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1、K26VK3?L?Vol. 26 No. 3 2003?7FACTA MATHEMATICAE APPLICATAE SINICAJuly, 2003?qxyq?v?y?(?Oe?N?200237)?(?d?N?200234)?oWWeibullk?Fw?KS(ti,ni),?S“?X?AE?”P?s?DAp?KF?P?J?e?w?Yw?KSF?h?1?FF?z?p?swpiFY?Bayes?h?k?K?fbDApmT?KF?F?t?J?p?R?th?k?w?KS?X?AE?Y?Bayes?1?K?Z?A?CxcCkJR?KN?CkA?C?“v?JR” (?K?NECk?z?).Sf?GE?M
2、?nE?UZt?“v?JR”E?EbEX?Y?Kt?Z?s?v?JR?U?Vv?JRI?Z?MEbEU?dx?W? “v?JR”s?E?Za?K?Z?A?N?ED?TEj?JF(t,), ilS?J?Kk?N?CkA?Ck?j?iti, i = 1,k (t1 0.?v?JR?“?W?D?”O?r?C?o?JE?O?IZ?d?v?Xv?JRE?g?1?EE?y?opi= P (T 0.(ti,ni), i = 1,kiv?JR?3.1?HVv?JREZa?Yu?k?N?CkA?oFA?E?j?Ck?ti?nivFA?FA?E?W?D?imT(ti),L ti+mT(ti)?iti?FA?E?f
3、D?W?ik?D?TE?(?J).?YuS1vFA?J?v?ED? T1:S1.?j?E?Oe? E(T) =k?i=1ni S1?t i+ mT(ti)?,E(T1:S1) =k?i=1ni S1?t i+ mT1:S1(ti)?,(3-3)?S1=k?i=1ni, mT(ti)i?TKti?E?W?D?mT1:S1(ti)im?a?nT1:S1KtiE?W?D?J2D?(3-3)?i? ? 1 +1 ? =k?i=1ni S1? ti+ exp?ti? ? ? 1 +1 ? (1/) Iyi(1/)? ,? ? 1 +1 ? =k?i=1ni S1? ti+ exp?ti? ? ? ? 1
4、 +1 ? ?(1/) Iyi?(1/)? ,(3-4)?= /(n1 ), yi?= (ti/). (),I ()?(3-4)?C? ,?ni,E?(3-4)?h?mI?n?Y = F(T) =1exp?T?,LY U(0,1).?E(ti,ni)?iU(0,1)?Ev?JR(i,ni).Y,Y1:S1Ki?E?W?D?j?imY(i),mY1:S1(i),cP?(3-3)? E(Y ) =k?i=1ni S1? i+ mY(i)?,E(Y1:S1) =k?i=1ni S1? i+ mY1:S1(i)?,(3-5)536?K?26V?Q?Y U(0,1),L?mY(i) =1 22i 1 i
5、,mY1:S1(i) =1 S1+ 1S1+1i (1 i)S1.J?R?H?d?(3-5)?i? 1 2=k?i=1ni S1? i+1 22i 1 i? ,1 S1+ 1=k?i=1ni S1? i+1 S1+ 1S1+1i (1 i)S1? ,(3-6)?i= 1 exp?t i ?.?(3-6)?JWea?G?,?n?,? .u?,? i, E?O?KYJj?m?JYJj?eaC?E?G?U?k?E?I?r?H?u?Krd?nN?Ly?Z?n?E?,? ,?C?G?a?dx?Xx?nZKm?v?iV?LnoO?3.2 piuBayes?C?rvpiEBayes?N?j?h?b?Yu?X
6、?BayeseaEr?u?X?Bayesea?rvp1= P (T 1,?j?iWHj?1,2(a) = U(0,1),1,2(b) = U(1,c),(3-8)?ci?J?1EXx?Sc?K5 9U?Ai?d?(3-7), (3-8)?Cp1E?j?i?1(p1) =?10?c11,1(p1|a,b)1,2(a)1,2(b)dbda=2 c 1?10?c11 B(a,b)?p1 0.5?a1? 1 p1 0.5?b1 dbda.(3-9)?I?K?T(0,t1)?nvFA?rv?P?Ji?L(p1,r) =?n r? p1r(1 p1)nr.3?i?l?h?k?w?KSFb?k?537J?j
7、?(3-9),?C?p1E?j?i?(p1|n,r) =L(p1,r)1(p1)?0.50L(p1,r)1(p1)dp1.(3-10)K?eT?p1E?j?E?f?i?Bayes?i? p1,L? p1=?0.50p1L(p1,r)1(p1)dp1?0.50L(p1,r)1(p1)dp1=?0.50p1r+1(1 p1)nr1(p1)dp1?0.50p1r(1 p1)nr1(p1)dp1.(3-11)io?H?j?n?Ic(i) =?10?c1B(a,b + i) B(a,b)dbda,A(n,p) =n?i=0?n i? (0.5)ni(0.5 p)iIc(i).L?0.50p1r(1 p1
