( λt ) ν () t = 1 exp( λt ) ν () t = exp( λt ) (ν, λ>0) (5.5) (5.6) (5.7) 5-4 5-5 0.5 2 L(ν,λ) 39
11 ν ( ν, λ) νλ ( 1 ν L t exp λt ) = i i i ν [ ( )] 4 ν [ ( )] 4 ν [ ( )] 33090 ν 1 exp 0.5 λ 1 exp 2 λ exp 0.5 λ [ exp( 2 λ) ] 9224 (5.8) t i, i=1~11 5.5 (5.8)(ν,λ) 5.2.4 WinBUGS 5-4 5-5 WinBUGS / R(t),F(t)WinBUGS zeros trick zeros trick I X00 ( I ) X 0 ~ Poisson (5.9) L zt (I) 0 zt ( I ) L = I 0 exp 0! ( I ) = exp ( I ) (5.10) I=-ln() (5.10) (5.6) T LC1 (=0.5h)N LC1 (=4)T LC2 (=2.0h)N LC2 (=4) I = ln = N NLC 1 NLC 2 ([ F( T )] [ F( T )] ) LC1 LC1 ln 1 LC 2 ν ν ( exp( λt )) N ln( 1 exp( λt )) LC1 LC 2 LC 2 (5.11) (5.7) T RC1 (=0.5h)N RC1 (=33090)T RC2 (=2.0h)N RC2 (=9224) 40
I N RC1 N RC ([ R( T )] [ R( T )] ) 2 = ln = N = N R C RC RC1 ν ν ( exp( T ) N ln( ( λt ) 1 ln exp ν RC1 1λT + N RC 2 λ RC1 RC 2 RC 2 ν RC 2λTRC 2 (5.12) λ( t) = νλ t ( ν 1) (5.13) τ λ 1 τ ( ν 1) ( τ ) λ() dt = λτ = τ 0 t (5.14) WinBUGS 5-2 41
model; { # Prior distributions for Weibull parameters v ~ dgamma(0.001,0.001) lambda ~ dgamma(0.001,0.001) # Likelihood for the complete data for( i in 1 : NCOM ) { TCOM[i] ~ dweib(v,lambda) } # Likelihood for the left censored data # zeros trick C <- 10000 XLC <- 0 XLC ~ dpois(ilc) ILC <- C - NLC[1] * log( 1- exp( - lambda * pow(tcen[1],v) )) - NLC[2] * log( 1- exp( - lambda * pow(tcen[2],v) )) # Likelihood for the right censored data #zeros trick XRC <- 0 XRC ~ dpois(irc) IRC <- C + NRC[1] * lambda * pow(tcen[1],v) + NRC[2] * lambda * pow(tcen[2],v) # 24-hour mean failure rate FR24 <- lambda*pow(24,v-1) } DATA list( # Complete data TCOM = c(4.17e-3, 5.56E-3, 1.67E-2, 1.67E-2, 3.33E-2, 5.00E-2, 1.67E-1, 1.83E-1, 4.33E-1, 1.07,1.83), NCOM = 11, ) # Censoring data TCEN[] NLC[] NRC[] 0.5 4 33090 2.0 4 9224 END INITS list(v=0.5,lambda=1.e-3) list(v=1.0,lambda=1.e-4) 5-2 WinBUGS 5-6 5-3 16 5-7 D/G 5-6 24 42
5-6 2.5% 5% 95% 97.5% EF 24 9.50E-5 3.56E-5 4.04E-5 8.22E-5 1.92E-4 2.29E-4 2.2 (FR24) λ(lambda) 5.03E-4 3.09E-4 3.36E-4 5.03E-4 7.20E-4 7.67E-4 ν(v) 0.43 0.23 0.26 0.43 0.66 0.71 1.50E+4 1.00E+4 5.00E+3 0.0 FR24 chains 1:2 sample: 100000 0.0 5.00E-4 0.001 4.00E+3 3.00E+3 2.00E+3 1.00E+3 0.0 lambda chains 1:2 sample: 100000 0.0 5.00E-4 0.001 4.0 3.0 2.0 1.0 0.0 v chains 1:2 sample: 100000 0.0 0.5 1.0 5-3 5-7 24 16 ν 0.529 0.43 λ 5.49E-4 5.03E-4 24 [/h] 1.20E-4 9.50E-5 5-4 30 2 WinBUGS 43
6 3 NUCIA PSA 1982 2002 21 49 21 5 6-1 6-2 2 0 0.5 2 χ 2 90 B 44
6-1 21 1/4 45 [h] 11 [1/h] [1/h] 90% [1/h] EF *5 6 [] 5% 95% [1/h] EF *7 [1/h] [1/h] 8 EF [1/h] 9 19 1.3E+07 1.5E-06 9.9E-07 2.2E-06 1.5 48.5 4.3E-06 2.8E-07 2.7E-06 1.2E-05 6.5 285% 434% 12 - - 3.3E-04 - - 30.0-9.5E-05 4.0E-05 8.2E-05 1.9E-04 2.2 29% 7% 2 6.2E+07 3.2E-08 5.7E-09 1.0E-07 4.2 5.4 1.3E-07 1.2E-09 3.5E-08 3.5E-07 17.3 415% 411% 24 7.7E+07 3.1E-07 2.2E-07 4.4E-07 1.4 61.7 1.1E-06 2.3E-08 4.1E-07 3.2E-06 11.8 341% 829% 2 3.7E+07 5.5E-08 9.7E-09 1.7E-07 4.2 5.2 2.6E-07 1.4E-09 5.8E-08 5.3E-07 19.2 470% 457% 1 1.8E+07 5.6E-08 2.9E-09 2.6E-07 9.6 3.0 2.8E-07 2.9E-09 6.9E-08 7.9E-07 16.4 510% 171% 2 9.7E+06 2.1E-07 3.7E-08 6.5E-07 4.2 5.1 7.7E-07 2.7E-09 1.8E-07 2.0E-06 27.3 376% 649% 1 3.1E+06 3.2E-07 1.7E-08 1.5E-06 9.6 2.7 1.6E-06 5.2E-09 2.7E-07 3.9E-06 27.4 483% 285% 6 6.8E+06 8.8E-07 3.8E-07 1.7E-06 2.1 15.7 4.1E-06 4.2E-09 3.2E-07 9.3E-06 47.3 462% 2221% 8 7.5E+06 1.1E-06 5.3E-07 1.9E-06 1.9 20.4 2.9E-06 3.7E-07 2.2E-06 6.9E-06 4.3 278% 227% 2 1.3E+05 1.5E-05 2.7E-06 4.8E-05 4.2 5.9 4.5E-05 6.6E-06 3.3E-05 1.2E-04 4.3 296% 102% 12 - - 4.4E-04 - - 30.0-2.6E-03 - - - 30.0 588% 100% 9 9.1E+08 9.9E-09 5.2E-09 1.7E-08 1.8 23.5 4.8E-08 3.0E-11 2.7E-09 1.1E-07 60.0 484% 3281% 0 9.1E+08 5.5E-10-2.5E-09 13.0 1.0 2.5E-09 7.2E-11 6.9E-10 6.4E-09 9.4 461% 72% 2 9.1E+08 2.2E-09 3.9E-10 6.9E-09 4.2 5.2 9.7E-09 8.6E-11 2.4E-09 2.1E-08 15.8 440% 375% 0 9.1E+08 5.5E-10-2.5E-09 13.0 1.0 2.5E-09 7.2E-11 6.9E-10 6.4E-09 9.4 461% 72% 1 9.1E+08 1.1E-09 5.7E-11 5.2E-09 9.6 3.0 4.1E-09 7.0E-11 1.5E-09 1.2E-08 13.3 375% 139% 0 3.4E+07 1.5E-08-6.8E-08 13.0 1.4 8.0E-08 4.1E-09 3.1E-08 2.4E-07 7.6 546% 58% 0 3.4E+07 1.5E-08-6.8E-08 13.0 1.4 8.0E-08 4.1E-09 3.1E-08 2.4E-07 7.6 546% 58% 0 3.4E+07 1.5E-08-6.8E-08 13.0 1.4 8.0E-08 4.1E-09 3.1E-08 2.4E-07 7.6 546% 58% 0 3.4E+07 1.5E-08-6.8E-08 13.0 1.4 8.0E-08 4.1E-09 3.1E-08 2.4E-07 7.6 546% 58% 0 3.4E+07 1.5E-08-6.8E-08 13.0 1.4 8.0E-08 4.1E-09 3.1E-08 2.4E-07 7.6 546% 58% 18 4.9E+08 3.7E-08 2.4E-08 5.4E-08 1.5 45.9 1.1E-07 7.1E-09 6.8E-08 2.9E-07 6.3 296% 418% 10 3 4.9E+08 6.1E-09 1.7E-09 1.6E-08 3.1 8.0 2.7E-08 5.4E-11 3.7E-09 7.4E-08 37.1 439% 1205% 1 4.9E+08 2.0E-09 1.0E-10 9.6E-09 9.6 2.9 1.0E-08 5.2E-11 1.9E-09 2.5E-08 21.8 515% 226% 1 4.9E+08 2.0E-09 1.0E-10 9.6E-09 9.6 2.9 1.0E-08 5.2E-11 1.9E-09 2.5E-08 21.8 515% 226% 10 2 4.9E+08 4.1E-09 7.2E-10 1.3E-08 4.2 5.8 2.0E-08 3.5E-11 2.2E-09 5.3E-08 39.1 501% 929% 12 1.0E+08 1.2E-07 6.7E-08 1.9E-07 1.7 30.8 4.5E-07 4.0E-09 1.4E-07 1.2E-06 17.3 387% 1031% 3 1.0E+08 2.9E-08 7.9E-09 7.5E-08 3.1 7.7 1.1E-07 8.8E-10 3.6E-08 2.7E-07 17.6 382% 573% 0 1.0E+08 4.8E-09-2.2E-08 13.0 1.0 2.2E-08 5.7E-10 5.9E-09 5.8E-08 10.1 446% 77% 0 1.0E+08 4.8E-09-2.2E-08 13.0 1.0 2.2E-08 5.7E-10 5.9E-09 5.8E-08 10.1 446% 77% 0 1.0E+08 4.8E-09-2.2E-08 13.0 1.0 2.2E-08 5.7E-10 5.9E-09 5.8E-08 10.1 446% 77% 1 6.5E+08 1.5E-09 7.9E-11 7.3E-09 9.6 3.0 7.1E-09 6.8E-11 1.9E-09 1.9E-08 16.8 460% 174% 4 6.5E+08 6.2E-09 2.1E-09 1.4E-08 2.6 10.8 3.4E-08 7.1E-11 4.2E-09 8.4E-08 34.4 558% 1328% 0 6.5E+08 7.7E-10-3.5E-09 13.0 0.9 2.8E-09 7.0E-11 8.1E-10 8.0E-09 10.7 364% 82% 1 6.5E+08 1.5E-09 7.9E-11 7.3E-09 9.6 3.0 7.1E-09 6.8E-11 1.9E-09 1.9E-08 16.8 460% 174% 3 1.5E+09 2.0E-09 5.6E-10 5.3E-09 3.1 7.6 8.3E-09 6.5E-11 2.5E-09 1.7E-08 16.4 408% 532% 4 1.5E+09 2.7E-09 9.3E-10 6.2E-09 2.6 10.2 8.5E-09 3.3E-11 2.3E-09 2.4E-08 27.0 313% 1043% 0 1.5E+09 3.4E-10-1.6E-09 13.0 0.9 1.7E-09 2.7E-11 3.5E-10 4.0E-09 12.2 509% 94% 1 1.5E+09 6.8E-10 3.5E-11 3.2E-09 9.6 2.8 3.7E-09 2.5E-11 7.1E-10 7.6E-09 17.3 544% 180% 0 1.7E+08 2.9E-09-1.3E-08 13.0 1.2 1.4E-08 5.7E-10 4.9E-09 3.9E-08 8.3 488% 64% 0 1.7E+08 2.9E-09-1.3E-08 13.0 1.2 1.4E-08 5.7E-10 4.9E-09 3.9E-08 8.3 488% 64% 0 1.7E+08 2.9E-09-1.3E-08 13.0 1.2 1.4E-08 5.7E-10 4.9E-09 3.9E-08 8.3 488% 64% 0 1.7E+08 2.9E-09-1.3E-08 13.0 1.2 1.4E-08 5.7E-10 4.9E-09 3.9E-08 8.3 488% 64% 10 1 1.7E+08 5.8E-09 2.9E-10 2.7E-08 9.6 2.8 2.2E-08 1.5E-10 5.1E-09 6.4E-08 20.8 375% 216%
