202,., IEC1123 (1991), GB8051 (2002) [4, 5],., IEC1123,, : 1) IEC1123 N t ( ). P 0 = , P 1 = , (α, β) = (0.05, 0.05), N t = [4]. [6

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1 Chinese Journal of Applied Probability and Statistics Vol.29 No.2 Apr (,, ) IEC1123,,,., IEC1123 (SMT),,,. :,,, IEC1123,. : O P.,,,, [1 5]. P, : H 0 : P = P 0 vs H 1 : P = P 1 (P 0 > P 1 ). (1.1), Wald (1947) (SPRT), [1] L 1 : S = h 1 + sn (h 2 < h 1 ), (1.2) L 2 : S = h 2 + sn, h 1, h 2, s, n, X i i, X i = 1, X i = 0, S n = i=n X i, n = 1, 2, 3,... n. i=1 SPRT : S n h 2 + sn, H 0, S n h 1 + sn, H 0, h 2 + sn < S n < h 1 + sn,. SPRT α, β (, (α, β) ), P 0 P 1. SPRT, [6, 7], ( J [2011]2094 ) ,

1), Wald (1947) (SPRT), [1] L 1 : S = h 1 + sn (h 2 < h 1 ), (1.

2 202,., IEC1123 (1991), GB8051 (2002) [4, 5],., IEC1123,, : 1) IEC1123 N t ( ). P 0 = , P 1 = , (α, β) = (0.05, 0.05), N t = [4]. [6 8], IEC1123 N t. 2) IEC1123 [9, 10]. (α, β) N t, IEC1123,,,. 3) IEC1123, α, β (α, β) [6 8],, (α, β). 4) IEC1123 α β, α β,, IEC1123 P 0, P 1, (α, β) 160, P 0, P 1, (α, β). IEC1123,,, (1.1), IEC [1 10], P : 2.1 L 1, L 2,..., L Nt U 1, U 2,..., U Nt, 0 L i+1 L i 1, 0 U i+1 U i 1, i = 1, 2,..., N t 1; L i + 2 U i, i = 1, 2,..., N t 1; (2.1) L Nt + 1 = U Nt. M = inf{n S n U n S n L n, n = 1, 2,..., N t }, S M L M, H 0, S M U M, H 0, L n < S n < U n (n = 1, 2,..., N t 1),., N t, U Nt ( N t, H 0 ), T (N t, U Nt ) = (U 1, U 2,..., U Nt ; L 1, L 2,..., L Nt ) (2.2) N t, U Nt (TST), (U 1, U 2,..., U Nt ), (L 1, L 2,..., L Nt ).

.., L Nt U 1, U 2,..., U Nt, 0 L i+1 L i 1, 0 U i+1 U i 1, i = 1, 2,..., N t 1; L i + 2 U i, i = 1, 2,..., N t 1; (2.1) L Nt + 1 = U Nt. M = inf{n S n U n S n L n, n = 1, 2,.

3 : 203 D n = {S n L n, L i < S i < U i, i = 1, 2,..., n 1}, Dn = {S n U n, L i < S i < U i, i = 1, 2,..., n 1}, n = 1, 2,... N t, (1.1) T α, β α (T ) = n=nt P{D n P 0, T }; β (T ) = n=nt P{ D n P 1, T }. T E(M P, T ) E(M P 0, T ) = n=nt n(p{d n P 0, T } + P{ D n P 0, T }); 2.2 E(M P 1, T ) = n=nt n(p{d n P 1, T } + P{ D n P 1, T }). (2.3) (2.4) (α, β) T, (1.1) α (T ) α, β (T ) β, T (1.1) (α, β).,, [11],, (α, β) T (N t, U Nt ),. 2.3 T LA (N t, U Nt ) (α, β), (α, β) T (N t, U Nt ), E(M P 0, T LA ) E(M P 0, T ); E(M P 1, T LA ) E(M P 1, T ), (2.5) T LA (N t, U Nt ) (1.1) N t, U Nt, (α, β) (LOANTST). 2.4 T A N t, (α, β), N t, (α, β) T, E(M P 0, T A ) E(M P 0, T ); E(M P 1, T A ) E(M P 1, T ), (2.6) T A (1.1) N t, (α, β) (OANTST) T LA T A : E(M P 0, T A ) = Min {E(M P 0, T LA (N t, U Nt )}; 0 U Nt N t E(M P 1, T A ) = Min {E(M P 1, T LA (N t, U Nt )}. 0 U Nt N t (2.7)

2 E(M P 1, T ) = n=nt n(p{d n P 1, T } + P{ D n P 1, T }). (2.3) (2.4) (α, β) T, (1.1) α (T ) α, β (T ) β, T (1.1) (α, β).,, [11],, (α, β) T (N t, U Nt ),. 2.

