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|Q=_Dv= VRQ= Q=Okt Q@ |vD@t |}=tv uwRwt lQLDt u}ov=}t Q=Owtv wO w uw}UQoQu}ov=}t w |atHD `tH pQDvm |=yQ=Owtv [8]u=Q=mty w xO=ROU= "OvOQm O=yvW}B|=Q@ Tm =m ?U=vDt xQ]=Nt |vw}UQoQ pOt R= xO=iDU= =@ =Q |}=tv uwRwt lQLDtQ=Qk |UQQ@ OQwt |oOWQwUv=U Qw[L sOa w Qw[L QO xDU@tyOwN C=Oy=Wt|=yOv}=Qi QO u=v}t]= C}r@=k |=yxO=O V}=B |=Q@ [9]u=Q=mty w |RQOwo "OvO=O`} QUD u=tR |vw}UQoQ pOt R= xm 'CU=Q R= |oOWQwUv=U Qw[L QO |}xrLQtxU|atHD `tH w |}=tv uwRwt lQLDt u}ov=}t pQDvm |=yQ=Owtv 'Ovm|t xO=iDU= xDi=}|vD@t xDi=} `} QUD CUmW u=tR pOt l} [10]|m =}v w |@ w}= OU= "Ov=xOQm x�=Q=|L=QH l} |HwQN Q@ xDUw}B CQ=_v |=Q@ xOW lU} Q p}OaD pQDvm Q=Owtv Q@x�=Q= Q}}eD |x]kv pOt R= xOt; CUO x@ |}=tvCUQO C@Uv uwtR; l} T=U= Q@x@ =yvD xv xDUw}B |HwQN 'OwHwt |=ypOt hqN Q@ Ov=xOQm C=@F= u}vJty "Ov=xO=OxO=ROU= "CU= xDU@=w R}v u=L=QH uwJ Qo}O Q=PoQ}F-=D |=yQ}eDt x@ xmr@ Q=t}@ \}=QWlQLDt u}ov=}t pQDvm Q=Owtv wO w |atHD `tH pQDvm Q=Owtv l} [11]|Q}rO=}m w2 wv |xOW QwUv=U u=v}t]= C}r@=k |=yxO=O Q@ CQ=_v Qw_vt x@ |}=tv uwRwtlQLDt u}ov=}t Q=Owtv l} [12]lUH w wR "Ov=xOQm x�=Q= |}xrLQtwO |=yOv}=Qi QO|=Q@ 1 wv |oOWQwUv=U CLD pw@} w |xO=O |=Q@ =Q xiQ]l} |vRw |}=tv uwRwtu}at CUmW |=yQ=mwR=U CLD CqwYLt u}ov=}t |=yQta pw] C=Q}}eD hWm|]QW |Q=_Dv= VRQ= Q@ |vD@t pQDvm Q=Owtv wO [13]u=Q=mty w =R=Q "OvO=O xaUwD`} RwD =@ 1 wv |xOW QwUv=U xO=O V}=B |WN@ QF= Qw_vt x@ =Q |]QW xt}v ww xDUw}B V}=B Qw_vt x@ =Q |O}OH pQDvm Q=Owtv [14]G} Qo "OvO=O O=yvW}B |r} Q|O}rwD |}xrLQtOvJ |=yOv}=Qi QO xm OQm x�=Q= =k@ |=yxO=O |xOW lU} Q p}OaD[15]u=Q=mty w Cv}m "Ovm|t pta |Ov@xWwN T=U= Q@ w OQ=O OQ@ Q=m |D=tON w|xQ=t; Q@ |vD@t xOW lU} Q p}OaD |atHD `tH pQDvm |=yQ=Owtv xm OvO=O u=WvxO=iDU= ?U=vt pOt l} =@ lU} Q C=R=}Dt= R= xm |}=tvCUQO C@Uv sD} Q=orQO QwmPt OQw=DUO &OwW =yQ=Owtv OQmrta uOW QDO@ Ea=@ CU= umtt Ovvm|tvV}=B [16]|}=k@ w xO=ROU= 'C}=yv QO "CU= jO=Y R}v |}xrLQtOvJ |=yOv}=QiOt |}xrLQtOvJ |=yOv}=Qi QO CQB |=yxO=O Qw[L QO =Q u=v}t]= C}r@=k |=yxO=Ou=tR uw}UQoQ |=ypOt =@ Q=wDU= uw}UQoQ |=yOQm} wQ Qw_vt u}O@ "Ov=xO=O Q=Qk Q_v|=yxO=O Qw[L s=ovy x@ =yQ}eDt u}@ j}kO \=@DQ= uDi=} |=Q@ xOW `} QUD CUmW