6-1 21 2/4 46 [h] 11 [1/h] [1/h] 90% [1/h] EF *5 6 [] BWR 0 3.6E+07 1.4E-08-6.3E-08 13.0 0.6 5.6E-08 5.0E-10 8.1E-09 1.3E-07 15.8 407% 122% 0 3.6E+07 1.4E-08-6.3E-08 13.0 0.6 5.6E-08 5.0E-10 8.1E-09 1.3E-07 15.8 407% 122% 0 3.6E+07 1.4E-08-6.3E-08 13.0 0.6 5.6E-08 5.0E-10 8.1E-09 1.3E-07 15.8 407% 122% 0 3.6E+07 1.4E-08-6.3E-08 13.0 0.6 5.6E-08 5.0E-10 8.1E-09 1.3E-07 15.8 407% 122% 0 3.6E+07 1.4E-08-6.3E-08 13.0 0.6 5.6E-08 5.0E-10 8.1E-09 1.3E-07 15.8 407% 122% (PWR) 0 2.2E+07 2.3E-08-1.1E-07 13.0 0.8 8.6E-08 1.3E-09 1.9E-08 2.8E-07 14.8 377% 114% 6 1.3E+09 4.8E-09 2.1E-09 9.4E-09 2.1 15.2 1.6E-08 1.7E-10 6.3E-09 4.3E-08 16.1 335% 757% 10 1 1.3E+09 7.9E-10 4.1E-11 3.8E-09 9.6 3.0 3.6E-09 2.1E-11 8.6E-10 9.8E-09 21.4 447% 222% 0 1.3E+09 4.0E-10-1.8E-09 13.0 1.2 2.1E-09 7.8E-11 6.8E-10 5.7E-09 8.6 517% 66% 1 1.3E+09 7.9E-10 4.1E-11 3.8E-09 9.6 3.2 4.0E-09 7.4E-11 1.1E-09 1.1E-08 12.0 502% 125% 1 1.3E+09 7.9E-10 4.1E-11 3.8E-09 9.6 3.2 4.0E-09 7.4E-11 1.1E-09 1.1E-08 12.0 502% 125% / 1 3.4E+07 2.9E-08 1.5E-09 1.4E-07 9.6 2.9 1.3E-07 1.2E-09 3.0E-08 3.3E-07 16.5 432% 172% 7 6.0E+07 1.2E-07 5.5E-08 2.2E-07 2.0 18.1 6.0E-07 1.4E-09 9.6E-08 1.4E-06 31.2 520% 1559% 12 - - 3.9E-05 - - 30.0-8.9E-05 - - - 31.2 231% 104% 1 3.9E+08 2.6E-09 1.3E-10 1.2E-08 9.6 3.1 1.1E-08 1.8E-10 3.5E-09 3.2E-08 13.3 420% 138% 0 3.9E+08 1.3E-09-5.9E-09 13.0 1.1 5.5E-09 2.3E-10 1.9E-09 1.7E-08 8.7 432% 67% 0 3.9E+08 1.3E-09-5.9E-09 13.0 1.1 5.5E-09 2.3E-10 1.9E-09 1.7E-08 8.7 432% 67% 0 3.9E+08 1.3E-09-5.9E-09 13.0 1.1 5.5E-09 2.3E-10 1.9E-09 1.7E-08 8.7 432% 67% 0 3.9E+08 1.3E-09-5.9E-09 13.0 1.1 5.5E-09 2.3E-10 1.9E-09 1.7E-08 8.7 432% 67% *1 1 1.6E+08 6.3E-09 3.2E-10 3.0E-08 9.6 3.1 2.6E-08 4.9E-10 8.1E-09 7.5E-08 12.3 406% 128% 10 0 1.6E+08 3.1E-09-1.4E-08 13.0 0.6 8.8E-09 7.1E-11 1.4E-09 2.5E-08 18.6 281% 143% 2 1.6E+08 1.3E-08 2.2E-09 4.0E-08 4.2 6.0 7.1E-08 1.8E-10 9.0E-09 1.6E-07 29.3 565% 695% 0 6.5E+07 7.7E-09-3.5E-08 13.0 0.8 3.2E-08 4.8E-10 6.8E-09 7.5E-08 12.5 416% 96% 0 6.5E+07 7.7E-09-3.5E-08 13.0 0.8 3.2E-08 4.8E-10 6.8E-09 7.5E-08 12.5 416% 96% 0 5.4E+08 9.2E-10-4.3E-09 13.0 0.9 3.2E-09 6.7E-11 8.7E-10 9.9E-09 12.2 345% 94% 0 5.4E+08 9.2E-10-4.3E-09 13.0 0.9 3.2E-09 6.7E-11 8.7E-10 9.9E-09 12.2 345% 94% 0 5.4E+08 9.2E-10-4.3E-09 13.0 0.9 3.2E-09 6.7E-11 8.7E-10 9.9E-09 12.2 345% 94% / 0 1.9E+08 2.6E-09-1.2E-08 13.0 0.9 9.9E-09 2.0E-10 2.6E-09 2.9E-08 12.0 377% 93% () 0 1.9E+08 2.6E-09-1.2E-08 13.0 0.9 9.9E-09 2.0E-10 2.6E-09 2.9E-08 12.0 377% 93% 0 1.9E+08 2.6E-09-1.2E-08 13.0 0.9 9.9E-09 2.0E-10 2.6E-09 2.9E-08 12.0 377% 93% / 0 2.4E+07 2.1E-08-9.5E-08 13.0 0.9 9.5E-08 1.4E-09 1.9E-08 2.4E-07 13.1 464% 101% ( 0 2.4E+07 2.1E-08-9.5E-08 13.0 0.9 9.5E-08 1.4E-09 1.9E-08 2.4E-07 13.1 464% 101% 2 2.4E+07 8.2E-08 1.5E-08 2.6E-07 4.2 5.3 2.8E-07 2.1E-09 9.5E-08 8.1E-07 19.5 340% 464% (BWR) 0 4.4E+08 1.1E-09-5.3E-09 13.0 0.8 6.5E-09 6.3E-11 9.3E-10 1.2E-08 13.9 570% 107% (PWR) 0 1.2E+08 4.3E-09-2.0E-08 13.0 0.8 1.6E-08 1.7E-10 3.1E-09 4.6E-08 16.3 376% 125% PLR MG 13 5.1E+06 2.6E-06 1.5E-06 4.1E-06 1.6 33.1 8.4E-06 5.2E-07 4.8E-06 2.0E-05 6.2 328% 381% RPS,CRDM MG 0 1.3E+07 3.8E-08-1.7E-07 13.0 1.0 1.6E-07 4.0E-09 4.1E-08 4.5E-07 10.5 425% 81% (PLR) 2 6.7E+05 3.0E-06 5.3E-07 9.5E-06 4.2 5.4 3.4E-05 1.1E-07 4.4E-06 6.1E-05 23.6 1141% 561% 1 1.9E+07 5.2E-08 2.7E-09 2.5E-07 9.6 3.1 3.8E-07 3.0E-09 6.5E-08 7.2E-07 15.6 732% 162% [1/h] 5% [1/h] [1/h] 95% [1/h] EF *7 8 EF 9
47 6-1 21 3/4 [h] 11 [1/h] [1/h] 90% [1/h] EF *5 6 [] 9 7.1E+08 1.3E-08 6.6E-09 2.2E-08 1.8 23.2 4.8E-08 2.2E-10 1.1E-08 1.4E-07 25.2 375% 1379% 12 7.1E+08 1.7E-08 9.7E-09 2.7E-08 1.7 30.6 4.7E-08 3.8E-09 3.3E-08 1.2E-07 5.5 277% 329% 1 7.1E+08 1.4E-09 7.2E-11 6.7E-09 9.6 3.0 8.7E-09 5.6E-11 1.7E-09 1.8E-08 17.9 617% 186% 5 6.2E+07 8.0E-08 3.2E-08 1.7E-07 2.3 12.9 2.6E-07 4.8E-09 1.3E-07 6.8E-07 11.9 319% 514% 0 3.4E+07 1.5E-08-6.7E-08 13.0 0.9 5.7E-08 1.6E-09 1.6E-08 1.6E-07 10.1 392% 78% 1 3.4E+07 2.9E-08 1.5E-09 1.4E-07 9.6 3.0 1.3E-07 1.4E-09 3.6E-08 3.6E-07 16.0 449% 167% *2 3 3.6E+08 8.4E-09 2.3E-09 2.2E-08 3.1 7.8 3.1E-08 2.4E-10 1.0E-08 7.7E-08 17.9 375% 581% *3 0 1.5E+10 3.4E-11-1.6E-10 13.0 0.9 1.3E-10 3.8E-12 3.7E-11 3.9E-10 10.2 394% 78% 1 1.5E+10 6.7E-11 3.5E-12 3.2E-10 9.6 2.9 2.7E-10 3.0E-12 7.0E-11 7.8E-10 16.2 401% 168% 3 1.5E+10 2.0E-10 5.5E-11 5.2E-10 3.1 7.6 7.6E-10 6.9E-12 2.5E-10 1.8E-09 16.0 375% 520% *4 0 3.7E+09 1.4E-10-6.3E-10 13.0 0.9 6.6E-10 1.0E-11 1.3E-10 1.4E-09 11.7 485% 90% 0 3.7E+09 1.4E-10-6.3E-10 13.0 0.9 6.6E-10 1.0E-11 1.3E-10 1.4E-09 11.7 485% 90% *4 13 2 8.3E+09 2.4E-10 4.3E-11 7.6E-10 4.2 5.3 1.0E-09 6.8E-12 2.7E-10 2.3E-09 18.5 421% 440% 0 8.3E+09 6.0E-11-2.8E-10 13.0 1.2 3.2E-10 1.2E-11 9.7E-11 8.5E-10 8.6 524% 66% 13 3 8.1E+09 3.7E-10 1.0E-10 9.6E-10 3.1 7.9 1.5E-09 2.0E-12 1.9E-10 4.1E-09 45.4 410% 1476% 13 4 8.1E+09 5.0E-10 1.7E-10 1.1E-09 2.6 10.3 3.0E-09 4.4E-12 3.7E-10 5.2E-09 34.4 596% 1330% 0 6.9E+08 7.2E-10-3.3E-09 13.0 1.4 4.7E-09 2.1E-10 1.7E-09 1.2E-08 7.8 649% 60% 0 6.9E+08 7.2E-10-3.3E-09 13.0 1.4 4.7E-09 2.1E-10 1.7E-09 1.2E-08 7.8 649% 60% 0 4.4E+08 1.1E-09-5.3E-09 13.0 1.2 5.8E-09 2.1E-10 1.9E-09 1.6E-08 8.7 501% 67% / 3 4.4E+08 6.9E-09 1.9E-09 1.8E-08 3.1 7.7 2.1E-08 2.8E-10 9.0E-09 6.0E-08 14.5 310% 471% 13 0 2.4E+08 2.1E-09-9.5E-09 13.0 0.5 6.6E-09 2.7E-11 6.4E-10 1.8E-08 25.7 320% 198% ( 4 2.4E+08 1.7E-08 5.7E-09 3.8E-08 2.6 10.6 9.2E-08 3.5E-10 2.0E-08 2.3E-07 25.4 554% 980% 0 1.3E+09 3.8E-10-1.8E-09 