�1398

u=DUtR�

'h}QWC

}Q}Otw

`}=vY

|UOvyt

9�3"X

'2/1|

xQ=tW'

35�1

|xQwO

Ori

gina

lArt

icle|Q}oQ=m x@ |=Q@ |}=yVwQ |x�=Q=

|Q=t; Ov}=Qi pQDvm QO pwYLt Q}wYD�|QDmO |wHWv=O� =Wwm |Oyt

�O=DU=� � <=vUr=Qwv pwUQu=Q}= CavY w sra x=oWv=O '`}=vY |UOvyt |xOmWv=O

|O}rwD CqwYLt uOW QDxO}J}B w =yOv}=Qi uOW QDxDiQW}B =@ u=tRsy Ov}=Qi |Q=t; pQDvmw =yOv}=Qi C}U=UL V}=Ri= x@ xHwD =@ "CU= xDW=O |O}rwD `}=vY QO |Q}otWJ VkvQ} wYD R= xO=iDU= 'Q}N= |=yp=U QO '|v=Uv= |UQR=@ Q@ |vD@t |=yVwQ uOw@ Ot;Q=m =v

'xr=kt u}= QO "CU= xDiQo Q=Qk xHwD OQwt u=QoWywSB \UwD |Q=t; Ov}=Qi pQDvm QO pwYLt=yVwQ u}= "CU= xOW x�=Q= Q} w=YD |Q=t; V}=B |=Q@ |Oa@l} lHwt Q@ |vD@t VwQ xUsqa= Q@ xwqa xH}Dv QO w Ovvm|t xO=iDU= |}=tvCUQO C@Uv OQm} wQ R= Ov}=Qi V}=B |=Q@

=@ =yVwQ u}= OQmrta "OvQ=O R}v =Q Q}}eD |x]kv |x�=Q= |}=v=wD 'pQDvm R= GQ=N \}=QWpw] \UwDt |=yXN=W Q_v R= w xDi=} s}taD |}=tvCUQO C@Uv pQDvm Q=Owtv R= xO=iDU=|R=Ux}@W C=ar=]t "CU= xOW |@=} RQ= |v}tND w |ak=w Q}}eD |x]kv u}@ Cw=iD w xr=@vO

?U=vt K]U |xOvyOu=Wv G}=Dv w CU= xOW s=Hv= xJQ=B |awv Q} wYD R= xO=iDU= =@"OvDUy Q}}eD |x]kv u}tND w pQDvm R= GQ=N |=yCr=L X}NWD QO =yVwQ |}=v=wD

koosha@iust.ac.irrassoul@iust.ac.ir

'2 R=i 'Q} wYD VR=OQB 'lHwt 'p}=iwQB V}=B 'pQDvm Q=Owtv %|O}rm u=oS=w"xDi=} s}taD |}=tvCUQO C@Uv

xtOkt "1nv}rDy w (MCUSUM)2xQ}eDt OvJ |atHD `tH '(MEWMA)1xQ}eDtOvJ|oO}J}B V}=Ri= =@ "OvOW x�=Q= |i}m |xYNWt OvJ u=tRsy V}=B |=Q@ T 2

|vw}UQoQ |x]@=Q '|i}m |=yxYNWt R= xO=iDU= |=H x@ u=kkLt '|O}rwD CqwYLtx]@=Q u}= x@ xm OvOQm |UQQ@ =Q pkDUt Q}eDt OvJ =} l} w |i}m |xYNWt u}@|=yxDUO x@ =yp}=iwQB '|vw}UQoQ |x]@=Q wv T=U= Q@ "OwW|t xDio p}=iwQB|xr=kt "OvwW|t |Ov@xDUO : : : w |oO=t;'xv=oOvJ |]N 'xO=U |]N pFt |irDNtV}=B hrDNt |=yVwQ |xQ=@ QO xar=]t |=Q@ |rt=m `HQt [2]u=Q=mty w <=vUr=QwvCqwYLt |Qy=_ C=YNWt|UQQ@ x@ xm|}=yp}=iwQB `=wv= R=|m} "CU=yp}=iwQBu}= x@ =yp}=iwQB R= xDUO u}= Q=m VwQ "CU= 3|UOvy |=yp}=iwQB 'OvR=OQB|t|i}m |xYNWt w u}}aD pwYLt K]U |wQ x]kv |O=} R O=OaD xm CU= CQwYu=mt w |i}m |=yxYNWt u}= u}@ |a@=D |x]@=Q "OwW|t |Q}oxR=Ov= \=kv u}= QOV}=B u=tR pw] QO |vw}UQoQ |x]@=Q l} CQwY x@ pwYLt |wQ \=kv |m} R}iw Q@u=tR u}vJty w |Q}oxR=Ov= |] QO pwYLt x@ uO}UQ ?}U; u=mt= "OwW|tu}= ?}=at xrtHR= pwYLt Qy |=R= x@ |Q}oxR=Ov= Q=@ u=Q=Ry =} =yOY uOw@ Q@ xv} Ry