4 204 (1.1) C(N t, U Nt ) (N t, S Nt U Nt, H 0,, H 0 ), N t 1 U Nt, N t, H 0, N t 2, N t 3,..., U Nt ; H 0., C(N t, U Nt ),. 2.5 (1.1) C(N t, U Nt ), T E U NtUNt = 1 U NtUNt U NtUNt +1 U NtNt (2.8) Nt UNt 0 Nt UNt +1 1 Nt UNt +2 (U Nt 1) Nt C(N t, U Nt ) (ETST),, 1 Nt UNt N t U Nt 1 H 0, N t U Nt 1,, H 0, 1 1, 1 2,..., 1 Nt UNt 2 1, 3 2,..., U NtUNt 1. 0 Nt UNt +1 N t U Nt + 1 0, H 0,, 0 Nt UNt +1, 1 Nt UNt +2,..., (U Nt 1) Nt U NtUNt,..., U NtNt. 1 C(15, 13) T E T E =. (2.9) ,. 2.1 (1.1) C(N t, U Nt ), P{S Nt <U Nt P 0 }=α, P{S Nt U Nt P 1 } = β, T E C(N t, U Nt ), n=n t n=n t P{D n P 0, T E } = α ; P{ D n P 1, T E } = β, P (0, 1), E(M T E, P ) N t. : T E P (0, 1), P{D n P, T E } = 0, n = 1, 2,..., N t U Nt ; P{ D n P, T E } = 0, n = 1, 2,..., U Nt 1; (2.10) D n {S Nt < U Nt }, n = N t U Nt + 1, N t U Nt + 2,..., N t ; D n {S Nt U Nt }, n = U Nt, U Nt + 1,..., N t.

0 Nt UNt +1 N t U Nt + 1 0, H 0,, 0 Nt UNt +1, 1 Nt UNt +2,..., (U Nt 1) Nt U NtUNt,..., U NtNt. 1 C(15, 13) T E 2 3 4 5 6 7 8 9 10 11 12 13 13 13 13 T E =. (2.9) 1 1 0 1 2 3 4 5 6 7 8 9 10 11 12,. 2.1 (1.

5 : 205 {S Nt < U Nt } = n=nt D n, {S Nt U Nt } = n=nt (i j), n=n t P{D n P 0, T E } = P{S Nt < U Nt P 0 } = α ; n=n t P{ D n P 1, T E } = P{S Nt U Nt P 1 } = β. D n D i D j = φ, Di D j = φ P (0, 1), P{D n P, T E } 0, P{ D n P, T E } 0 n=nt (P{D n P, T E } + P{ D n P, T E }) = 1, E(M P, T E ) = n=nt n(p{d n P, T E } + P{ D n P, T E }) N t. 2.1 T E (N t, U Nt ) C(N t, U Nt ),,. 2.2 (α 1, β 1 ), (α 2, β 2 ). T 1 (N t, U Nt ) T 2 (N t, U Nt ) i) i 0 {1, 2,..., N t 1}, L i0 (T 1 ) L i0 (T 2 ), i i 0, L i (T 1 ) = L i (T 2 ); j {1, 2,..., N t 1}, U j (T 1 ) = U j (T 2 ), α 1 α 2, β 1 β 2, E(M P 0, T 1 ) E(M P 0, T 2 ); E(M P 1, T 1 ) E(M P 1, T 2 ). (2.11) ii) j 0 {1, 2,..., N t 1}, U j0 (T 1 ) U j0 (T 2 ), i j 0, U j (T 1 ) = U j (T 2 ); i {1, 2,..., N t 1}, L i (T 1 ) = L i (T 2 ), α 1 α 2, β 1 β 2, E(M P 0, T 1 ) E(M P 0, T 2 ); E(M P 1, T 1 ) E(M P 1, T 2 ). : i), ii). γ 1 = n=nt P{ D n D i0 = L i0 (T 1 ), P 0, T 2 },, γ 1 0, α 1 α 2. n=i 0 +1 α 1 = n=nt P{D n P 0, T 1 } = α 2 + γ 1 α 2, (2.12) E(M P 0, T 1 ) = E(M P 0, T 2 ) n=nt n=i P{ D n D i0 = L i0 (T 1 ), P 0, T 2 }) E(M P 0, T 2 ), (n i 0 )(P{D n D i0 = L i0 (T 1 ), P 0, T 2 }