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b(5)

u} QDlJwm FSSEV (z) |atHD `} RwD `@=D w fSSEV (z) p=tDL= |r=oJ `@=D xm%R= CU= CQ=@a OQ=Ov=DU= |OL Q=Okt

fSSEV (z) = exp[z � exp(z)]

FSSEV (z) = 1� exp[� exp(z)] (6)

p}mWD Q@ |rY= RmQtD '|HwQN |i}m Q}eDt Q@ |OwQw |i}m Q}eDt QF= p}OaD R= TB"CU= |O=yvW}B pQDvm |=yQ=Owtv

|atHD `tH pQDvm Q=Owtv |Q}oQ=m x@ w uO=yv =v@ Q@ pw= |O=yvW}B V}=B OQm} wQhWm x@ C}=va =@ 'OW xQ=W= QDV}B xm Qw] u=ty "CU= Q=wDU= 7 (CUSUM)

xHwD OQwt xiQ]l} CUSUM Q=Owtv 'MU=B Q}eDt u}ov=}t QO |Wy=m |=yCi}W%R= CU= CQ=@a CUSUM |xQ=t; "OQ}o|t Q=Qk(

Qi = min(0; Qi�1 � wi)Q0 = 0 (7)

%CU= x@U=Lt p@=k 8 |x]@=Q R= w xOw@ CUSUM R=}Dt= 'wi u; QO xmwi = log(L(zij�i1)

L(zij�i0) ) (8)

xOW QwUv=U |=yxO=O uDiQo Q_v QO =@ xm CU= |}=tvCUQO `@=D L x]@=Q u}= QO%s} Q=O AJ R=

L(zi; �i) = [fSSEV (zi)]�i [FSSEV (zi)]1��i (9)

%CW=O s}y=wN 8 QO 9 |x]@=Q |Q=Po}=H =@

Mv |=yxDWQ xm CQwY u}O@ "OvQ}o|t Q=Qk|UQQ@ OQwtAJCtU R=|oOWQwUv=UV}=tR; OQwtGvUs=mLDU= x=oDUO\UwD xv=NQ=mC}i}m pQDvm u=tDQ=BO QO xOW O}rwDx=oDUO \UwD OW=@ QDnQR@ |oOWQwUv=U K]U R= Qo = Ctw=kt Q=Okt "OQ}o|t Q=Qk%s} Q=O =Pr "OW Oy=wN QwUv=U xO=O ,=Lq]Y= CQwY u}= Q}e QO 'OwW|t VQ=Ro

�i =

( 0 if ti < c

1 if ti > c(2)

wkw Ov}=Qi u}= QO '1 |x]@=Q x@ xHwD =@ "CU= AJ R= |oOWQwUv=U OL c u; QO xmx=oDUO\UwD w xOy=Wt |Q}oxR=Ov= p@=k xO=O xm u}=CUNv %CU= umtt O=ONQ wOxmCU= K[=w "��i = 0� OvwW QwUv=U =yxO=O xm u}= swO w ��i = 1� OwW VQ=RoCQwY x@ w ODi=|t j=iD= xOW xDioCr=L wO R=Cr=Ll}\ki '|Q}oxvwtv Q=@ Qy QO|=y`} RwD '\}=QWu}= QOu}vJty "OwW|tu=}@|oOWQwUv=U OLwMU=B Q}eDt xv}W}@R= 6pw@} w `} RwD 'u=}t u}= QO &OwW `k=w O}it |R=UpOt |=Q@ CU= umtt |irDNtR= |@ wN OQmrta hrDNt \}=QW QO xm CU=y`} RwD u} QDOQ@ Q=m QB w u} QD?w@Ltl} R= |OQwt |xar=]t QO |HwQN Q}eDt xm u}= x@ xHwD =@ =Pr "CU= xO=O u=Wv OwN%R= Ow@ Oy=wN CQ=@a u; |=k@ `@=D w p=tDL= |r=oJ `@=D 'Ovm|t |wQ}B pw@} w `} RwDf(t) = �

�( t�

)��1 exp��t�

��S(t) = exp

��t�

��(3)

uOQm xDU@=w =@ "Ow@ Oy=wN T=}kt QDt=Q=B � > 0 w pmW QDt=Q=B K > 0 u; QO xm%R= CU= CQ=@a =k@ `@=D 'Q[=L Ov}=Qi QO OwHwt Q=PoQ}F-=D Q}eDt =yvD x@ T=}kt QDt=Q=BS(tijxi) = exp

��

tiexp(�0 + �1xi)

��(4)

x@ u=wD|t =Q pw@} w `} RwD |=yQDt=Q=B =Pr "Ov=|vw}UQoQ pOt|=yQDt=Q=B�1 w�0 u; QO xm�i0 = (�; � exp(�1xi)) p=L "O=OV}=tv �i = (�; � exp(�1xi)) CQwYQO =yQDt=Q=B Q=OQ@ �i1 = (�; �0 � exp(�1xi)) w pQDvm CLD |=yQDt=Q=B Q=OQ@CLD |tU= Q=Okt xm CU= |@} Q[ �0 u; QO xm CU= pQDvm R= GQ=N Cr=L|i}m |xYNWt =yvD Q@ RmQtD =@ C}=yv QO "OyO|t Ci}W =Q T=}kt QDt=Q=B pQDvmu} QDswUQt w u} QDOQ@ Q=m QB R= xm p=tQv `} RwD '|OQwt |xar=]t QO |OwQw Q=PoQ}F-=DOwQ|t Q=m x@ `} RwD u}= |R=UpOt QO =Pr w OW VR=Q@ =yxO=O |wQ Q@ CU=y`} RwDV}=B hOy xm CW=O u=aP= u=wD|t pm QO "X � N(�x; �2

x) xm |Qw] x@l} QO AJ R= xOW QwUv=U �Mv |=yxDWQ Ctw=kt� u=v}t]= C}r@=k |=yxO=O|i}m |xYNWt =@ \@DQt Q}O=kt R= Q}O=kt u}= xm |}xvwo x@ CU= |}xrLQtwO Ov}=QiC}Y=N =Pr w OvQF-=Dt �Mv |=yxDWQ x}rw= O=wt ?}mQD C@Uv =} u=R}t� pw= |xrLQt

"CU= Q=QkQ@ R}v |Q=W@;

|O=yvW}B xOW uw}UQoQ p}OaD pQDvm |=yQ=Owtv "3|oOWQwUv=U Qw[L QO QwmPt |}xrLQtwO Ov}=Qi V}=B |=yOQm} wQ 'VN@ u}= QO

Wi = Log( [exp[(Log(ti)�u1b )�exp(Log(ti)�u1

b )]]�i [1�exp[� exp(Log(c)�u1

b )]]1��i

[exp[(Log(ti)�u0b )�exp(Log(ti)�u0

b )]]�i [1�exp[� exp(Log(c)�u0

b )]]1��i )

�10�

67

"""QOAJ

R=xOW

QwUv=U

|=yxO=O

V}=BQ=Owtv '|oOWQwUv=U OYQO R= dQ=i xm CU= u}= R= |m =L G}=Dv j}kO |UQQ@

uwRwt lQLDt u}ov=}t pQDvm Q=Owtv x@ C@Uv |QDy@ OQmrta |atHD `tH pQDvmpw] 'XNWt Ci}W l} |=R= x@ =Q} R 'OQ=O |Q=_Dv= VRQ= Q}O=kt Q@ |vD@t |}=tvuwRwt lQLDt u}ov=}t pQDvm Q=Owtv u}vJty "CU= QDmJwm \UwDt Q}O=kt |xr=@vOCi}W �10 =D� lJwm |=yCi}W hWm QO |QDq=@ CQOk � = 0=05 =@ |}=tv"OQ=O |R=UQ=wty QDt=Q=B Qo}O Q}O=kt =@ pQDvm Q=Owtv u}ty =@ xU}=kt QO �|Wy=muwRwt lQLDt u}ov=}t pQDvm Q=Owtv 'OwW|t QDnQR@ Ci}W u=R}t xJQy 'Tmar=@"OwW|t QDq=@ hWm CQOk =Pr w QDlJwm ARL Q}O=kt |=Q=O � = 0=2 =@ |}=tvOQmrta Q@ |oOWQwUv=U xm CW=O u=aP= u=wD|t |oOWQwUv=U u=R}t =@ \=@DQ= QO=@ |O=yvW}B VwQ wO Qy QO xm swyit u}O@ "OQ=O |ivt Q}F-=D V}=B |=yOQm} wQxr=@vO pw] \UwDt Q}O=kt X=N Ci}W l} |=R= x@ w |oOWQwUv=U OYQO V}=Ri=OwW s}_vD |}xvwo x@ Ov}=Qi \}=QW CU= QDy@ u=mt= CQwY QO =Pr "O@=}|t V}=Ri==@ `k=w QO &OvQ}ov Q=Qk |oOWQwUv=U ZQat QO Ov}=Qi |=yxO=O R= |O=} R OYQO xm