"CU= Ov}=Qi V}=B VwQR= "CU= CqwYLt Q} w=YD R= xO=iDU= Ov}=Qi V}=B u} wv |=yVwQ R= |m}QO |tWJ |UQR=@ R= xO=iDU= =@ w |DvU CQwY x@ pwYLt Q} wYD R= QwO u=}r=U=@ xRwQt= "OW|t xO=iDU= ?w}at R= sr=U CqwYLt |R=U=OH w =yXkv X}NWDQO pwYLt l} R= xO=O =yuw}r}t |DL =} u=Q=Ry '4u}W=t |}=v}@ |=yxv=t=U Qwy_

x@ ?w}at pwYLt uO}UQ R= |Q}owrH Qw_vt x@ `}=vY 'QwO Q=}U@ |=yp=U R=|=yOv}=Qi |=yDv= QO ?w}at R= sr=U CqwYLt |R=U=OH x@ s=Ok= '|QDWt CUOxm OwW|t u=yvB |xv=NQ=m l} O=H}= Ea=@ Ck}kL QO Q=m u}= "OvOQm|t |O}rwD'Cq;u}W=t lqyDU= 'x}rw= O=wt '|v=Uv= |wQ}v |xv} Ry xrtH R= |O=} R |=yxv} Ryu}@ O=} R C@=kQ OwHw sOa p}rO x@ xDWPo QO "Ovm|t p}tLD xv=t=U x@ =Q : : : ww swO |v=yH nvH u=}=B =@ =t= "OW|t |WwBsWJ =yxv} Ry u}= R= ,qta '`}=vYpwYLt O}rwD R= |Q}oV}B |=Q@ `}=vY w =yCmQW '|DavY ?qkv= u=QwO wQW

"OvOQm VqD |O}rwD |=yOv}=Qi V}=B |xr}Uw x@ ?w}atOv}=Qi |Q=t; pQDvm |=Q@ CQ=ywW pQDvm |=yQ=Owtv '1920 |=yp=U OwOL QO|Q}oQ=m x@ CqmWt R= |m} "OvOW xOQ@ Q=m x@ u=QoDavY \UwD w OvOW |iQatu}= x@ "CU= u=tR pw] QO |i}m |xYNWt l} \ki V}=B u=mt= '=yQ=Owtv u}=u=tRsy CQwY x@ |i}m |xYNWt OvJ =} wO V}=B x@ pwYLt l} QO Qo = ?}DQDu}= xm OwW xO=iDU= R=}v u=tRsy CQwY x@ CQ=ywW Q=Owtv OvJ R= O}=@ ,qta 'OW=@x=@DW= |=yQ=OWy V}=Ri= xH}Dv QO w l} wv |=]N p=tDL= V}=Ri= ?Hwt Qt=

[1]"OwW|t pQDvm |=yQ=Owtv|}=tv uwRwt lQLDt u}ov=}t |=yQ=Owtv pFt xQ}eDtOvJ pQDvm |=yQ=Owtv