13.0 0.9 2.3E-09 2.6E-11 3.7E-10 4.1E-09 12.7 605% 98% 3 1.3E+09 2.3E-09 6.2E-10 5.9E-09 3.1 7.9 9.5E-09 6.2E-11 2.6E-09 2.4E-08 19.6 415% 636% 3 2.4E+09 1.3E-09 3.4E-10 3.2E-09 3.1 7.8 5.5E-09 3.7E-11 1.5E-09 1.2E-08 18.2 437% 592% 1 5.9E+08 1.7E-09 8.7E-11 8.1E-09 9.6 3.0 7.6E-09 7.3E-11 1.8E-09 2.1E-08 16.8 448% 175% / 4 5.9E+08 6.8E-09 2.3E-09 1.6E-08 2.6 10.2 2.0E-08 3.6E-10 1.0E-08 5.5E-08 12.2 294% 473% 0 7.5E+08 6.7E-10-3.1E-09 13.0 1.0 2.9E-09 6.6E-11 7.5E-10 7.9E-09 10.9 435% 84% / 8 7.5E+08 1.1E-08 5.3E-09 1.9E-08 1.9 20.6 3.5E-08 1.1E-09 1.9E-08 8.2E-08 8.5 330% 448% 0 3.0E+08 1.6E-09-7.6E-09 13.0 1.1 1.4E-08 2.3E-10 2.2E-09 2.2E-08 9.9 826% 76% / 2 3.0E+08 6.6E-09 1.2E-09 2.1E-08 4.2 5.2 2.2E-08 2.2E-10 7.2E-09 6.0E-08 16.7 333% 398% 0 2.0E+09 2.5E-10-1.2E-09 13.0 0.9 1.1E-09 2.6E-11 2.9E-10 2.9E-09 10.6 423% 82% [1/h] / 5 2.0E+09 2.5E-09 1.0E-09 5.3E-09 2.3 13.0 1.3E-08 4.8E-11 2.9E-09 2.7E-08 23.7 496% 1027% 5% [1/h] [1/h] 95% [1/h] EF*7 8 EF 9
48 6-1 21 4/4 [h] 11 [1/h] 13 13 0 5. 6E+07 8.9E-09-4.1 E-08 13.0 0.7 3.4E-08 5. 7E-10 6.7E-09 8.5E-08 12.2 / 1 5. 6E+07 1.8E-08 9. 1E-10 8.4E-08 9.6 2.9 7.3E-08 4. 3E-10 1.7E-08 2.0E-07 21.8 0 3. 6E+08 1.4E-09-6.4E- 09 13.0 1.1 7.1E-09 2. 1E-10 2.0E-09 1.9E-08 9.5 0 3. 6E+08 1.4E-09-6.4E- 09 13.0 1.1 7.1E-09 2. 1E-10 2.0E-09 1.9E-08 9.5 1 9. 9E+08 1.0E-09 5.2E-11 4.8E-09 9.6 3.1 5.0E-09 6. 7E-11 1.4E-09 1.3E-08 13.9 6 9. 9E+08 6.0E-09 2.6E-09 1.2E-08 2.1 15.6 2.0E-08 3. 3E-11 2.3E-09 6.1E-08 43.0 1 7. 1E+08 1.4E-09 7.2E-11 6.7E-09 9.6 3.0 8.2E-09 8. 0E-11 1.8E-09 1.7E-08 14.8 2 7. 1E+08 2.8E-09 5.0E-10 8.9E-09 4.2 5.3 9.0E-09 1. 3E-11 1.1E-09 2.7E-08 44.9 0 3. 4E+08 1.5E-09-6.7E- 09 13.0 1.1 1.1E-08 2. 0E-10 2.0E-09 1.9E-08 9.9 2 3. 4E+08 5.8E-09 1.0E-09 1.8E- 08 4.2 5.4 2.5E-08 3. 9E-11 2.8E-09 5.6E-08 37.9 3 2. 2E+09 1.4E-09 3.7E-10 3.5E-09 3.1 7.7 5.5E-09 4. 5E-11 1.7E-09 1.2E-08 16.3 1 2. 2E+09 4.5E-10 2.3E-11 2.2E-09 9.6 3.1 3.1E-09 2. 5E-11 6.0E-10 5.7E-09 15.1 2 3. 5E+09 5.8E-10 1.0E-10 1.8E-09 4.2 5.3 1.9E-09 3.0E-11 7.3E-10 5.4E-09 13.5 0 3. 5E+09 1.4E-10-6.7E- 10 13.0 1.2 1.1E-09 2. 7E-11 2.4E-10 2.1E-09 8.8 0 4. 3E+08 1.2E-09-5.3E- 09 13.0 0.8 4.0E-09 6. 7E-11 1.0E-09 1.2E-08 13.3 1 4. 3E+08 2.3E-09 1. 2E-10 1.1E-08 9.6 2.8 1.4E-08 6. 8E-11 2.1E-09 2.7E-08 20.1 12 - - 3.4E-11 - - 30.0-3.1E-10 - - - 30.0 12 - - 1.1E-10 - - 30.0-5.9E-10 - - - 30.0 12 - - 6.4E-10 - - 30.0-2.1E-09 - - - 30.0 333% 100% 12 - - 4.0E-09 - - 30.0-1.3E-08 - - - 30.0 329% 100% 12 - - 3.8E-10 - - 30.0-3.1E-09 - - - 30.0 814% 100% 1. 2. 3. 4. 5.EF 2 ( = 0EF=13 6. 90% EF *5 5% [1/h] 6 [] [1/h] [1/ h] [1/ h] [1/h] 7.EF 2 ( = 8. 9.EFEF 10. µ-1. 0-2.0-0.5 11. 0.5 12. 13. WinBUGSµ-1.03-0.5 95% [1/h] EF *7 8 381% 410% 507% 507% 497% 338% 580% 320% 784% 432% 401% 681% 332% 734% 342% 622% 926% 543% EF 9 94% 227% 73% 73% 145% 2021% 154% 1067% 76% 900% 531% 157% 320% 68% 102% 209% 100% 100%
6-2 21 *1 [1/d] 90% [1/d] [1/d] EF *2 *3 [1/d] 5% [1/d] 95% [1/d] [ 1/d] EF *4 *5 EF 6 49 0 1315 3.8E-04-1.8E-03 13.0 0.7 1. 4E-03 1. 4E-05 2.4E-04 4.0E-03 17.1 358% 131% DG 19 42332 4.5E-04 2.9E-04 6.6E-04 1.5 49.0 1. 5E-03 5.8E-05 7.7E-04 4.4E-03 8. 7 334% 580% 3 143096 2.1E-05 5.7E-06 5.4E-05 3.1 7.8 8. 0E-05 7. 3E-07 2.6E-05 2.1E-04 16.9 383% 550% 6 11776 5.1E-04 2.2E-04 1.0E-03 2.1 15.5 1. 6E-03 2.1E-06 1.7E-04 5.2E-03 49. 6 322% 2328% 2 271 7.4E-03 1.3E-03 2.3E-02 4.2 6.1 2.3E-02 3. 2E-03 1.6E-02 6.1E-02 4. 3 304% 103% 1 50481 2.0E-05 1.0E-06 9.4E-05 9.6 3.2 1. 1E-04 1. 4E-06 2.7E-05 2.6E-04 13. 8 531% 144% 7 490002 1.4E-05 6.7E-06 2.7E-05 2.0 18.0 4. 7E-05 4.8E-08 4.4E-06 1.3E-04 51. 7 330% 2583% 1 490513 2.0E-06 1.0E-07 9.7E-06 9.6 2.9 9. 7E-06 6. 4E-08 1.9E-06 2.5E-05 19. 8 477% 206% 1 153155 6.5E-06 3.3E-07 3.1E-05 9.6 3.6 4. 2E-05 1. 7E-06 1.5E-05 1.0E-04 7. 7 636% 80% 6 154627 3.9E-05 1.7E-05 7.7E-05 2.1 16.2 3. 2E-04 4.3E-07 2.6E-05 7.4E-04 41. 4 814% 1946% 5 132460 3.8E-05 1.5E-05 7.9E-05 2.3 12.8 1. 4E-04 2.5E-06 6.0E-05 3.4E-04 11. 6 382% 504% 0 132365 3.8E-06-1.7E-05 13.0 1.1 1. 9E-05 5.8E-07 5.7E-06 5.5E-05 9. 7 511% 75% 0 259336 1.9E-06-8.9E-06 13.0 1.1 9. 7E-06 2.1E-07 2.4E-06 2.5E-05 10. 8 501% 83% 1 252416 4.0E-06 2.0E-07 1.9E-05 9.6 3.3 2. 2E-05 5. 6E-07 6.6E-06 5.5E-05 9. 9 556% 103% 1 41714 2.4E-05 1.2E-06 1.1E-04 9.6 3.1 1. 2E-04 1. 2E-06 2.9E-05 3.3E-04 16. 3 508% 169% 1 41378 2.4E-05 1.2E-06 1.1E-04 9.6 3.4 1. 4E-04 4. 3E-06 4.8E-05 3.5E-04 9.0 591% 94% 0 1179 4.2E-04-2.0E-03 13.0 0.7 1. 5E-03 1. 4E-05 2.6E-04 4.3E-03 17.7 360% 136% 0 8323 6.0E-05-2.8E-04 13.0 0.8 2. 7E-04 3. 9E-06 5.3E-05 6.8E-04 13.3 452% 102% 0 8165 6.1E-05-2.8E-04 13.0 0.8 2. 9E-04 4. 1E-06 5.6E-05 7.0E-04 13.2 478% 101% 3 307782 9.7E-06 2.7E-06 2.5E-05 3.1 7.8 3. 4E-05 8. 3E-07 1.4E-05 8.7E-05 10.3 349% 334% 1 230491 4.3E-06 2.2E-07 2.1E-05 9.6 3.1 2. 2E-05 1. 7E-07 5.1E-06 5.4E-05 17.7 506% 184% 3 230325 1.3E-05 3.6E-06 3.4E-05 3.1 7.8 4. 8E-05 3. 7E-07 1.6E-05 1.2E-04 18.1 366% 587% 1 185281 5.4E-06 2.8E-07 2.6E-05 9.6 3.0 2. 5E-05 2. 0E-07 5.9E-06 6.8E-05 18.4 467% 191% 0 185949 2.7E-06-1.2E-05 13.0 0.9 1. 1E-05 2.0E-07 2.5E-06 2.8E-05 11.9 392% 91% 1.0. 5 2 ( 2.EF = 0EF=13 3. 4.EF 2 (= 5. 6.EFEF
7 () () 7.1 λ λ ( µ σ ) λ ~ Lognormal, (λ,µ,σ>0) (7.1) µlogλσlogλ µ ex p( µ)=λµλ σ ex p (1.645σ)=λEF=(λ 95%)/(λ)σ λ 95% 7.2 pd pd ( µ,σ ) logit( pd ) ~ Normal 0<pd<1, µ,σ> 0 (7.2) pd logit( pd) = log 1 pd µlogit( pd)σ logit(pd) pd logit( pd) r = 1 pd ( ) µ,σ r ~ Lognormal (7.3) µlog r σlog r pd << 1 r pd pd ( µ,σ ) pd ~ Lognormal (7.4) 50
µlog pd σlog pd a) µ exp(µ)=pdµpd σ exp(1.645σ)=pdef=(pd 95%)/(pd) σ pd 95% µσ/ EF 7-1 7-2 7-1 µ/ µ (/hr) -19.0-8.5 5.6E-09 2.0E-04 1-25.0-14.5 1.4E-11 5.0E-07 2-15.5-5.0 1.9E-07 6.7E-03 3-21.6-5.9 4.2E-10 2.7E-03-25.0-14.0 1.4E-11 8.3E-07 1-27.8-16.8 8.4E-13 5.1E-08 2-23.0-12.0 1.0E-10 6.1E-06 3-27.6-11.0 1.0E-12 1.7E-05 µ DG -12.0-0.99 6.1E-06 3.7E-01 1-18.0-6.99 1.5E-08 9.2E-04 2-8.0-3.01 3.4E-04 4.9E-02 3-14.8-1.81 3.7E-07 1.6E-01-14.0-3.0 8.3E-07 5.0E-02 1-16.0-5.0 1.1E-07 6.7E-03 2-12.0-1.0 6.1E-06 3.7E-01 3-16.8-0.2 5.1E-08 8.2E-01 51