1 T E (N t, U Nt ) C(N t, U Nt ),,. 2.2 (α 1, β 1 ), (α 2, β 2 ). T 1 (N t, U Nt ) T 2 (N t, U Nt ) i) i 0 {1, 2,..., N t 1}, L i0 (T 1 ) L i0 (T 2 ), i i 0, L i (T 1 ) = L i (T 2 ); j {1, 2,.

6 206 E(M P 0, T 1 ) E(M P 0, T 2 )., γ 2 = n=nt P{ D n D i0 = L i0 (T 1 ), P 1, T 2 }, γ 2 0,, n=i 0 +1 β 1 = n=nt P{ D n P 1, T 1 } = β 2 γ 2 β 2, β 1 β 2. E(M P 1, T 1 ) = E(M P 1, T 2 ) n=nt n=i P{ D n D i0 = L i0 (T 1 ), P 1, T 2 }) E(M P 1, T 2 ), E(M P 1, T 1 ) E(M P 1, T 2 ). (n i 0 )(P{D n D i0 = L i0 (T 1 ), P 1, T 2 } 2.2,,, α, β ;,.,. 2.3 (α, β) LOANTST. T LA (1.1) N t, U Nt, i) T LA T, α (T ) > α. ii) T LA T, β (T ) > β. : ( ) i) α (T ) α,, T T LA, 2.2, α (T ) α, β (T ) β, E(M P 0, T ) E(M P 0, T LA ); E(M P 1, T ) E(M P 1, T LA ). LOANTST, T LA (1.1) N t, α, β LOANTST,. ii). 2.3 (α, β) LOANTST T LA.,, , (1.1) N t, U Nt LO- ANTST T LA, C(N t, U Nt ) T E,

(n i 0 )(P{D n D i0 = L i0 (T 1 ), P 1, T 2 } 2.2,,, α, β ;,.,. 2.3 (α, β) LOANTST. T LA (1.1) N t, U Nt, i) T LA T, α (T ) > α. ii) T LA T, β (T ) > β.

7 : 207.,,., C(N t, U Nt ) T E T 0 : U1 U 2 U 3 U Nt 1 U Nt T 0 =. (3.1) L 1 L 2 L 3 L Nt 1 L Nt, T 0 i=nt (U i L i + 1), 2N t, T 0 i=1. T 1, : i) U i, T 1,Ui, U1 U 2 U i 1 U i 1 U i+1 U Nt T 1,Ui =. (3.2) L 1 L 2 L i 1 L i L i+1 L Nt ii) L i, T 1,Li, U1 U 2 U i 1 U i U i+1 U Nt T 1,Li =. (3.3) L 1 L 2 L i 1 L i + 1 L i+1 L Nt U i L i? T 0 (3.2) (3.3) T 1 2.1,. 1) U i L i 2, i = 1, 2,..., N t, U i L i, T 1 N t. 2) T 0 L i, L i = 1, L i = 1 L i+1 = 0; T 0 U i, U i > i, U i > i U i+1 = i ) T 0 L i, L i = L i+1, L i ; T 0 U i, U i = U i 1, U i. 3.1 T 0., {L i, i Θ 0 } {U i, i Θ 1 }, Θ 0, Θ 1. (2.3), (2.4), T 0 T 1 α (T 0 ) = n=nt P{D n P 0, T 0 }; β (T 0 ) = n=nt P{ D n P 1, T 0 }, α (T 1 ) = n=nt P{D n P 0, T 1 }; β (T 1 ) = n=nt P{ D n P 1, T 1 }, (3.4) (3.5)

T 0 (3.2) (3.3) T 1 2.1,. 1) U i L i 2, i = 1, 2,..., N t, U i L i, T 1 N t. 2) T 0 L i, L i = 1, L i = 1 L i+1 = 0; T 0 U i, U i > i, U i > i U i+1 = i + 1.