pw�Ut xOvU} wv �"1397 7 15 VQ}PB '1397 6 27 x}LqY= '1396 1 27 Ci=} QO %M} Q=D

DOI:10.24200/J65.2018.50530.1854

"""pwYL

tQ}wYD

|Q}oQ=m

x@|=Q@|

}=yVwQ|

xaUwD`} QU uOv=OQoR=@ w |@=}x[Q=a |=Q@ u=QoDavY w u=Q@ Q=m Q=}DN= QO =Q |OvtWRQ=

"OvyO Q=Qk pQDvm CLD Cr=L x@ Ov}=Qi|Q=t; V}=B |=Q@ |}=[i |xvt=O |xRwL QO =Q |WwQ [10]u=Q=mty w Oy=otlQLDt |=ylU=t =OD@= '=yv; VwQ QO "OvO=O x�=Q= pwYLt Q} wYD R= xO=iDU= =@ Ov}=QiCOW Q}O=kt u}ov=}t w Ovvm|t CmQL Q} wYD |=[i |wQ hrDNt |=yxR=Ov= =@u}O@ "OwW|t C@F Q=OQ@ l} QO |oS} w u=wva x@ xQHvB Qy pN=O |=ypUm}B QwvxO=iDU= =@ Q=OQ@ u}= "OwW|t p}O@D u}ov=}t Q}O=kt R= |Q=OQ@ x@ Q} wYD Qy '?}DQD"OwW|t pQDvm u=tR pw] QO 15xDi=}s}taD |}=tvCUQO C@Uv pQDvm Q=Owtv l} R==@ u=tRsy CQwY x@ ?}a OvJ X}NWD |=Q@ =Q VwQ u}= [11]u=Q=mty w xy[12]u=Q=mty w Rrw "OvO=O xaUwD |}=tvCUQO C@Uv pQDvm Q=Owtv s}taD R= xO=iDU=l} x@ =yv; p}O@D w |Oa@xU |Q} wYD |=yxO=O V}=B |=Q@ Q-Q16 pQDvm Q=Owtv R=17QwUvD u}}=B K]U |x} RHD R= [13]u=Q=mty w u} "OvOQm xO=iDU= |]N p}=iwQB|=yVwQ XwYN QO [14]wt}Uwrwm "OvOQm xO=iDU= Q} wYD QO ?}a X}NWD |=Q@"CU= xDN=OQB |UQQ@ w EL@ x@ |Q} wYD |=yxO=O V}=B w |R=UpOt hrDNt`@=D V}=B x@ 18|a@=D |rY= |=yxir-wt p}rLD R= xO=iDU= =@ [15]u=Q=mty w w}rowi=vt

"OvDN=OQB Q} wYD |=[i QO =y|oS} w uO=O MQ p=tDL= |r=oJ"CU= xOW xO=iDU= Q} w=YDV}=B |=Q@ |}=[i |xvt=O R= 'xOW QmP C=k}kLD QO|wQ lHwt QDr}i |Q}oQ=m x@ Q@ |vD@t |}=yVwQ CU= xOW |aU xr=kt u}= QO|Q=t; pQDvm |=Q@ QDr}i u}= |xr}Uw x@ xOW G=QNDU= |=y|oS} w R= xO=iDU= w Q} w=YDR= '|Ot=U@ |xvt=O |xRwL QO =yVwQ |xaUwD =@ w ?}DQD u}= x@ "OwW x�=Q= Ov}=QiOv=wD|t w[wt u}= w O};|t pta x@ |QDy@ |xO=iDU= Q} wYD QO QDDUt C=aq]=u}= |xt=O= "OwW hrDNt `}=vY QO =yVwQ |}=Q=m Ow@y@ w CkO V}=Ri= x@ QHvt

"CU= Q} R CQwY x@ xr=kt'3 VN@ QO "OwW|t |UQQ@ =yv; `=wv= w X=wN w =ylHwt '2 VN@ QO|ak=w |=yxO=O |wQ =Q |R=Ux}@W G}=Dv 4VN@ "OvwW|t x�=Q= |O=yvW}B |=yVwQQO xOW x�=Q= |=yVwQ OQmrta |xU}=kt x@ w OyO|t u=Wv xJQ=B |awv x@ \w@ QtVN@ C}=yv QO "OR=OQB|t Q}}eD |x]kv u}tND w pQDvm R= GQ=N Cr=L X}NWD

"CW=O Oy=wN X=YDN= |Q}oxH}Dv w |Ov@`tH x@ 5

lHwt "2'|O}rwD CqwYLt uOW QDxO}J}B =@ 'OW xQ=W= p@k VN@ QO xm Qw] u=ty|QDW}@ |xrY=i swUQt |=yp}=iwQB R= R}v CqwYLt u}= R= pY=L |=yp}=iwQB"OwW|t xOy=Wt p}=iwQB Qy QO |O=} R |=yVyH w 19|v=yo =v C=Q}}eD w OvQ}o|t|m} "OvwW|t xDiQo Q=m x@ `@=wD ?} QkD |=Q@ |QDt=Q=B Q}e |=yOQm} wQ OQ=wt u}= QO`@=wD R= xO=iDU= =@ =ylHwt "OvDUy =ylHwt xv}tR u}= QO OQ@ Q=mQB w syt `@=wD R=s_vtQ}e C=v=Uwv w O=} R |oO}J}B =@ `@=wD ?} QkD QO |Q=}U@ |}=v=wD hrDNt |x}=BQO =yxO=O u=tRsy p}rLD |}=v=wD =ylHwt Cwk \=kv R= Qo}O |m} u}vJty "OvQ=Oj}kO hWm x@ |O=} R Q=}U@ ltm w[wt u}= xm CU= |Ot=U@ w |}=[i |xvt=O