"OwW|t QDy@ pQDvm |=yQ=Owtv OQmrta '|oOWQwUv=U Vy=mu} QDlJwm `} RwD x@ pw@} w `} RwD p}O@DCra xm OW u=}@ p@kVN@ QO |iQ] R=MU=B Q}eDt R= pw= |xrLQt |i}m Q}eDt QF= Vy=m =} hPL 'OQ=Ov=DU= |OL Q=OktC}i}m u=}t R}=tD Qw_vt x@ O}=@ |vw}UQoQ pOt Q@ |vD@t V}=B OQm} wQ =Pr "CU=QO xOW O=H}= |=yCi}W hWm '=DU=Q u}= QO "OwW p}OaD pm C}i}m w X=N|xrLQt x@ \w@ Qt =yCi}W u}= =Q} R CU}v Q_v Ot p@k |xrLQt |i}m |xYNWtCLD |O=yvW}B pQDvm |=yQ=Owtv OQmrta 'Qw_vt u}O@ "OvDU}v |UQQ@ CLD |Q=H|@=} RQ= OQwt �20 |oOWQwUv=U OYQO w x u}ov=}t QO � |W}=Ri= |=yCi}W

"CU= xOW x�=Q= 4 pwOH QO G}=Dv "CU= xDiQo Q=Qk|=yOQm} wQ Q@|mOv= Q}F-=D pw= |xrLQt|i}m |xYNWt QOCi}W 'Q=_Dv= j@=]t,=@} QkD |Q=t; ^=Lr R= xr=@vO pw] \UwDt Q}O=kt Ck}kL QO &OQ=O |O=yvW}B V}=B|HwQN Q}eDt Q@ p@k |xrLQt Q}eDt QF= uDiQo Q_v QO R= |W=v syt u}= "Ov=xOv=tC@=FQw_vt x@ |OL Q=Okt u} QDmJwm `} RwD x@ pw@} w `} RwD p}O@D w |R=UpOt \UwDOQwt R}v x QO |Wy=m |=yCi}W xwqa x@ "CU= p@k |xrLQt Q}eDt QF= hPLVQ=Ro x@=WD p}rO x@ xm Ow@ |W}=Ri= |=yCi}W x@=Wt u; G}=Dv w CiQo Q=Qk |@=} RQ=

"CU= xOWv

|OQwt |xar=]t "5w |R=UxO=t; |xv}tR QO p=ai 'h} Q_ ?=DlD |xv=NQ=m QO xr=kt |OQwt |xar=]txv=NQ=m u}= |O}rwD C}iQ_ "CU= �|i=@xU}m � |H=Uv CavY QO h=}r= |oOvU} Q|=yxU}m R= sa= Cw=iDt |vwo |=yxU}m `=wv= O}rwD |=Q@ RwQ QO uD 5 3 pO=at

"CU= xQ}e w u=t}U 'Io 'QmW 'OQ;u} R=e; |xrLQt "CU= xOW p}mWD Ov}=QiQ} R wO R= |rm Qw] x@ |i=@xU}m Ov}=Qix=oDUO \UwD QDt|r}t 7 2 ZQa x@ Mv |=yxDWQ |R=UxO=t; R= CU= CQ=@a|=yuRw w =yZQa QO xm CU= xU}m |oOvi=@ VN@ swO |xrLQt w QOwQDUm =QOwQDUm = x=oDUO =OD@= '|O}rwD Ov}=Qi u}= QO "Ovm|t O}rwD =Q Q_v OQwt xU}m 'Cw=iDtxrLQt u}= QO x Q}eDt =Pr &Ovm|t ?}mQD |YNWt CaQU w C@Uv =@ =Q x}rw= O=wt|=y=tO =@ xrLQt 6 |] TBU "CU= Mv |xOvyOp}mWD O=wt |vRw �C@Uv� OYQOuwOQ=t l} |] x}rw= O=wt VN@ u}= QO "OvwW|t ?wP O=wt ?}mQD u}= Cw=iDt'Oa@ w OyO|t CmQL wrH x@ wQ =Q O=wt I}B Q=t uwOQ=t u}= xm Ov=pYDt Qo}Om} x@O=wt 'uOW x}iYD R= TB "OvwW|t x}iYD QDr}i l} Qw[L QO xOW ?wP O=wt