7-2 σ EF () σ EF 0.10 3.0 1.18 139 1 0.01 1.5 1.02 12 2 1.00 3.3 5.18 228 3 0.01 3.3 1.02 228 7.3 σ σ 7.3.1 4 - σµ Unif a b = 1 b + a (b a) 2 ( σ µ ) ~ (, ) = (7.5) b a 2 12 σ Unif ( 0.1,3) 7-3 7-3 σ EF Unif 0.1,3 1.6 0.70 1.2~139 ( ) 1 ( 0.01,1.5 ) 2 ( 1,3.3) Unif 0.76 0.19 1.02~12 Unif 2.2 0.44 5~228 Unif 1.7 0.90 1.02~228 3 ( 0.01,3.3) 7.3.2 WinBUGS 7.3.3 7-4 7-5 7-6 C 52
7-4(1) 1 53
7-4(2) 1 54
7-4(3) D/G 1 55
7-4(4) 1 56
7-5(1) 2 57
7-5(2) 2 58
7-5(3) D/G 2 59
7-5(4) 2 60
61 7-6(1) 3
7-6(2) 3 62
7-6(3) D/G 3 63
7-6(4) 3 64
7.3.4 a) σ σ 1 σ b) 1 1) 1 1 0 - λ i - 1 7-1- 2) 0-65
1 - - 1 0 7-1 - c) 2-1 d) 3-1 2 σ 7.3.5 -σ - σ σ 66
1.0 0.75 0.5 0.25 0.0 sigma sample: 100000 0.0 1.0 2.0 3.0 0.8 0.6 0.4 0.2 0.0 sigma sample: 100000 0.0 1.0 2.0 3.0 1.0 0.75 0.5 0.25 0.0 sigma sample: 100000 0.0 1.0 2.0 3.0 0.8 0.6 0.4 0.2 0.0 sigma sample: 100000 0.0 1.0 2.0 3.0 D/G 7-2(1) σ 67
sigma sample: 100000 1.5 1.0 0.5 0.0 0.0 0.5 1.0 1.5 1.5 1.0 0.5 0.0 sigma sample: 100000-0.5 0.0 0.5 1.0 1.5 1.0 0.75 0.5 0.25 0.0 sigma sample: 100000-0.5 0.0 0.5 1.0 1.5 1.0 0.75 0.5 0.25 0.0 sigma sample: 100000-0.5 0.0 0.5 1.0 1.5 D/G 7-2(2) 1 σ 68
1.5 1.0 0.5 0.0 sigma sample: 100000 0.0 1.0 2.0 3.0 sigma sample: 100000 1.5 1.0 0.5 0.0 0.0 1.0 2.0 3.0 1.5 1.0 0.5 0.0 sigma sample: 100000 sigma sample: 100000 1.5 1.0 0.5 0.0 0.0 1.0 2.0 3.0 0.0 1.0 2.0 3.0 D/G 7-2(3) 2 σ 69
1.0 0.75 0.5 0.25 0.0 sigma sample: 100000-1.0 0.0 1.0 2.0 3.0 0.8 0.6 0.4 0.2 0.0 sigma sample: 100000-1.0 0.0 1.0 2.0 3.0 0.8 0.6 0.4 0.2 0.0 sigma sample: 100000-1.0 0.0 1.0 2.0 3.0 0.8 0.6 0.4 0.2 0.0 sigma sample: 100000-1.0 0.0 1.0 2.0 3.0 D/G 7-2(4) 3 σ 70
7.4 µ µ 4 D/G 7.4.1 - µσ Unif a b = 1 b + a ( b a) ( µ σ ) ~ (, ) = b a 2 12 2 (7.6) µ 10 5 7-7 1 2 µ 3/4 20% 3 1.5 71
7-7 µ DG Unif(-19,-8.5) Unif(-25,-14) Unif(-12,-0.99) Unif(-14,-3.0) 1 Unif(-25,-14.5) Unif(-27.8,-16.8)* Unif(-18.0,-6.99) Unif(-16,-5.0) 2 Unif(-15.5,-5.0) Unif(-23,-12) Unif(-8.0,3.01) Unif(-12,-1.0) 3 Unif(-21.6,-5.9) Unif(-27.6,-11) Unif(-14.8,1.81) Unif(-16.8,-0.2) ) WinBUGS 7.4.2 WinBUGS 7 5 10 7.4.3 7-8 7-9 7-10 C 72
7-8(1) 1 73
7-8(2) 1 74
75 7-8(3) D/G 1
7-8(4) 1 76
77 7-9(1) 2
7-9(2) 2 78
79 7-9(3) D/G 2
7-9(4) 2 80
81 7-10(1) 3
7-10(2) 3 82
7-10(3) D/G 3 83
7-10(4) 3 84
7.4.4 a) 1) 1 7-3 µµµ mu sample: 100000 1.0 0. 75 0.5 0.25 0.0-1 8.0-16.0-14.0 1.0 0.75 0.5 0.25 0.0 mu s ample: 1 00000-12.0-10.0-8.0-6.0 DG 7-3 1 µ 2) 0 7-4 µµµ µ 0 mu sample: 100000 0.8 0.6 0.4 0.2 0.0-2 6.0-24.0-22.0 0.8 0.6 0.4 0.2 0.0 mu s ample: 1 00000-16.0-14.0-12.0-10.0 7-4 0 µ b) 1 1) 1 1 0 95% 5% EF EF 7-5 µ σ 7-6 σσ σ EF σ 1 1 85
0 mu sample: 100000 1.5 1.0 0.5 0.0-19.0-17.0-15.0 mu sample: 100000 1.5 1.0 0.5 0.0-12.0-10.0-8.0 DG 7-5 1 µ 1 7-6 µσ 2) 0 EF 7-7 µ 7-4 µ µµ µ EF 86
mu sample: 100000 0.3 0.2 0.1 0.0-28.0-26.0-24.0-22.0 0.4 0.3 0.2 0.1 0.0 mu sample: 100000-1 8.0-1 4.0-1 0.0 7-7 0 µ 1 b) 2 1) 1 EF 7-8 µ 7-3 1 (1)µ µµ EF 1.0 0.75 0.5 0.25 0.0 mu sample: 100000-1 6.0-15.0-14.0 1.0 0.75 0.5 0.25 0.0 mu sample: 100000-9.0-8.0-7.0-6.0 DG 7-8 1 µ 2 2) 0 EF 7-8 µ 7-4 µ µµ µef 87
mu sample: 100000 1.5 1.0 0.5 0.0-2 4.0-23.0-2 2.0-21.0 mu sample: 100000 1.5 1.0 0.5 0.0-1 3.0-12.0-1 1.0-10.0 7-9 0 µ 2 c) 3 1) 1 µ 7-10 µ EF 1 µ1 µ µ 1.0 0.75 0.5 0.25 0.0 mu sample: 100000-2 0.0-18.0-1 6.0-14.0 1.0 0.75 0.5 0.25 0.0 mu sample: 100000-1 2.0-10.0-8.0-6.0 DG 7-10 1 µ 3 2) 0 µ 7-11 µµ EF 0 µ 88
0.4 0.3 0.2 0.1 0.0 mu sample: 100000-2 8.0-26.0-2 4.0-22.0 mu sample: 100000 0.3 0.2 0.1 0.0-1 8.0-14.0-10.0 7-11 0 µ 3 7. 4.5 0 µ 0 µ 0.5 µ 2 µ a) NRCNUREG/CR-6928 [8] 1998~2002 NRCPRAstandardized plant analysis risk(spar)nureg/cr-6928 µ 1) NUREG/CR-6928 NUREG/CR-6928 EPIX 1998 2002 Jeffreys 6.53E-10 [/h][/h/ft] EF 18.8 LLLower allowable limit 1.30E-5[/d] EF 8.4 7-11 2) 7-12 µ 21 7-11 7-12 µ 7-12 89
µ µ µ 7-11 NUREG/CR-6928 EF 6.53E-10 1.59E-10 18.8 [/h] [/h] 1.30E-5 5.90E-6 8.4 [/d] [/h] -2 µ µ 19.0µ8.5 5.6E-9λ[/h]2.0E-4 25.0µ14.0 1.4E-11λ[/h]8.3E-7 D/G 12.0µ0.99 6.1E-6pd[/d]3.7E-1 14.0µ3.0 8.3E-7pd[/d]5.0E-2 90
7-12 µ NUREG/CR-6928 b) µ µ 7-13 µ- lnλa µ b µ λ max λ min E(µ) Var(µ) µλ max λ min 0.5 λ max λ min λ min λ min λ min Feasibility Study λ max 91
µλ max λ min - µ µ PSA 92
- λi µ- λj µ ln λ Var(µ) =10 a µ b µ aµ = E(µ) 3Var( µ ) b µ = E( µ ) + 3Var( µ ) a µ E(µ) bµ µ λ 5-5%95% E(µ) E( σ ) = ln(95% / 5% ) / 3.29 E( µ ) = ln95% 1.645E( σ ) 5% E(µ) ln(λ min ) 5% 95% 95% ln λ ln(λ max /p exp ) 95% p exp 0.4 T Y [hour] =Y/T [/hour] 1 0 5.0E+6 1.0E-7 λ min 2 4 1.0E+5 4.0E-5 λ max : 49 0 1.0E+5 5.0E-6 Y= 0 0.5 7-13 µ 93
7.4.6 -µ 1 0 µ 0 0 0.5 µ µ 1/2 µ 1 WinBUGS µ 94
8 8.1 p i PSAFFFFp i NUCIAPSAFF ipsaffx i y i NUCIA y ~ Binomial i ( p, x ) yi xi yi f ( y ) = C p ( 1 p ) i x i y i i i i 0 y x x i,y i 0 p 1 (8.1) i i < i p i ( 4,6) p i ~ Beta (8.2) 8-1 f ( p ) i 1 4 = p 1 1 i i B ( 4,6) ( p ) 6 1 B(4,6) (8.3) dbeta(x, 4, 6) 0.0 1.0 2.0 0.0 0.2 0.4 0.6 0.8 1.0 p pd( ) 8-1 PSA NUCIA PSA 1 9 95
, y i =0 x i 0 x i ( x, y, p λ,θ t) f ( θ ) ( p ) f ( θ ) f ( x λ,t ) f ( y p, x ) f, f i λ i i i i i i i (8.4) i i i i () () x i xx i y i ( NUCIA) yy i p i pp i λi λλ i θ i t i ( ) tt i i ix i pifull conditional distribution( fcd ) (8.4)x i p i (8.5) f ( x, p y,, θ, t ) f ( x λ, t ) f ( y p, x ) f ( p ) i i i λ (8.5) i i i i i i i i i (8.5) 3 (8.6) (8.7) (8.8) f ( λ, ) = Poisson( x ; λ t ) xi ( λ i t ) exp( λ t ) i i i x i i t i i i i = (8.6) xi 96
xi y f ( y i p i, x i ) ial ( y i ;, x i ) = p x i i yi = Binom pi i ( 1 pi ) (8.7) yi f 1 6 1 p i = Beta i = i i (8.8) B 4,6 ( ) ( p ;4,6) ( p ) 4 1 ( 1 p ) xi (8.6)(8.7) x i (8.6)t i = 2E6[h] λ i =5E-7[ /h] x i 8-2 (8..11)y i =0 x i 8-3 ( 8.8) p i ~Beta (4,6) 8-2 (8.6)x i λ i t i =5E-7[ 1/h] 2E 6 [h] =1 8-3 (8.7)x i y i =0, pi~beta(4,6) 97