"Ovm|t C=Q}}eD RwQ@ u=mt w u=tRxO=iDU= 20p=tQv Ot=aDt |x}=B p}mWD |=Q@ xm OvDUy |}x}=B `@=wD =ylHwtC=a@ Qt xm OvwW|t xO=iDU= `@=wD R= |Y=N |xDUO u=}@ |=Q@ x}=B `@=wD u}= "OvwW|tQOB |=ylHwt R= xO=iDU= =@ p=tQv Ot=aDt |x}=B Qy "OvW=@ Q}PBp=QoDv= O}=@ =yv;Q@ "OvwW|t xO=O V}=tv (x) w �(x) =@ ?}DQD x@ xm OwW|t xDN=U QO=t w

u}W=t|}=v}@ |=yx=oDUO "CU= TQDUO QO lOv=|}xv} Ry hQY =@ w x}v=F R= |QUml} 'Q} wYD C@F |=Q@ u}@ QwO OvJ =} l} 'pwYLt Qw@a |=Q@ xr=kv Q=wv l} pt=W=yxO=O p}rLD |xv=t=U l} w |Q=OQ@Tma R= p@k pwYLt C}@FD |=Q@ 5Ov@ w O}k"OvwW|t |Ov@s}UkD |ovQ w |QDUm =N 'O}iU w x=}U xwQo xU x@ Q} w=YD "OvDUy"OvDUy Qo}Om} x@ p}O@D p@=k Q} w=YD VR=OQBV}B Cq}O@D R= xO=iDU= =@ xwQo xU u}=u=wva x@ OOa l} |=Q=O s=Om Qy xm CU= pUm}B |O=} R O=OaD pt=W Q} wYD l}|Q=Okt 6pUm}B Qy '|QDUm =N Q} wYD l} QO p=Ft u=wva x@ "OvDUy Qwv COWw Q} wYD l} Q=DN=U '1 pmW "Ovm|t Q=}DN= �O}iU� 255 =D �|mWt� QiY u}@

"OyO|t V}=tv =Q =ypUm}B V}=tv |xwLvCqwYLt|R=U=OHQw_vt x@\kiu}W=t|}=v}@|=yxv=t=U'x}rw=|=yOQ@ Q=m QO=@ xv=t=U xm CQwY u}= x@ "OvOW|t xO=iDU= |O}rwD CqwYLt Q}=U R= ?w}atR= xO=iDU= =@ =Q ?w}at CqwYLt '`HQt Q} wYD =@ pwYLt Qy Q} wYD |xU}=ktw 7|}=[i |xvt=O xDUO wO x@ C=ar=]t u}= "OQm|t GQ=N S=Dvwt \N R= |tQy=Qwv COW Q}O=kt R= '|}=[i |xvt=O |xRwL QO "OvwW|t s}UkD 8|Ot=U@ |xvt=Ol} ,qwtat xDUO u}= QO "OwW|t xO=iDU= QDr}i uwO@ w s}kDUt CQwY x@ =ypUm}B|}xDUO CQwY x@ =ypUm}B w Ovm|t CmQL Q} wYD |=[i |wQ lQLDt |xQHvB|xRwL QO "CU= xOW s=Hv= |D=k}kLD xv}tR u}= QO [4w3]`H=Qt QO "OvwW|t |UQQ@p=ta= Q} wYD |wQ |oS} w |xOvvm G=QNDU= u=wva x@ QDr}i l} =OD@= '|Ot=U@ |xvt=Opt=W Cq}O@D u}= "OvwW|t |UQQ@ xOW G=QNDU= |=y|oS} w TBU w OwW|t|oS} w G=QNDU= w `@=wD ?} QkD |=Q@ xm OvDUy: : : w pvQm 'lHwt 'x} Qwi p}O@DCWov= QF= X}NWD |=Q@ lHwt p}O@D R= [5]u=Q=mty w 9wm}D "OvwW|t xO=iDU=lHwt Q@ |vD@t VR=OQBV}B R= [6]11OQ=Owo w 10h=QU - |Q=U "OvOQm xO=iDU=|=Q@ =Q |WwQ [7]u=Q=mty w 12u=ov= "OvOQm xO=iDU= xJQ=B QO ?}a X}NWD |=Q@[8]u}r "OvOQm x�=Q= lHwt p}O@D T=U= Q@ Q=OKQ] |=yxJQ=B QO ?}a X}NWD?}a X}NWD |=Q@ lHwt |=y|oS} w T=U= Q@ =Q Q=mOwN |UQR=@ VwQ l}QO Q} wYD R= xO=iDU= OQ=wt QDW}@ QO "OQm x�=Q= 13 (SBL) K]U ^i=Lt |x}qOQwt ?w}at R= sr=U CqwYLt |R=U=OH =} |@=QN X}NWD '|Q=t; C}i}m pQDvmxRwL u}= C=k}kLD QO Ov}=Qi pQDvm w |Q=t; x=ov CQOv x@ w CU= xDiQo Q=Qk xHwDxO=iDU= OQ=wt |wQ =Q |at=H w j}ta |xar=]t [9]u=Q=mty w Oy=ot "OQ=O OwHw|xaUwD =@ "OvO=O s=Hv= ?}a X}NWD |=Q@ pQDvm |=yQ=Owtv Q=vm QO Q} wYD R=|xv}tR QO |}=yxO=iDU= Q} wYD R= pY=L |=yxO=O R= '14u}W=t |Q}oO=} |=yVwQC=aq]= Ovv=wD|t xm OwW|t Q}}eD |x]kv w ?}a RwQ@ u=mt hWm 'Ov}=Qi V}=B