X=N hOy Q=Okt l} R= 'CUSUM Q=Owtv xOW RwQ x@ xQ=t; xm u; ZLt x@u}}=B pQDvm OL 'LCL1 Qo}O CQ=@a x@ "OyO|t p=vo}U 'OwW QDtm (LCL1)�ARL� xr=@vO pw] u}ov=}t x@ xm OwW|t ?=NDv= u=vJ w CU= CUSUM Q=Owtv

"s}UQ@ Q_v OQwt pQDvm CLDlQLDt u}ov=}t pQDvm |=yQ=Owtv uO=yv =v@ w xaUwD Q@ |U=U= RmQtD 'xt=O= QO|wQ xm |DvU EWMA |xQ=t; "OwW|t hw]at 8 �EWMA� |}=tv uwRwt

%R= CU= CQ=@a OwW|t h} QaD xOW xOy=Wt Q}O=ktEWMAi = �zi + (1� �)EWMAi�1 (11)

x}rw= Q=Okt "CU= 0 < � � u}@ |D@=F Q=Okt =@ |R=UQ=wty QDt=Q=B � 'u; QO xmu}ov=}t =@ CU= Q@=Q@ 'OwW|t xO=iDU= u; R= pw= |xvwtv u=tR QO xm �EWMA0�QO �t Q=Okt R= pY=L�z Q}eDt R= xO=iDU= =t= "OQ}o|t Q=Qk V}=B OQwt xm |}xQ=t;x@ xW}ty MU=B Q}eDt |ak=w Q=Okt =Q} R 'OUQ|tv Q_v x@ |k]vt EWMA |xQ=t;C=Oy=Wt |Q=Po}=H xr=kt u}= QO |U=U= |xO}= xH}Dv QO "OwW|tv C@F j}kO Qw]Q}O=kt |=yuRw "CU=yv; 9 �CEV� |]QW |Q=_Dv= VRQ= Q}O=kt =@ xOW QwUv=U=Pr w O};|t CUO x@ MU=B Q}eDt |x}=B `} RwD =@ ?U=vDt |]QW |Q=_Dv= VRQ=x@ |]QW |Q=_Dv= VRQ= Q}O=kt 'Ov}=Qi u}= QO "Ov=Cw=iDt Qo}O `} RwD x@ |a} RwD R=

%O};|t CUO x@ 12 |x]@=Q |xr}Uw

CEV = E(t < c)P (t < c)

=

cR0tf(t)dt

cR0f(t)dt

=

cR0tf(t)dt

F (c)=

cR0t �� ( t� )��1e�( t� )�dt

1� e�( c� )� (12)

%CW=O s}y=wN AJ R= xOW QwUv=U |=yxO=O OQwt QO =Pr

z = Log(CEV )� ub

(13)

R= QDtm u; |xOW p}OaD |xQ=t; xm OyO|t p=vo}U |v=tR R}v pQDvm Q=Owtv u}=Qw_vt x@ CU= QmP u=}=W "OW=@ u; |=Q@ xOW ?=NDv= �LCL2� u}}=B pQDvm OLQ=Owtv R= u=wD|t OwHwt |=yCi}W hWm |=Q@ pQDvm Q=Owtv C}U=UL V}=Ri=

"OQm xO=iDU= R}v 10xOvQ=OR=@ OL =@ EWMA pQDvm

OQmrta |@=} RQ= "4`tH |O=yvW}B pQDvm |=yQ=Owtv OQmrta |UQQ@ w |R=Ux}@W x@ VN@ u}= QOpQDvm OL '|R=Ux}@W pw] QO "s} R=OQB|t |}=tv uwRwt lQLDt u}ov=}t w |atHDpw] \UwDt x@ xm CU= xOW u}}aD |}xvwo x@ |O=yvW}B pQDvm |=yQ=Owtv u}}=B'=]N Q=Okt |R=Uxv}tm Qw_vt x@ "s}UQ@ 200 ,=@} QkD pQDvm CLD �ARL� xr=@vOQ}O=kt Q=vm QO �SE� OQ=Ov=DU= |=]N Q}O=kt w xOW Q=QmD Q=@ 10 000 |R=Ux}@W|=yxR=Ov= =@ u}ov=}t QO (�) |Wy=m |=yCi}W u}vJty "CU= xOW C@F ARL