p 8.4 (8.5)x i p i λit i=5e-7 [1/h] 2E6 [h] = 1y i =0pi~Beta( 4,6) ( 8.5)x i 8-2 8-3 8-4 pi 0 0~5 0.6 8.2 piyixi 8.2.1 ip i full conditional dist ribution, (fcd)(8.4) p i (8.9) f ( p x,,, θ ) f ( ) f ( y p, x ) i i y i i,t i p i i λ (8.9) i i (8.9) 2 f f 4-1 ( ) = Beta( ;4,6) ( 1 p ) 6 i i 1 p (8.10) p i p i yi xi yi ( y p, ) = Binomial ( ; p, x ) p ( 1 p ) i (8.11) i x i y i i i i i (8.12) p i ( 8.9)(8.13) 98
f yi + 4 1 xi yi + 6 1 ( p x, y,, θ, t ) ( 1 p ) f i i i λ (8.12) i i p i ( p x,,, θ, t ) Beta( p ; y + 4, y + 6) i i y i i i = i i x i i i λ (8.13) WinBUGSp i (8.13)fcdx i p i (8.13)p i (yi+4)/(x i + 10) y 0 0 x i i p i 0.4 y i 0 y i x i y i /xi 0.4 p i 0.4 0.4 p i 0. 4 2 y i p i / 0 8.2.2 D/ G 4 p i 8-1 8-4 0 0.4 0 8-1 8-3 0. 4 0.4 8-1 8-3 0.4 0. 4 99
8-1 5% 95% y i y i + xi p[1] 0.4216 0.1952 0.4159 0.6671 1 2.001 0.4166 p[2] 0.4667 0.2399 0.4637 0.7025 3 5.445 0.4532 p[3] 0.3832 0.1576 0.375 0.64 0 0.510 0.3806 p[4] 0.4647 0.2353 0.462 0.7008 3 5.509 0.4514 p[5] 0.3826 0.1577 0.3739 0.6368 0 0.542 0.3794 p[6] 0.4205 0.194 0.4144 0.6672 1 2.057 0.4147 p[7] 0.4611 0.2323 0.4591 0.6979 3 5.647 0.4474 p[8] 0.4185 0.1912 0.4129 0.6661 1 2.123 0.4124 p[9] 0.4219 0.1953 0.4162 0.6695 1 2.008 0.4164 p[10] 0.3831 0.1568 0.3751 0.6377 0 0.518 0.3803 p[11] 0.3814 0.1555 0.3731 0.636 0 0.556 0.3789 p[12] 0.3860 0.1598 0.3777 0.6413 0 0.394 0.3848 p[13] 0.3895 0.1608 0.382 0.6445 0 0.324 0.3874 p[14] 0.3902 0.1627 0.3822 0.6439 0 0.292 0.3886 p[15] 0.3864 0.1596 0.378 0.6413 0 0.416 0.3840 p[16] 0.3828 0.1563 0.3743 0.6377 0 0.525 0.3801 p[17] 0.4461 0.2182 0.4428 0.6876 2 3.718 0.4374 p[18] 0.3844 0.1576 0.3759 0.6397 0 0.462 0.3823 p[19] 0.3879 0.161 0.3798 0.6432 0 0.359 0.3862 p[20] 0.3869 0.159 0.378 0.6442 0 0.371 0.3857 p[21] 0.3827 0.1553 0.3746 0.6386 0 0.515 0.3804 p[22] 0.3904 0.1614 0.3828 0.6466 0 0.274 0.3893 p[23] 0.3809 0.1557 0.3719 0.637 0 0.603 0.3772 p[24] 0.3851 0.1588 0.3762 0.6401 0 0.455 0.3826 p[25] 0.4630 0.2366 0.4604 0.699 3 5.550 0.4502 p[26] 0.4635 0.2373 0.4603 0.6995 3 5.539 0.4505 p[27] 0.3827 0.1564 0.3752 0.6363 0 0.515 0.3804 p[28] 0.3855 0.1587 0.3772 0.6415 0 0.450 0.3828 p[29] 0.3824 0.1569 0.3737 0.6379 0 0.552 0.3791 p[30] 0.3810 0.1544 0.3726 0.637 0 0.586 0.3779 p[31] 0.4403 0.2128 0.4356 0.683 2 3.953 0.4300 p[32] 0.4180 0.1927 0.412 0.6654 1 2.131 0.4122 p[33] 0.4184 0.1923 0.4125 0.6657 1 2.099 0.4133 p[34] 0.3836 0.157 0.375 0.6381 0 0.510 0.3806 p[35] 0.3829 0.157 0.3742 0.6381 0 0.507 0.3807 p[36] 0.3833 0.1566 0.3747 0.6385 0 0.523 0.3801 p[37] 0.3834 0.1568 0.3751 0.6394 0 0.506 0.3807 p[38] 0.4274 0.199 0.4227 0.6729 1 1.829 0.4227 p[39] 0.3874 0.1598 0.379 0.6435 0 0.349 0.3865 p[40] 0.3803 0.1552 0.3715 0.6358 0 0.607 0.3771 p[41] 0.3778 0.153 0.3683 0.6359 0 0.663 0.3751 p[42] 0.3884 0.1611 0.38 0.643 0 0.333 0.3871 p[43] 0.3923 0.1627 0.3845 0.6484 0 0.237 0.3907 p[44] 0.3798 0.1539 0.3707 0.6375 0 0.623 0.3765 p[45] 0.3800 0.1553 0.3706 0.6347 0 0.581 0.3780 p[46] 0.3779 0.1551 0.3686 0.6337 0 0.665 0.3751 p[47] 0.3785 0.1534 0.3693 0.635 0 0.675 0.3747 p[48] 0.3894 0.1615 0.3815 0.6453 0 0.322 0.3875 p[49] 0.3805 0.1545 0.3714 0.6378 0 0.609 0.3771 x i ( 4 ) ( +10) 100
8-2 5% 95% y i y i + xi p[1] 0.3988 0.1678 0.3918 0.6538 0 0.022 0.3991 p[2] 0.3990 0.1672 0.3927 0.6544 0 0.018 0.3993 p[3] 0.3991 0.1681 0.3921 0.6533 0 0.018 0.3993 p[4] 0.3995 0.1679 0.3927 0.655 0 0.019 0.3992 p[5] 0.3991 0.1673 0.3922 0.6544 0 0.019 0.3992 p[6] 0.3991 0.1688 0.392 0.6549 0 0.023 0.3991 p[7] 0.3989 0.1671 0.3919 0.6544 0 0.025 0.3990 p[8] 0.3992 0.1692 0.3919 0.6532 0 0.022 0.3991 p[9] 0.3994 0.1687 0.3918 0.6542 0 0.018 0.3993 p[10] 0.3997 0.1688 0.393 0.6553 0 0.018 0.3993 p[11] 0.3990 0.1685 0.3919 0.6542 0 0.022 0.3991 p[12] 0.3996 0.1684 0.3923 0.6546 0 0.015 0.3994 p[13] 0.3998 0.1688 0.3927 0.6557 0 0.012 0.3995 p[14] 0.3992 0.168 0.3925 0.6529 0 0.011 0.3996 p[15] 0.3984 0.1688 0.3915 0.6534 0 0.018 0.3993 p[16] 0.3997 0.1679 0.3933 0.6549 0 0.017 0.3993 p[17] 0.3988 0.1679 0.3919 0.6535 0 0.019 0.3992 p[18] 0.3997 0.168 0.3928 0.6545 0 0.019 0.3992 p[19] 0.4001 0.1689 0.3929 0.6548 0 0.012 0.3995 p[20] 0.3996 0.1678 0.3928 0.6543 0 0.012 0.3995 p[21] 0.3992 0.1683 0.3923 0.6559 0 0.017 0.3993 p[22] 0.3999 0.1688 0.3931 0.6541 0 0.010 0.3996 p[23] 0.3997 0.169 0.3922 0.6541 0 0.023 0.3991 p[24] 0.3997 0.1676 0.3931 0.6539 0 0.019 0.3992 p[25] 0.3996 0.1704 0.3928 0.654 0 0.022 0.3991 p[26] 0.3987 0.1682 0.3913 0.6544 0 0.025 0.3990 p[27] 0.3990 0.1692 0.3915 0.6555 0 0.014 0.3994 p[28] 0.3995 0.1667 0.3922 0.6552 0 0.014 0.3994 p[29] 0.3993 0.1674 0.3923 0.6542 0 0.018 0.3993 p[30] 0.3996 0.1671 0.3928 0.6551 0 0.018 0.3993 p[31] 0.3987 0.169 0.3913 0.6544 0 0.024 0.3990 p[32] 0.3983 0.168 0.3912 0.6537 0 0.022 0.3991 p[33] 0.3994 0.1702 0.3917 0.6536 0 0.020 0.3992 p[34] 0.3999 0.1695 0.3926 0.6555 0 0.022 0.3991 p[35] 0.3999 0.1687 0.3926 0.6549 0 0.022 0.3991 p[36] 0.3994 0.1684 0.3921 0.6551 0 0.026 0.3990 p[37] 0.3989 0.1679 0.3917 0.6545 0 0.025 0.3990 p[38] 0.3990 0.1667 0.3923 0.6539 0 0.017 0.3993 p[39] 0.3988 0.1675 0.3917 0.6539 0 0.016 0.3994 p[40] 0.3996 0.1697 0.3925 0.6539 0 0.019 0.3992 p[41] 0.3993 0.1678 0.3919 0.653 0 0.023 0.3991 p[42] 0.3997 0.1692 0.3929 0.6556 0 0.014 0.3994 p[43] 0.3997 0.1683 0.3929 0.655 0 0.009 0.3996 p[44] 0.3995 0.1682 0.3923 0.6556 0 0.024 0.3990 p[45] 0.3993 0.1697 0.3923 0.6531 0 0.021 0.3992 p[46] 0.3983 0.1668 0.3914 0.6521 0 0.023 0.3991 p[47] 0.3986 0.1675 0.3916 0.6554 0 0.024 0.3991 p[48] 0.3990 0.1691 0.3914 0.6546 0 0.011 0.3995 p[49] 0.3989 0.1686 0.392 0.6533 0 0.022 0.3991 x i ( 4 ) ( +10) 101