"Q}wYD Q=DN=U "1 pmW

4

2 1|xQ

=tW'35

�1|xQwO

'�139

8u=DUt

R�h}QW

C}Q}Ot

w`}=vY

|UOvyt w u=QwO 'Q} wYD |xR=Ov= Q}}eD '21O=[D V}=Ri= 'O�=wR hPL 'O}iU w x=}U x@ |ovQ

QDy@ |}=U=vW |=Q@ |@U=vt `HQt [17]ROww w Tr=Rvwo "OW=@ Q} w=YD 22uOQm R=QDsy"OvDUy =ysD} Qwor= u}=

"OwW|t xDN=vW `HQt Q} wYD u=wva x@ xOt; CUO x@ Q} wYD 'pL=Qt u}= R= TBxDW=O OwHw pwYLt R= OOaDt `HQt Q} w=YD G=QNDU= u=mt= Qo = xrLQt u}= QOxO=iDU= =@ s}v=wD|t u=mt= sOa CQwY QO =t= "O@=}|tV}=Ri= C=@U=LtCkO 'OW=@'R}J=v Q=}at h=QLv= w QiY u}ov=}t =@ p=tQv |iO=YD |=y=]N uOQm xi=[= R=|=yxO=O u=wva x@ =yv; R= xm s}vm O=H}= |rY= Q} wYD |wQ R= =Q |OOaDt Q} w=YDXN=W R= |iO=YD |=]N Q=}at h=QLv= u=R}t u}}aD |=Q@ "OwW|t xO=iDU= 1 R=iSNR |=Q@ |QDt=Q=B Q}e |=yVwQ "OwW|t xO=iDU=23�SNR� xiwv x@ p=vo}U|x]@=Q R= xO=iDU= =@ SNR XN=W "OvQ=O |@U=vt OQmrta 25 =@ |w=Ut =} QDnQR@Tv=} Q=w �2

Img 'x]@=Q u}= QO "OwW|t x@U=Lt SNR = 10log10�

�2Img

�2noise

�|=]N Tv=} Q=w �2

noise w pQDvm CLD Q} wYD |=ypUm}B Qwv COW x@ Q}O=kt"CU= |iO=YD

|R=UQ=OQ@ "2"3x@ "OwW|t p}O@D Q=OQ@ l} x@ Q} wYD Qy '24|R=UQ=OQ@ R= xO=iDU= =@ =OD@= 1 R=i QO|=Q@ "OwW|t p}O@D 1�n2 xR=Ov=x@ Q=OQ@ l} x@ n�n Q} wYD l} xm CQwY u}=Q=Qk |UQQ@ OQwt p}YiD x@ [18]`HQt QO xm OQ=O OwHw |OOaDt |=yVwQ Q=m u}=|R=UQ=OQ@ swUQt VwQ u} QDxO=U R= xr=kt u}= |O=yvW}B |=yVwQ QO "CU= xDiQoxOW xO=iDU= 'O};|t CUO x@ Q} wYD |=yQ]U uO=O Q=Qk sy Q=vm R= xO=iDU= =@ xmx@ 'u}=Q@=v@ "O}; pta x@ |} wHxiQY |oO}J}B w sHL Q_v R= C=@U=Lt QO =D CU=xm O};|t CUO x@ pkDUt Q}eDt |O=} R O=OaD pt=W p}=iwQB l} 'Q} wYD Qy |=HC=Q}}eD w O=} R C=v=Uwv |=Q=O Ov=wD|t =ypUm}B Qwv COW Q}O=kt C=Q}}eD Cra x@