8、)nr1(p1)dp1=1 c 1r?j=0(1)rj?r j?nj?i=0?n j i? (0.5)njIc(i)=1 c 1r?j=0(1)rj?r j? A(n j,0),?0.50p1r+1(1 p1)nr1(p1)dp1=1 c 1r+1?j=0(1)r+1j?r + 1 j?nj+1?i=0?n j + 1 i? (0.5)nj+1Ic(n i j + 1)=1 c 1r+1?j=0(1)r+1j?r + 1 j? A(n j + 1,0).c?nt?m?C? p1=r+1?j=0(1)r+1j?r+1 j? A(n j + 1,0)r?j=0(1)rj?r j? A(n j,0)
9、.(3-12)?n?En = S1, r = 0,U? p1=A(S1,0) A(S1+ 1,0) A(S1,0)= 1 A(S1+ 1,0) A(S1,0).(3-13)538?K?26VV?pi, i = 2,k;pi= P (T pi1.rd?cP?EXx?d?ipi ti,?T(j) l= ? nj! (l 1)!(n l)!? 1 +1 ?l1?r=0(1)r?l 1 r? (nj l + r + 1)1+1 ,Of?T(j) li?Hg?j?ninjE?EJlv?a?n?OnjvFA?Jlv?E?T(j) 1 ti,Lsfj= 0.3?i?l?h?k?w?KSFb?k?5392)s
10、ri=i1?j=1fj, riN?(0,ti)?S1vFA?E?J?r2 r3 rk,?Hjz?r2,r3,rk? 3)Y?I?rk= 0?E?W?tk,Lstk+1=? n1? ? 1 +1 ? ,rk+1= 1, r1= r2= = rk= 0.?HA?tk+1?HeaC?Eri,?Ni= S1, i = 1,k?(3-16)?C?pi, i = 1,2,kEBayes? pi.?H?j?CE? pi?“?”?3.3r?,?wu?rvpi= P (T ti) = 1 exp? ?ti? .m?VJ?s = ln, =1 ,L?lnti= + lnln(1 pi)1,i = 1,k.(3-1
11、7)?pi? pi?y?ii,?lnti= + lnln(1 ? pi)1+ i,i = 1,2,k.(3-18)?LSea?C? =BC AD kB A2,? =kD AC kB A2,(3-19)?A =k?i=1lnln(1 ? pi)1,B =k?i=1?lnln(1 ? pi)1?2,C =k?i=1lnti,D =k?i=1(lnti)lnln(1 ? pi)1.?C?J,?ZRR(t)E? ,?,?R(t):? = e?,? =1 ? ,?R(t) = exp? ?t? ? .(3-20)540?K?26V4?D?3?y?E?P?ED?A?JRii?H?HeaE?QE?1y?o?
12、P?Ev?JR(ti,ni),?Si=i?j=1nj.p1?Q?Gx?MTitiniSi 1100.18351 2109.932148 3115.01227 4130.15125 5150.00324 6179.94821 7190.36113 8250.15112 9783.00411 10849.9437 11870.0314 12909.7713 131450.3022?N?S?P?ED?g?j?Wei(x;,)bKP?1EJR?R?Ejz?C,E?O? = 6964.2,? = 1.035,?Z?C?rvpi?ZRR(t)E?W?p2?SG?X(?p?G?Qc)it?SR(t) 110
13、00.9877 22000.9750 33000.9621 44000.9494 55000.9366 66000.9240 77000.9114 88000.8990 99000.8867 1010000.8744 1111000.8624 1212000.8504 1313000.8386 1414000.8269 1515000.81543?eaC?mv?JE?Wj?i? = 7943.314,? = 1.015993,?ZRE?W?3y?2B?3JR?A?nZ?E?O?C?E?ZR?3?E?eaC?E?ZR?C?D?K?nU?eaYuol?E?j“?W?”?W?D?V?X?Bayes?R?y?EQa?C?Yu?QAimI?Z?K?i?UC?ZR?WB?H?O?W?iB3?i?l?h?k?w?KSFb?k?541K?J?H?p3?SG?X(?gc3)it?SR(t) 11000.988339 22000.976559 33000.96