8-3 DG 5% 95% y i y i + xi p[1] 0.3887 0.1619 0.3805 0.6442 0 0.334 0.3871 p[2] 0.3878 0.1608 0.3797 0.6438 0 0.352 0.3864 p[3] 0.3881 0.1613 0.379 0.6444 0 0.336 0.3870 p[4] 0.3884 0.1613 0.3803 0.6439 0 0.365 0.3859 p[5] 0.3874 0.1611 0.3798 0.6423 0 0.362 0.3860 p[6] 0.3870 0.1586 0.3785 0.6435 0 0.385 0.3852 p[7] 0.4570 0.2291 0.4543 0.6951 2 3.329 0.4501 p[8] 0.4291 0.201 0.4246 0.6749 1 1.759 0.4252 p[9] 0.3887 0.1614 0.3808 0.6431 0 0.323 0.3875 p[10] 0.3889 0.1599 0.3809 0.6451 0 0.324 0.3874 p[11] 0.4609 0.2332 0.4574 0.6995 2 3.215 0.4540 p[12] 0.3906 0.1618 0.3835 0.6452 0 0.278 0.3892 p[13] 0.3924 0.1635 0.3848 0.6483 0 0.216 0.3916 p[14] 0.3929 0.1642 0.3855 0.6474 0 0.200 0.3922 p[15] 0.4337 0.2038 0.4292 0.679 1 1.629 0.4300 p[16] 0.3922 0.1629 0.3847 0.6478 0 0. 250 0.3902 p[17] 0.4338 0.2052 0.4287 0.6792 1 1.610 0.4307 p[18] 0.3893 0.1598 0.3816 0.6458 0 0.312 0.3879 p[19] 0.3926 0.1629 0.3856 0.6463 0 0.214 0.3916 p[20] 0.4365 0.2076 0.4317 0.6818 1 1.547 0.4330 p[21] 0.3904 0.1642 0.3828 0.6445 0 0.267 0.3896 p[22] 0.3932 0.1642 0.3856 0.6497 0 0.183 0.3928 p[23] 0.3906 0.1627 0.3822 0.6457 0 0.303 0.3883 p[24] 0.3932 0.1643 0.3858 0.6468 0 0.216 0.3915 p[25] 0.3868 0.1588 0.3789 0.6416 0 0.380 0.3853 p[26] 0.4638 0.234 0.4614 0.7005 2 3.153 0.4562 p[27] 0.3933 0.164 0.3862 0.6489 0 0.183 0.3928 p[28] 0.3949 0. 165 0.3876 0.6491 0 0.168 0.3934 p[29] 0.3823 0.1563 0.3731 0.6379 0 0.504 0.3808 p[30] 0.3813 0.1556 0.3726 0.6369 0 0.568 0.3785 p[31] 0.3783 0.1542 0.3694 0.6339 0 0.666 0.3750 p[32] 0.3788 0.1542 0.3697 0.6346 0 0. 638 0.3760 p[33] 0.3798 0.1544 0.3714 0.6372 0 0.611 0.3770 p[34] 0.4200 0.193 0.4143 0.6667 1 2.036 0.4154 p[35] 0.3821 0.156 0.374 0.6383 0 0.549 0.3792 p[36] 0.4422 0.2165 0.4384 0.6839 2 3.875 0.4324 p[37] 0.3759 0.1518 0.3664 0.6319 0 0.766 0.3716 p[38] 0.3814 0.1563 0.373 0.6353 0 0.550 0.3791 p[39] 0.4719 0.2418 0.4697 0.7078 3 5.230 0.4596 p[40] 0.3745 0.1512 0.3656 0.6297 0 0.790 0.3707 p[41] 0.4100 0.1862 0.4029 0.6586 1 2.398 0.4033 p[42] 0.3886 0.1592 0.3808 0.644 0 0.310 0.3880 p[43] 0.3926 0.1641 0.3851 0.6465 0 0.210 0.3918 p[44] 0.3730 0.1499 0.3639 0.6288 0 0.861 0.3683 p[45] 0.3733 0.1505 0.3644 0.6284 0 0.821 0.3697 p[46] 0.4110 0.1862 0.404 0.6584 1 2.375 0.4040 p[47] 0.3733 0.1502 0.3637 0.6286 0 0.853 0.3686 p[48] 0.3885 0.1603 0.3809 0.6424 0 0.315 0.3878 p[49] 0.4262 0.1977 0.421 0.6734 1 1.837 0.4224 x i ( 4 ) ( +10) 102
8-4 5% 95% y i y i + xi p[1] 0.3989 0.1678 0.3924 0.6543 0 0.022 0.3991 p[2] 0.3987 0.1672 0.3917 0.6527 0 0.029 0.3989 p[3] 0.3990 0.1685 0.392 0.6538 0 0.029 0.3989 p[4] 0.3988 0.168 0.3924 0.6522 0 0.029 0.3988 p[5] 0.3985 0.1682 0.391 0.6527 0 0.031 0.3988 p[6] 0.3990 0.1679 0.3922 0.6551 0 0.035 0.3986 p[7] 0.3988 0.1679 0.3925 0.6525 0 0.037 0.3985 p[8] 0.3991 0.1679 0.3922 0.6539 0 0.034 0.3986 p[9] 0.3991 0.169 0.3922 0.6535 0 0.029 0.3989 p[10] 0.3995 0.169 0.393 0.6532 0 0.029 0.3988 p[11] 0.3993 0.1673 0.3923 0.6539 0 0.030 0.3988 p[12] 0.3984 0.1682 0.3912 0.6529 0 0.024 0.3990 p[13] 0.3995 0.1684 0.3928 0.6551 0 0.018 0.3993 p[14] 0.3990 0.1685 0.3915 0.6547 0 0.018 0.3993 p[15] 0.3984 0.1686 0.3916 0.6513 0 0.025 0.3990 p[16] 0.3990 0.1684 0.3924 0.6553 0 0.040 0.3984 p[17] 0.3985 0.1683 0.3916 0.6553 0 0.047 0.3981 x i ( 4 ) ( +10) p[18] 0.3997 0.1688 0.3928 0.6545 0 0.024 0.3990 p[19] 0.4001 0.1685 0.3936 0.6542 0 0.016 0.3994 p[20] 0.4001 0.1689 0.3931 0.655 0 0.013 0.3995 p[21] 0.3992 0.1681 0.392 0.6542 0 0.029 0.3988 p[22] 0.4000 0.1681 0.3928 0.6565 0 0.012 0.3995 p[23] 0.3986 0.1679 0.3919 0.6537 0 0.038 0.3985 p[24] 0.3992 0.1679 0.3926 0.6538 0 0.030 0.3988 p[25] 0.3992 0.1686 0.3918 0.6545 0 0.025 0.3990 p[26] 0.3999 0.1701 0.3924 0.6554 0 0.013 0.3995 p[27] 0.3996 0.1672 0.393 0.6554 0 0.007 0.3997 p[28] 0.3990 0.1684 0.3912 0.6549 0 0.006 0.3998 p[29] 0.3996 0.1681 0.3928 0.6569 0 0.013 0.3995 p[30] 0.3992 0.1684 0.3923 0.6548 0 0.014 0.3994 p[31] 0.3994 0.1692 0.3927 0.6539 0 0.022 0.3991 p[32] 0.3995 0.1677 0.3923 0.6566 0 0.022 0.3991 p[33] 0.3997 0.1689 0.3925 0.6564 0 0.020 0.3992 p[34] 0.3997 0.1681 0.3931 0.6549 0 0.013 0.3995 p[35] 0.3992 0.1679 0.3927 0.655 0 0.013 0.3995 p[36] 0.3985 0.1684 0.3912 0.6535 0 0.020 0.3992 p[37] 0.3995 0.1697 0.3925 0.6538 0 0.023 0.3991 p[38] 0.3996 0.169 0.3924 0.6549 0 0.015 0.3994 p[39] 0.3999 0.1683 0.3932 0.6553 0 0.014 0.3995 p[40] 0.3995 0.1675 0.3924 0.6538 0 0.015 0.3994 p[41] 0.3992 0.1678 0.392 0.6555 0 0.016 0.3994 p[42] 0.3997 0.1678 0.393 0.6545 0 0.010 0.3996 p[43] 0.3999 0.1688 0.3925 0.656 0 0.006 0.3998 p[44] 0.3990 0.1684 0.3918 0.6541 0 0.015 0.3994 p[45] 0.3998 0.1679 0.3932 0.6535 0 0.014 0.3995 p[46] 0.3987 0.1677 0.3915 0.6539 0 0.020 0.3992 p[47] 0.3997 0.1687 0.3926 0.654 0 0.019 0.3992 p[48] 0.3980 0.1667 0.3913 0.6524 0 0.009 0.3996 p[49] 0.3995 0.1681 0.3924 0.6554 0 0.019 0.3992 103
8.3 pi Beta(4,6)pi 8.3.1 Beta( 4,6) 0.4 0.022 8-5 8-5 8-5 Beta 4,6 0.4 0.022 ( ) 1 Beta ( 120,180) 0.4 0.0008 2 Beta ( 7,3) 0.7 0.019 3 Beta ( 37,13) 0.74 0.004 104
1 Beta( 120,180) 0.4 0.0008 2 Beta( 7,3) 0.7 0.019 3 Beta( 37,13) 0.74 0.004 8-5 105
8.3.2 4-1 4 2 3 a µ b µ 8-6 8-6(1) 2 D/G a µ b µ 2.0E+1 8.7E+0 2.5E+1 1.4E+1 1.2E+1 1.2E+0 1.4E+1 3.3E+0 8-6(2) 3 D/G a µ b µ 2.0E+1 8.8E+0 2.5E+1 1.4E+1 1.2E+1 1.3E+0 1.4E+1 3.3E+0 8.3.3 8-7 8-8 8-9 106
8-7(1) 1 107
8-7(2) 1 108
8-7(3) D/G 1 109
8-7(4) 1 110
8-8(1) 2 111
8-8(2) 2 112
8-8(3) D/G 2 113
8-8(4) 2 114
8-9(1) 3 115
8-9(2) 3 116
8-9(3) D/G 3 117
8-9(4) 3 118
8.3.4 1 /EF 2 / 6 7 EF 3 2 // // a) 1 / / EF / EF / EF Y X Y=0 Y=3 X 8-6 8-7 D / 8-6 8-7 / 1) / EF 8-6 8-7 / EF 2) / EF 8-6 8-7 / EF Y=3 b) 2 D/G EF 6 / 119
/ 7 EF 8-8 X EF c) 3 1 2 / 2 3 3 2 d) / 120
8-6 X Y=3 8-7 X Y=0 121
9 9.1 MCMC 3 a) 1) Brooks Gelman Rubin WinBUGS 1 9-1 2) Geweke (e.g. 5%) b) 0 2 thinning over-relaxing 9-1 thinning BUGS µ µ0,µ1, µ2, µ3, µ4, µ5, µ6, µ7, µ8, µ9, µ10, µ11, µ12, µ13, µ14, µ15, µ16, µ17, µ18, thinning=5 thinning µ0, µ5, µ10, µ15, µ1, µ6, µ11, µ16, µ2, µ7, µ12, µ17, µ3, µ8, µ13, µ18, 5%95% etc. c) 5%95% etc. MC 5% 122
alpha0 chains 1:2 0.5 0.0-0.5-1.0-1.5 101 200 400 600 iteration (a) alpha0 chains 1:2 10.0 7.5 5.0 2.5 0.0-2.5 101 200 400 600 iteration (b) 9-1 [WINBUGS Manual] (a) 9-2 (b) 9.2 WinBUGS MCMC a) 7 D/G 5 Gelman and Rubin (1992) Brooks and Gelman (1998) 123