8 208 E(M P 0, T 0 ) = n=nt n(p{d n P 0, T 0 } + P{ D n P 0, T 0 }); E(M P 1, T 0 ) = n=nt n(p{d n P 1, T 0 } + P{ D n P 1, T 0 }), E(M P 0, T 1 ) = n=nt n(p{d n P 0, T 1 } + P{ D n P 0, T 1 }); E(M P 1, T 1 ) = n=nt n(p{d n P 1, T 1 } + P{ D n P 1, T 1 }). (3.6) (3.7) T 0,., T 0 T 1 α (T 1 ) α (T 0 ), β (T 1 ) β (T 0 ), P 0, P 1 E(M P 0, T 0 ) E(M P 0, T 1 ), E(M P 1, T 0 ) E(M P 1, T 1 ), T 0 α (T 0 ), β (T 0 ) (α, β). T 0, g(l i ) = [E(M P 0, T 0 ) E(M P 0, T 1,Li )] [α α (T 0 )] [α (T 1,Li ) α (T 0 )] [β (T 0 ) β, (T 1,Li )] i Θ 0, (3.8) g(u j ) = [E(M P 1, T 0 ) E(M P 1, T 1,Uj )] [β β (T 0 )] [β (T 1,Uj ) β (T 0 )] [α (T 0 ) α, (T 1,Uj )] j Θ 1. (3.9), W 1 : i) α (T 0 ) < α β (T 0 ) β, W 1, g(w 1 ) = Max{g(L i ), i Θ 0 }. (3.10) ii) α (T 0 ) α β (T 0 ) < β, W 1, g(w 1 ) = Max{g(U j ), j Θ 1 }. (3.11) iii) α (T 0 ) α β (T 0 ) β, W 1 g(w 1 ) = Max{Max{g(L i ), i Θ 0 }, Max{g(U j ), j Θ 1 }}. (3.12) W 1, T 0 W 1 T 1. T 0, T 1 W 2, T 1 W 2 T 3,,,, T 0, T 1,..., T n,.... m = sup{n β (T n ) < β and α (T n ) < α}. (3.13) , T m (1.1) N t, U Nt, (α, β) LOANTST T LA. N t OANTST T A, (2.7), U Nt 0 N t, LOANTST T LA,, T A.

, T 0 T 1 α (T 1 ) α (T 0 ), β (T 1 ) β (T 0 ), P 0, P 1 E(M P 0, T 0 ) E(M P 0, T 1 ), E(M P 1, T 0 ) E(M P 1, T 1 ), T 0 α (T 0 ), β (T 0 ) (α, β).

9 : IEC1123 SMT IEC1123, [6] (SMT) IEC1123,,, IEC1123 SMT. 2, (α, β) = (0.2, 0.2), : H 0 : P 0 = 0.9, H 1 : P 1 = 0.7. (4.1) N t = 15, U Nt = 13, C(15, 13) α = < 0.2, β = < 0.2., C(15, 13) 15. T E C(15, 13) ETST, 3.1, T E 1 (2.9)., T E α = , β = E(M 0.9, T E ) = < 15; (4.2) E(M 0.7, T E ) = < 15. C(15, 13), ETST T E,. (4.1) N t = 15, U Nt = 13, (0.2, 0.2) LOANTST T LA, (2.9) T E, LO- ANTST T LA T LA =. (4.3) , T LA α = , β = , E(M 0.9, T LA ) = ; (4.4) E(M 0.7, T LA ) = (4.2) (4.4),, T LA T E,. N t = 15, U Nt = 0, 1, 2,..., 15 LOANTST,, (4.3) T LA N t = 15, (0.2, 0.2) OANTST T A. (4.1), IEC1123 N t = 15, U Nt = T IEC =. (4.5)

2) LOANTST T LA, (2.9) T E, LO- ANTST T LA 2 3 4 5 6 6 7 8 9 10 10 11 12 13 13 T LA =. (4.3) 1 0 1 2 3 4 5 5 6 7 8 9 10 11 12, T LA α = 0.1983, β = 0.1894, E(M 0.9, T LA ) = 7.7656; (4.4) E(M 0.