3 w 2 '1 |=ypwOH QO "CU= xOW xDiQo Q_v QO OYQO 30 w 20 '10 '5 '2 5|=R= x@ '|O=yvW}B |}=tv uwRwt lQLDt u}ov=}t w |atHD `tH |=yQ=Owtv OQmrta"CU= xOW xO=O u=Wv OYQO 80 w 50 '20 O=} R w \UwDt 'sm |=y|oOWQwUv=U

68

2 1|xQ

=tW'36

�1|xQwO

'�139

9u=DUt

R�h}QW

C}Q}Ot

w`}=vY

|UOvyt "�20 |oOWQwUv=U CLD |O=yvW}B pQDvm |=yQ=Owtv |=Q@ OQ=Ov=DU= |=]N w xr=@vO pw] \UwDt Q}O=kt "1 pwOH

� |atHD `tHlQLDt u}ov=}t lQLDt u}ov=}t lQLDt u}ov=}t|}=tv uwQwt |}=tv uwQwt |}=tv uwQwt� = 0=05 � = 0=1 � = 0=2

xr=@vO pw] \UwDt =]N xr=@vO pw] \UwDt =]N xr=@vO pw] \UwDt =]N xr=@vO pw] \UwDt =]N1 200 14 1 6 199 70 1 6 200 25 1 7 200 23 1 8

0 975 145 83 1 1 158 53 1 2 161 45 1 4 169 91 1 60 95 113 34 0 8 129 02 0 9 132 73 1 1 140 92 1 30 9 72 63 0 4 89 06 0 5 91 07 0 7 99 74 0 90 8 35 9 0 2 51 31 0 2 47 27 0 3 49 39 0 40 7 21 68 0 1 31 55 0 1 28 81 0 1 29 60 0 2

"�50 |oOWQwUv=U CLD |O=yvW}B pQDvm |=yQ=Owtv |=Q@ OQ=Ov=DU= |=]N w xr=@vO pw] \UwDt Q}O=kt "2 pwOH



0 975 147 52 1 1 160 28 1 1 163 31 1 3 170 97 1 50 95 114 87 0 7 131 8 0 8 135 56 1 1 143 19 1 20 9 74 97 0 4 92 30 0 4 94 20 0 6 100 80 0 80 8 37 11 0 2 55 08 0 2 49 26 0 2 51 51 0 30 7 22 63 0 11 36 31 0 1 33 37 0 1 31 54 0 1

"�80 |oOWQwUv=U CLD |O=yvW}B pQDvm |=yQ=Owtv |=Q@ OQ=Ov=DU= |=]N w xr=@vO pw] \UwDt Q}O=kt "3 pwOH



0 975 152 43 1 1 165 28 1 1 168 81 1 3 173 83 1 50 95 119 09 0 8 137 65 0 7 139 46 1 0 145 89 1 20 9 79 96 0 5 101 97 0 4 104 75 0 6 106 02 0 80 8 44 50 0 2 59 23 0 2 56 64 0 2 54 84 0 40 7 29 18 0 1 44 92 0 1 40 61 0 1 37 61 0 2

"x u}ov=}t QO � |W}=Ri= |=yCi}W CLD |O=yvW}B pQDvm |=yQ=Owtv |=Q@ OQ=Ov=DU= |=]N w xr=@vO pw] \UwDt Q}O=kt "4 pwOH


xr=@vO pw] \UwDt =]N xr=@vO pw] \UwDt =]N xr=@vO pw] \UwDt =]N xr=@vO pw] \UwDt =]N0 200 14 1 6 199 70 1 6 200 25 1 7 200 23 1 81 199 65 1 5 199 78 1 6 201 04 1 7 199 67 1 72 200 45 1 6 200 51 1 5 201 15 1 6 201 32 1 73 199 67 1 7 198 98 1 6 199 67 1 8 200 43 1 74 198 56 1 6 197 94 1 7 199 74 1 7 198 83 1 7