"OW=@ |v=yo =v

|Oa@ l} lHwt p}O@D 3"3K]U QO w OwW|t p=ta= pY=L 1 � n2 Q=OQ@ |wQ lHwt p}O@D s=o u}= QO1� n2

2 =yv; R= s=OmQy O=a@= xm d1 26C=}�RH w a1 25?} QkD Q=OQ@ wO 'x} RHD pw=Q=OQ@ Q=@ Qy '|Oa@ |x} RHD Kw]U QO "Ov};|t CUO x@ Q} wYD Qy |=Q@ CU=s}UkD C=}�RH w ?} QkD |w=Ut CtUk wO x@ p@k |xrLQt R= pY=L ?} QkDOvR|t u}tND |}xvwo x@ =Q ?}=Q[ 'u}}=B Ot=U@ QDr}i l} Ovv=t QOB `@=D "OwW|tx}rw= p=vo}U u}}=B Ot=U@ C=v=Uwv R= |@U=vt h}YwD 'pY=L ?} QkD Q=OQ@ xm|r}N C=v=Uwv 'q=@ Ot=U@ QDr}i l} Vkv QO 'QO=t lHwt `@=D "OW=@ xDW=O'OW=@ QDnQR@ x} RHD K]U QOkJQy u}=Q@=v@ "Ovm|t G=QNDU= p}=iwQB R= =Q |�RHCkO Vy=m ?Hwt hQ]l} R= Qt= u}= "Ow@ Oy=wN QDtm ?} QkD ?}=Q[ O=OaDQHvt Qo}O |wU R= w OwW|t ?} QkD ?}=Q[ Q=OQ@ |xr}Uw x@ p}=iwQB h}YwDK]U TB "OW Oy=wN C=@U=Lt s=Hv= |=Q@ R=}v OQwt |=[i w u=tR Vy=m x@QO xwkr=@ C=Q}}eD |xR=Ov= w wv x@ xDU@ xm CU= |}=yQDt=Q=B R= |m} x} RHD?=NDv= CkO =@ w xv=OvtWwy O}=@ 's}DUy =yv; hWm x@ Ovtxkqa xm |rwYLt

"OwW|xrLQt |x} RHD R= pY=L ?} QkD Q=OQ@ 'x} RHD R= xrLQt Qy QO xmu}= x@ xHwD =@|OwQw ?} QkD Q=OQ@ O=a@= hYv s=Om Qy O=a@= xm - C=}�RH w ?} QkD Q=OQ@ wO x@ p@kpt=W - C=}�RH w ?} QkD |=yxir-wt ?}=Q[ O=OaD wtHt 'OwW|t p}O@D - CU=

j0 � 0 |=Q@ f�j0k(x);jk(x); j � j0;2 Zg |xawtHt '[16]uOo ; T=U=QOB `@=wD T=U= Q@ Ov=wD|t f(x) `@=D Qy "OyO|t =Q p=tQv Ot=aDt x}=B l} p}mWD

[16]"OwW xO=O V}=tv Q} R CQwY x@ QO=t w

f(x) =2j0�1Xk=0

cj0k�j0k(x):::

:::+J�1Xj=j0

2j0�1Xk=0

djk jk(x) (1)

"OvDUy QO=t w QOB `@=wD w |rY= `@=D |rN=O ?Q[pY=L djk w cj0k 'x]@=Q u}= QOK]U u} QDu}}=B j0 QDt=Q=B "Ov=xOW |Q=Po s=v lHwt ?}=Q[ u=wva x@ ?}=Q[ u}=QO "OW=@ lHwt ?} Q[ n R= pY=L Q=OQ@ � O}vm ZQi "OyO|t u=Wv =Q x} RHD

%OwW x@U=Lt Q} R CQwY x@ Ov=wD|t Q=OQ@ u}= CQwY u}=� = wf (2)