10 210 T IEC α = , β = , E(M 0.9, T IEC ) = ; E(M 0.7, T IEC ) = (4.6) (4.4) (4.6),, IEC1123. IEC1123 SMT, [6 8]. 3 (α, β) = (0.2, 0.2), : H 0 : P 0 = 0.9, H 1 : P 1 = 0.8. (4.7) IEC1123 N t = 49, U Nt = 43 T IEC LOANTST T LA 1: 1 IEC1123 α β E(M 0.9) E(M 0.8) IEC1123 T IEC T LA , (α, β) = (0.2, 0.2), T LA T IEC. U Nt, N t = 49 OANTST T A U Nt = 43 LOANTST T LA. N t U Nt, (4.7) N t = 37, U Nt = 32., α = < 0.2, β = < 0.2, E(M 0.9, T A ) = ; (4.8) E(M 0.8, T A ) = N t = 37 [6] SMT 37,, [6] N t = 38, U Nt = 33 SMT α = < 0.2, β = > 0.2, β = > 0.2,, SMT (4.7) (0.2, 0.2). [8], SMT N t = 39, U Nt = 34,,, (4.7) SMT N t = 39 N t = 37., N t = 39, U Nt = 34 α, β, 2.

7) N t = 37, U Nt = 32., α = 0.1993 < 0.2, β = 0.1999 < 0.2, E(M 0.9, T A ) = 29.5141; (4.8) E(M 0.8, T A ) = 21.3090. N t = 37 [6] SMT 37,, [6] N t = 38, U Nt = 33 SMT α = 0.1749 < 0.2, β = 0.2039 > 0.

11 : (SMT) α β E(M 0.9) E(M 0.8) T SMT T LA ,, SMT,. IEC1123, IEC , 1, 1, 4 IEC1123, IEC1123., IEC1123 SMT, N t,,. 3, α, β,, 1 IEC LOANTST, OANTST,,, 2, 3 1, IEC1123 SMT. 1 IEC1123 IEC1123 T LA P 0 P 1 α = β N t U Nt α β E(M P 0 ) E(M P 1 ) α β E(M P 0 ) E(M P 1 ) * * * * *.

7360 0.2576 0.1984 2.0880 1.7360 2 0.8 0.4 0.2 5 4 0.1962 0.1907 2.7808 2.7488 0.1962 0.1907 2.7808 2.7488 3 0.8 0.4 0.1 12 8 0.0820 0.0828 6.3538 5.8481 0.0973 0.0907 5.8768 5.2512 4 0.8 0.4 0.05 17 11 0.

12 212 [1] Wald, A., Sequential Analysis, Wiley and Sons, New York, [2],,,,, 30(3)(2008), [3],,,, 1(2001), [4] IEC1123, Reliability Testing-Compliance Test Plans for Success Ratio, 1991, [5] GB/T , [6],,,, ( ), 125(2006), [7],,,,, 23(1)(2007), [8],,,, 30(1)(2010), [9],,,,, 34(3)(2010), [10] Hu, S.G., Optimum truncated sequential test of binomial distribution, 2011 ICRMS, Guiyang, China, Vol.I: [11],, :, Truncated Sequential Test for a Proportion and it s Sample Space Ordering Method Hu Sigui (College of Basic Medical Science, Guiyang Medical University, Guiyang, ) This paper proposes a new sampling plan, the sample space ordering method, to compute the optimum truncated sequential test in order to overcome the disadvantages of the widely use sequential sampling methods that IEC1123 has presented. The main ideal of this new method is to establish an order at the truncated sequential sample space, and optimize point by point to arrive the optimal truncated sequential test. The paper presents in detail how to realize the new plan, and shows that this new plan has most powerful to control the sample number and least average sample number comparing with the methods which IEC1123 and SMT have proposed. Keywords: Success/failure test, sequential analysis, truncated sequential test, IEC1123, sample space ordering method. AMS Subject Classification: 90B25.

[9],,,,, 34(3)(2010), 287 290. [10] Hu, S.G., Optimum truncated sequential test of binomial distribution, 2011 ICRMS, Guiyang, China, Vol.I: 293 298. [11],, :, 2005.

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