WinBUGS bgr-diag chain 5 1) 9-3(1)µσλ BGR pooledchain withinchain R R 1 1.2 chain R 1 1.5 1.0 0.5 0.0 2.0 1.5 1.0 0.5 0.0 mu chains 1:5 501 20000 40000 60000 sigma chains 1:5 iteration 501 20000 40000 60000 iteration 1.5 1.0 0.5 0.0 4.0 3.0 2.0 1.0 0.0 mu chains 1:5 501 2000 4000 sigma chains 1:5 iteration 501 2000 4000 iteration 1.0 0.5 lambda[50] chains 1:5 1.0 0.5 lambda[50] chains 1:5 0.0 501 20000 40000 60000 iteration 0.0 501 2000 4000 iteration 9-3(1) µσλ BGR 7 5 9-3(2) 124
1.0 0.5 0.0-0.5-1.0 1.0 0.5 0.0-0.5-1.0 mu 0 20 40 lambda[50] lag 1.0 0.5 0.0-0.5-1.0 sigma 0 20 40 lag 0 20 40 lag 9-3(2) 2) µσλ BGR 9-3(3) mu chains 1:5 1.5 1.0 0.5 0.0 501 20000 40000 60000 iteration sigma chains 1:5 1.5 1.0 0.5 0.0 501 20000 40000 60000 iteration lambda[50] chains 1:5 1.0 0.5 0.0 501 20000 40000 60000 iteration 2.0 1.5 1.0 0.5 0.0 2.0 1.0 0.0 2.0 1.5 1.0 0.5 0.0 mu chains 1:5 501 2000 4000 sigma chains 1:5 iteration 501 2000 4000 iteration lambda[50] chains 1:5 501 2000 4000 iteration 9-3(3) µσλ BGR 125
7 5 9-3(4) 1.0 0.5 0.0-0.5-1.0 mu 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 sigma 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 lambda[50] 0 20 40 lag 9-3(4) 3) D/G D/G µσλ(p) BGR 9-3(5) 126
mu chains 1:5 1.5 1.0 0.5 0.0 501 20000 40000 iteration sigma chains 1:5 1.5 1.0 0.5 0.0 501 20000 40000 iteration 2.0 1.0 0.0 2.0 1.5 1.0 0.5 0.0 mu chains 1:5 501 2000 4000 sigma chains 1:5 iteration 501 2000 4000 iteration 1.0 0.5 p[50] chains 1:5 1.0 0.5 p[50] chains 1:5 0.0 501 20000 40000 iteration 0.0 501 2000 4000 iteration 9-3(5) D/G µσλ BGR 5 5 9-3(6) D/G 1.0 0.5 0.0-0.5-1.0 mu 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 sigma 0 20 40 lag p[50] 1.0 0.5 0.0-0.5-1.0 0 20 40 lag 9-3(6) D/G 127
4) µσλ(p) BGR 9-3(7) 2.0 1.5 1.0 0.5 0.0 1.5 1.0 0.5 0.0 2.0 1.5 1.0 0.5 0.0 mu chains 1:5 501 20000 40000 sigma chains 1:5 iteration 501 20000 40000 p[50] chains 1:5 iteration 501 20000 40000 iteration 3.0 2.0 1.0 0.0 1.5 1.0 0.5 0.0 2.0 1.5 1.0 0.5 0.0 mu chains 1:5 501 2000 4000 sigma chains 1:5 iteration 501 2000 4000 p[50] chains 1:5 iteration 501 2000 4000 iteration 9-3(7) µσλ BGR 5 5 9-3(8) 128
1.0 0.5 0.0-0.5-1.0 mu 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 sigma 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 p[50] 0 20 40 lag 9-3(8) b) R 1 4 4 D/G 2 3 7 5 µσµσ 9.3 9.3.1 Thinning thinning thinning Thinning D/G 4 thinning1 thinning=10 µ σ a) µ(mu)σ(sigma) λ(lambda) thinning=1 thinning=1010 1 9-4(1) 129
1.0 0.5 0.0-0.5-1.0 1.0 0.5 0.0-0.5-1.0 mu 0 20 40 sigma lag 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 1.0 0.5 0.0-0.5-1.0 mu 0 20 40 lag sigma 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 lambda[50] 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 lambda[50] 0 20 40 lag thinning=1 thinning=10 9-4(1) thinning thinning=1 thinning=10 9-4(1) thinning 130
9-4(1) 131
b) µ(mu)σ(sigma)λ(lambda) thinning=1 thinning=10 9-4(2) 1.0 0.5 0.0-0.5-1.0 1.0 0.5 0.0-0.5-1.0 1.0 0.5 0.0-0.5-1.0 mu 0 20 40 sigma lag 0 20 40 lambda[50] lag 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 1.0 0.5 0.0-0.5-1.0 1.0 0.5 0.0-0.5-1.0 mu 0 20 40 lag sigma 0 20 40 lag lambda[50] 0 20 40 lag thinning=1 thinning=10 9-4(2) thinning thinning=1 thinning=10 9-4(2) thinning 132
9-4(2) 133
c) D/G D/G µ(mu)σ(sigma) thinning=1 thinning=10 9-4(3) 1.0 0.5 0.0-0.5-1.0 sigma 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 mu 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 sigma 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 mu 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 p[50] 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 p[50] 0 20 40 lag thinning=1 thinning=10 9-4(3) thinning D/G D/G thinning=1 thinning=10 9-4(3) thinning 134
9-4(3) D/G 135
d) µ(mu)σ(sigma) thinning=1 thinning=10 9-4(4) 1.0 0.5 0.0-0.5-1.0 mu 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 mu 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 sigma 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 sigma 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 p[50] 0 20 40 lag 1.0 0.5 0.0-0.5-1.0 p[50] 0 20 40 lag thinning=1 thinning=10 9-4(4) thinning thinning=1 thinning=10 9-4(4) thinning 136
9-4(4) 137
9.3.2 µσ thinning Thinning µσ thinning thinning=1 thinning=10 9-5 MC error thinning 9-5 µσ thinning 9.3.3 thinning 10 µσ (λ,p)thinning thinning thinning=10 10 2 1 138
10 21 FF 10.1 2 EF ) EF ) EF 1 EF 3 1 D/G a) =4.8E-08/hEF=60.0 =2.9E-06/hEF=4.3 b) 4.7E-05/dEF=51.7 D/G 1.5E-03EF=8.7 10.2 NUCIA 21 16 5 5 10-1 10-1 139
10.2 1 5 5 2 PSA RISKMAN 10-2 10-2 10-1 1 140
a) b) c) D/G d) 10-1 1 10-2 5 10-3 5 2 141
a) b) c) D/G d) 10-2 5 a) b) c) D/G d) 10-3 5 2 142
10.3 EF 10-2 5 EF EF EF=60. EF=51.7 40 EF EF 5 EF EF / 3 PSA 10 EF 1 10-15 10-2 5 EF 10-3 5 143
11 21 (CDF)BWRPSA PWR CDFBWRPWR 1982 ~1997 49 [2 ] 16 16 [3] EF 11.1 BWR PWR CDF 11-1 11-2 CDF 11-3 11-4 16 CDF 1 11.2 a) BWR 21 CDF 16 21 TQUV CDF 21 D/G 16 30 21 2 CDF 11-5 11-1 21 10,000 CDF 1 CDF 10-6 CDF b) PWR 21 CDF 16 21 TRIP CDF TRIP ATWS 21 16 144
TQUX TQUV LOCA LOCA TB TW TC 11-1 BWR 145
RECIRC INJ ISO SUP TRIP SPRAY HEAT ECCS ECCS 2 11-2 PWR 146
TQUX TQUV LOCA LOCA TB TW TC 11-3 BWR 147
RECIRC INJ ISO SUP TRIP SPRAY HEAT ECCS ECCS 2 11-4 PWR 148
10,000 1 11-5 BWR 149
11-1 BWR 10,000 1 150
10,000 1 11-6 BWR 151
12 PSA PSA A.3 A.4 12.1 PSA NUCIA PSA 20 function failure, FFFF PSA FF NUCIA PSA PSA E FF PSAFF JEAC4209-2007 FF FF 2 CDF 1 PSA FF PSA 12.2 FF PSA 152
a), PSA b) D/G c) 0.10.3 0.1 0.9 = 153
NUCIA PSA 154
13 NUCIA PSA PSA PSA 155