`@=wD R= xO=iDU= =@ xm CU= lHwt Ot=aDt p}O@D T} QD=t l} W 'x]@=Q u}= QOOwW|tv xOy=Wt f(x) `@=D ,qwtat |rta |=yOQ@ Q=m QO "OwW|t u}}aD lHwtZQi "OvDUy xOy=Wt p@=k pkDUt Q}eDt hrDNt Kw]U |=R= x@ MU=B Q}O=kt wQ}O=kt =@ Q_=vDt MU=B Q}eDt Q=Okt n pt=W |Q=OQ@ y = (Y1; Y2; :::Yn)0 O}vmQ} R CQwY x@ Ov=wD|t f w y u}@ |x]@=Q 'T=U= u}= Q@ "OW=@ pkDUt Q}eDt hrDNt

"OwW u=}@y = f + " (3)

xQ}eDt n p=tQv `} RwD R= ,qwtat xm CU= |iO=YD |=]N Q=OQ@ " 'x]@=Q u}= QOQO q=@ |x]@=Q u}iQ] ?Q[ =@ "Ovm|t |wQ}B �2I Tv=} Q=w w QiY u}ov=}t =@

%O};|t CUO x@ 4 |x]@=Q 'W T} QD=t� = � + � (4)

� = W" w xOW xOR u}tND lHwt ?}=Q[ Q=OQ@ =@ Q@=Q@ � = Wy x]@=Q u}= QO|wQ}B Nn(0; �2I) `} RwD R= u=vJty xm CU= xDi=} u=QwO |iO=YD |=]N Q=OQ@Tv=} Q=w w � u}ov=}t =@ p=tQv `} RwD R= � xm CU= |y}O@ CQwY u}= QO "Ovm|t|}=v=wD '1 R=i QO �2 w � Q}O=kt u}tND R= TB =t Q=DWwv u}= QO "Ovm|t |wQ}B �2I"s}vm|t |UQQ@ 2 R=i QO Q}}eD hrDNt Cq=L hWm QO =Q |O=yvW}B |=yVwQ

|O=yvW}B |=yVwQ "3CqwYLtC}i}mV}=B QO Q} wYD R= xO=iDU= |=Q@ |O=yvW}B |=yVwQVN@ u}= QOQO xm OvDUy u=Um} |x}rw= |=ys=o |=Q=O |O=yvW}B VwQ xU Qy "OwW|t |UQQ@

%s} R=OQB|t pL=Qt u}= |UQQ@ x@ xt=O=

VR=OQBV}B w pwYLt R= |Q=OQ@ Q}wYD "1"3u}= "OwW|t x}yD u}W=t |}=v}@ x=oDUO \UwD pwYLt R= Q} wYD l} xrLQt u}= QOx@ xDU@ xm OQ=O VR=OQBV}B pL=Qt x@ R=}v '|O=yvW}B Ov}=Qi QO xO=iDU= |=Q@ Q} wYDQO VR=OQB V}B pL=Qt R= |irDNt `=wv= pwYLt w Ov}=Qi 'Q} wYD wv 'u}@ QwO wvQ} wYD p}O@D pt=W Ov=wD|t pL=Qt u}= "CU= OwHwt Q} w=YD VR=OQB |=yVywSB

5

"""pwYL

tQ}wYD

|Q}oQ=m

x@|=Q@|

}=yVwQ|

xaUwD"OyO|t u=Wv =Q CNU |R=Uxv=DU; '3 pmW

30sQv |R=Uxv=DU; R= xO=iDU= =@ |}=ORxiwv "3"4"3u}= QO "CU= hwQat sQv |R=Uxv=DU; x@ xm OQ=O OwHw R}v |R=Uxv=DU; R= |Qo}O wv=t= 'OvwW|t xO=O Q=Qk QiY Q@=Q@ xv=DU; OL R= QDlJwm C=}�RH ?}=Q[ R}v VwQ|Q=Po|=H xv=DU; OL R= u=W|ak=w Q}O=kt p[=iD =@ 'xv=DU; OL R= QDnQR@ ?}=Q[

"OyO|t u=Wv =Q sQv |R=Uxv=DU; OQmrta Ov}=Qi '6 |x]@=Q "OvwW|t

fsoft(�) =

8>>>><>>>>:0 j�j � �� � � � > �

� + � � < �

(6)

"OyO|t V}=tv =Q sQv |R=Uxv=DU; '4 pmWw OW Ovy=wN Q=Qk |UQQ@ xr=kt u}= |R=Ux}@W C=ar=]t QO OQm} wQ xU u}=