69

"""QOAJ

R=xOW

QwUv=U

|=yxO=O

V}=B

|xYNWt V}=B Qw_vt x@ |O=Qiv= C=Oy=Wt |=Q@ CQ=ywW pQDvm Q=Owtv "1 pmW"pw= |xrLQt |i}m

xv=NQ=m |OQwt |xar=]t QO |O=yvW}B |atHD `tH pQDvm Q=Owtv OQmrta "2 pmW"h} Q_ ?=DmD

xOvyOCQ=QL x=oDUO QO OwHwt C=v=Uwv w O@ OQmrta x@ u=wD|t =Q |O}rwD |=yMvu}= `iQ x@ |Q=Oyov w C=Q}taD s}D xm &O=O C@Uv QN; |xrLQt QO Mv |=yxDWQ

"OvDN=OQB pmWt

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=yCWwv=B1. cascade property2. censoring3. location-scale4. log-location-scale5. accelerated failure time regression models6. weibull7. cumulative sum8. exponentially weighted moving average9. conditional expected values10. re ecting barriers11. frailty models12. Martingale Residuals

�References� `@=vt1. Asadzadeh, Sh., Aghaie, A. and Niaki, S.T.A. \AFT

regression-adjusted monitoring of reliability data in cas-cade processes", Quality and Quantity, 47(6), pp. 3349-3362 (2015).

2. Niaki, S.T.A., Soleimani, P. and Eghbali, M. \Perfor-mance evaluation of simple linear pro�le monitoringmethods in two-stage processes", Journal of Quality En-gineering and Management, 1(1), pp. 1-13 (2012).

3. Lawless, J.F., Statistical Models and Methods for Life-time Data. John Wiley & Sons Inc., 2nd Edition, (2003).

4. Sego, L.H., Reynolds, M.R. and Woodall, W.H. \Riskadjusted monitoring of survival times", Statistics inMedicine, 28(9). pp. 1386-1401(2009).

5. Steiner, S.H. and Jones, M. \Risk-adjusted survival timemonitoring with an updating exponentially weightedmoving average (EWMA) control chart", Statistics inMedicine, 29 (4), pp.444-454 (2010).

6. Zhang, L., Gan, F.F. and Loke, C.K. \Phase I study ofsurgical performances with risk-adjusted shewhart con-trol charts", Quality Technology and Quantitative Man-agement, 9(4), pp. 375-382 (2012).

7. Asadzadeh, Sh. and Aghaie, A. \Improving the productreliability in multistage manufacturing and service oper-ations", Journal of Industrial and Systems Engineering,28(4), pp. 397{407 (2012).

8. Asadzadeh, Sh., Aghaie, A., Shahriari, H. and et al. \Im-proving reliability in multistage processes with autocor-related observations", Journal of Quality Technology andQuantitative Management, 12(2), pp. 143-157 (2015).

9. Goodarzi, A., Amiri, A. and Asadzadeh, Sh. \Monitoringthe censored lognormal reliability data in a three-stageprocess using AFT model", Journal of Industrial Engi-neering International, 13(1), pp. 67-80 (2017).

10. Asadayyoobi, N. and Niaki, S.T.A. \Monitoring patientsurvival times in surgical systems using a risk adjustedAFT regression chart", Quality Technology & Quantita-tive Management, 14(2), pp. 237-248 (2017).

11. Asadzadeh, Sh. and Kiadaliry, F. \Monitoring type-2censored reliability data in multistage processes", Qual-ity and Reliability Engineering International, 33(8), pp.2551-2561 (2017).

12. Xu, S. and Jeske, D.R. \Weighted EWMA charts formonitoring type-1 censored Weibull lifetimes", Journalof Quality Technology. 50(2), pp. 220-230 (2018).

13. Raza, S.M.M., Ali, S. and Butt M.M. \DEWMA controlcharts for censored data using Rayleigh lifetimes", Qual-ity and Reliability Engineering International, 38(4), pp.1675-1684 (2018).

14. Grigg, O. \The STRAND chart: A survival time con-trol chart", Statistics in Medicine, 38(9), pp. 1651-1661(2019).

15. Knoth, S., Wittenberg, P. and Gan, F.F. \Risk-adjusted CUSUM charts under model error", Statisticsin Medicine, 38(12), pp. 2206-2218 (2019).

16. Asadzadeh, Sh. and Baghaei, A. \Robust AFT-basedmonitoring procedures for reliability data", Journalof Quality Technology and Quantitative Management,17(1), pp. 1-15 (2020).

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