[1] http://nucia.jp/ [2] (1982 1997 16 49 ) 13 2, P00001,() [3] PSA 9 3, [4] C.L.Atwood, et al., Handbook of Parameter Est imation for Probabil istic Risk Assessment, NUREG/CR-6823, USNRC, September 2003. [5] http://www.mrc-b su.cam.ac.uk/bugs/ [6] Meng Yue, Tsong-Lun Chu, Estimation offailure Rates of Digital Components Using a Hierarchical Bayesian Method, PSAM-8th, May 2006. [7] [8] S.A.Eide, et al, Industry-Average PerformancEFor Components and Initiating Events at U.S. Commercial Nuclear Power Plants, NUREG/CR-6928, US NRC, February 2007. 156
A PSA A.1 A.2 A.3 3 A.4 PSA 157
A.1 20 9 24 1. PSA PSA PSA 18 PSA PSA PSA 17 19 2. PSA 19 PSA PSA PSA PSA 3. a. NUREG/CR-6823, Handbook of Parameter Estimation for PRA,NRC, 158
2002 ASME, St andard for PRA for Nuclear Power Plant Applications, ASME RA-Sb-2005 b. PSA 1PSA PSA 4. ( ) 1-2 PSA PSA 20 5 5. 4 PSA H20.10 H20.11 H20.12 CDF 159
A.2 160 () ( ) FBR GE ) 2 2
A.3 3 PSA 2008 9 24 16:2518:15 ( ) ()JAEA)(), NELJAEA,TEPSYS, GE (JNES) 17 MHI()JAEA CTINELJAEA 1-1 PSA 1-2 PSA 1-3 PSA 1-4 C() 1-5 E() (1) (2) 1-1 1-2 161
1-3 (3) C() 1-4 10 PSA P13SC10-2-4 Xi λi Beta(4,6) Pi SPAR EF SPAR (4) E() 1-5 10 PSA P13SC10-2-5 (5) 1-4,1-5 162
2 PSA 2008 11 7 13:3016:30 () ()JAEA)(), NELJAEA,TEPSYS, GE MHI 17 ()JAEA CTIJAEATEPSYS 2-1 PSA 2-2 PSA 2-3 2-4-1 µ 2-4-2 σ 2-5 2-6 PSA 2-7 2-8 2-9 C() (1) (2) 163
(3) 2-3 pd pd (4) µ 2-4-1µ µ µ µ 0.5 1 µ 0.5 µ 0.5 µ (5) σ 2-4-2σ σ σ 2-3 Y=0 X 5 Y=0 X 0.02-164
1/10001000 2-3 (6) 2-5 (7) PSA 2-6 PSA PSA PSA FF (8) 2-8 / 2. 2-8 (9) 2-7 165
EF EF CDF BWR CDF (10) 1 166
PSA 2008 12 19 13:3016:30 ( ) ()JAEA)(), NEL)TEPSYS, () GE ()MHI 16 ()JAEAJAEA CTIJAEA 3-1 PSA () 3-2 3-3 pd () 3-4 3-5 µ 3-6 3-7 3-8 (1) (2) (3) 3-2 167
14 19 FF (4) pd () 3-3 pd () pd (5) 3-4 (6) µ 3-5 µ µ µ EPIX µ 0.5 168
(7) 3-6 PWR (8) 3-7 Winbugs DG 30 30 (9) 3-8 FF 169
FF WEB (10) 170
A.4 PSA - ), - 0 µ,σ µ, σ 0 SPAR NUREG/CR-6928 0 EF SPAR L07005, 20 6 NUREG/CR-6928 171
8.1 Y i X i p i λ i 2-3 X i Y i X i Y i =0 X i 5 Y i =0 X i 1 2-3 X i λ i T i λ i =1/1000T i =1000Y i =0 X i p i ~Beta(4,6) 0.10.3 = 3-3 8.1 NUCIA 1 9 PSA 172
X Y NUCIA X Y, PSA PSA 3-4 8.2 173
µ 3-5 7.4.5 0 µ 0.5 b) Beta(4,6)[ 0.4] µ 0.5 3-5 µ µ µ 0.5 0.5 µ 7.4.5 0 µ a) µ 0.5 µ PSA FF FF CDF 1 EF EF EF PSA EF 5.2 D/G 2 3-6 30 CDF 174
CDF 3-6 11 BWR 3-6 11 CDF EDG EDG 3-7 D/G 24 5.2 D/G 175
FF 3-8 PSA PSA 176
B B.1 NUCIA NUCIA PSA NUCIA P SA NUCIA NUCIA NUCIA PSA MPFF FF NUCIA NUCIA NUCIA B.2 B.2.1 PSA PSA 5. 3.4 a) 6.2 NUREG/CR-6823 1 1 177
B.2.2 ASME PRA ASMEPRAPSA ASME HLR-DA-B Grouping components into a homogeneous population for parameter estimation shall consider both the design, environmental, and service condition of the components in the as-built and as-operated plant. DA-B2 DO NOT INCLUDE outliers in the definition of a group (e.g. do not group valves that are never tested and unlikely to be operated with those that are tested or otherwise manipulated frequently) DA-B2 Category When warranted by sufficient data, USE appropriate hypothesis tests to ensure that data from grouped components are from compatible population. B.2.3 NRC PSA SPAR NUREG/CR-6928 NUREG/CR-6928Industry-Average Performance for Components and Initiating Events at U.S. Commercial Nuclear Power Plants U.S. NRC February 2007 NUREG/CR-6928 PSA EPIX 95% EF 178
NUREG/CR-6928 a) NUCIA NUCIA Positive Displacement Pump Emergency Diesel Generator Combustion Turbine Generator Hydro Turbine Generator Cooling Tower Fan Circuit Breaker b) NUREG/CR-6928 Service Water System Non-Service Water System d) NUREG/CR-6928 (standby)/(running/alternating) 1 1 2 BWR RCIC HPCI HPCS PSA FT 179
B.3 NUCIA NUCIA PSA B-1 B.2 PSA NUCIA B.3.1 a) PSA NUREG/CR-6928 BWR Positive Displacement Pump NUCIA NUCIA NUCIA MG NUREG/CR-6928 b) NUCIA B-2 NUCIA B-2 B-1 PSA c) NUCIA 180
4 PSA B.3.2 B.3.1 a) b) 1) NUCIA 2) PSA 3) c) 1) 4 2) 3) 181
B-1 NUCIA PSA 182
B-2(1) NUCIA BWR 183
B-2(2) NUCIA PWR 184
C C-1 4 (µ,σ) (WinBUGS dflat())µ-σ µ-σ 7.37.4 (µ,σ) C-1 0 C-1 0 / C-1 0 / =0 (µ,σ) MCMC 185
( 0) (=0) DG ( 0) (=0) C-1 186
D Y X p Y ~ Bin f ( Y; p, X ) ( p, X ) Y X Y = X CYp (1 p) (D.1) p Beta ( 4,6) p=0.5 Y 3 X g( X p, Y ) f ( Y p, X ) g( X ) (D.2) p=0.5y=3 g( X p = 0.5, Y = 3) X 3 X 3 C 30.5 (1 0.5) g( X ) (D.3) g(x) X D-1 Y 3 p 0.10.9 X D-2 D-2 D-1 p X MCMC p p MCMCD-2 Beta p i ( 4,6) p0.1~0.9 PY=3 (i=1,2,,9)p 1 =0.1p 2 =0.2p 3 =0.3 p 9 =0.9 P i [X] i D-3 D-3 Beta( 4,6) D-2 p=0.3~0.6 (p 3 ~p 6 ) D-3 D-4 187
P i [ X ] i (D.4) D-4 Beta( 4,6) Y=3 X 1 Beta( 120,180) p 0.4 1 D-4 X D-2 p=0.4 1 X D-5 D-5 Y=0 X D-6 188
D-1 p=0.5y=3 X D-2 p=0.10.9y=3 X 189
D-3 p i =0.10.9Y=3 P [ X] i i D-4 Beta(4,6) X Y=3 190
D-5 X Y=3 D-6 X Y=0 191
E PSA E.1 2 PSA PSA E.2 1 PSA E.1 PSA E.2 PSA 192
E.1 PSA 193
194
195
196
197
198
199
200
E.2 PSA 201
F PSA /MCMC PSA PSA PSA 2 2-1 1/2 5% 50%95%(95%/5%)P P 7 λ(f.1) 2 1 (ln λ µ ) f ( λ; µ, σ ) = exp ( > 0) 2 2 2 λ (F.1) πσλ σ µlnλ σlnλ µσµσ ( 50% ) = exp( µ ) (F.2) 2 σ ( ) = exp µ + 2 (F.3) (95% ) (50% ) (95% ) EF ( error factor) = = = = exp(1.645σ ) (50% ) (5% ) (5% ) (F.4) 202
TP*PT MCMC (F.4) (95% ) (50% ) = = (50% ) (5% ) (95% ) (5% ) * TP PTF.1 2 EFBUB=(95%)/(50%)=42.1 EFBLB=(50%)/(5%)=87.4 2-1 1/2 EFBUBEFBLB(EFBUBEFBLB)P P F.1 MCMC 2-1 9 [h] 9.4E+0 8 [] [1/h] 5% [1/h] 50% [1/h] 95% [1/h] EFBUB 95 % 95 % 5% 50% EFBLB 50% 5% 23.3 5.2E-08 2.8E-11 2.4E-09 1.0E-07 60.7 42.1 87.4 MCMC 50% 50%EFBUB 1/2 ((95%)/(5%))P P EFBLB 1/2 ((95%)/(5%))P PEFBUB= (95%)/(50%) F.2 1/2 EF=((95%)/(5%))P P EFBUB= (95%)/(50%) 203
F.2 5% 50% 95% EF µ σ 5.21E-08 2.78E-11 2.43E-09 1.02E-07 - - - EF= (95%/5%) 5.48E-08 4.01E-11 2.43E-09 1.48E-07 60.7-19.83 2.50 EF=95%/50% 3.22E-08 5.78E-11 2.43E-09 1.02E-07 42.1-19.83 2.27 EF= (95%/5%) 5.21E-08 3.82E-11 2.31E-09 1.40E-07 60.7-19.88 2.50 EF=95%/50% 5.21E-08 9.34E-11 3.93E-09 1.65E-07 42.1-19.35 2.27 204
故障件数の不確実さを考慮した国内一般機器故障率の推定 以下は, 報告書公開 (2009 年 5 月末 ) 以降に判明した誤記部分の訂正箇所です 報告書内では修正済みです 正誤表 頁箇所誤正修正日 160 A.2 委員構成戸塚昌義戸塚真義 2009/6/10 6 国内一般機器故 44 障率の計算 附録 A 11 行目 附録 B 2009/6/10 ( その他附録 B 乱丁修正 ) 16 式 (3.7) f ( pd ) = σ 1 2 π exp 1 2 logit( pd ) σ µ 2 2 1 1 logit( pd ) µ f ( pd ) = exp 2009/8/11 σ 2π pd 2 ( 1 pd ) σ i i i i i i