"OW Oy=wN xU}=kt Qo}Om} =@ hrDNt C=Q}}eD hWm QO =yv; OQmrtapQDvm Q=Owtv R= xO=iDU= =@ Ov}=Qi V}=B "5"3

'OW Oy=wN s=Hv= q=@ |=yVwQ R= |m} x@ xm =yxO=O O=a@= Vy=m |xrLQt |=yDv= QOQ=OQ@ V}=B |=Q@ 31 �GLR� xDi=}s}taD |}=tvCUQO C@Uv pQDvm Q=Owtv l} R=pQDvm |=Q@ Q=Owtv u}= QO xm |}xQ=t; "OwW|t xO=iDU= u=tR pw] QO pY=L ?}=Q[

%CU= Q} R CQwY x@ 'OwW|t xO=iDU= Ov}=Qi

Rm;s=

8><>: max0<�<S;k(S��)

2�2k

(�1;�;S(k)� �0;k)2 s = 1; 2; :::;mmax

S�m<�<S;k(S��)

2�2k

(�1;�;S(k)��0;k)2 s=m+1;m+2; :::(7)

"CNU |R=Uxv=DU; "3 pmW

"sQv |R=Uxv=DU; "4 pmW

Q} wYD |=ypUm}B O=OaD Q@=Q@ - |r@k |x} RHD Kw]U w |rai |x} RHD K]U C=}�RH|}=yVwQ x@ w OvDUy nQR@ Q=}U@ u=tR pw] QO V}=B |=Q@ O=a@= u}= "CU= |rY=

"CU= R=}v =yxO=O O=a@= Vy=m |=Q@

=yxO=O O=a@= Vy=m "4"3R= |m} "CU= |UQQ@ p@=k C=}�RH |=yxir-wt p=@k QO OQm} wQ wO 'Oa@ Vy=m |=Q@K}[wD p}YiD x@ xt=O= QO =yVwQ u}= "28|}=ORxiwv |Qo}O w 27|R=UxOQWi =yv;

"OvwW|t xO=O|R=UxOQWi "1"4"3

R= 'C=}�RH w ?} QkD |=yxir-wt x@ Q=OQ@ |r=wDt |=yx} RHD R= TB 'VwQ u}= QOC=aq]= R= |O=} R VN@ ?} QkD |xir-wt l}miD R= xrLQt Qy QO xm |}=Hu;x@ C=}�RH ?}=Q[ |=yQ=OQ@ R= ,qta 'Ovm|t xQ}NP OwN QO =Q |rY= Q=OQ@QO =ylHwt R= xO=iDU= u=}=B QO 'CQwY u}= x@ "OwW|t Q_vhQY xOt; CUOx@ ?} QkD Q=OQ@ l} '1 � n2 O=a@= x@ |rY= Q=OQ@ |=Hx@ 'j0 |x} RHD K]U|O=} R OL =D =Q |rY= Q=OQ@ C=}YwYN xm CU= TQDUO QO 1 � n2

2j0 O=a@=u=Wv =Q 2 |x} RHD K]U QO |R=UxOQWi '2 pmW "CU= xOQm xQ}NP OwN QO

"OyO|tC=}�RH Q=OQ@ d1 'x} RHD pw= K]U R= pY=L ?} QkD Q=OQ@ a1 '2 pmW QOd2 w 'x} RHD swO K]U R= pY=L ?} QkD Q=OQ@ a2 'x} RHD pw= K]U R= pY=LR= xO=iDU= s=ovy QO T=U= u}= Q@ "CU= x} RHD swO K]U R= pY=L C=}�RH Q=OQ@"OW s}y=wN xH=wt : : : w d4 'a4 'd3 'a3 Q}_v |}=yxir-wt =@ QDq=@ |x} RHD Kw]U?} QkD |xir-wt R= xO=iDU= =@ Ov}=Qi |Q=t; V}=B |x} wQ ,qta '|R=UxOQWi QOR= x@ QHvt Ov=wD|t Qt= u}= "OwW|t Q_vhQY C=}�RH |xir-wt R= w O@=}|t xt=O=|=Q@ R=}v OQwt |=[i w u=tR 'u; |=R= QO =t= "OwW C=aq]= R= |WN@ uDiQ CUO

"CW=O Oy=wN |Q}otWJ Vy=m C=@U=Lt s=Hv=29CNU |R=U xv=DU; R= xQ=iDU= =@ |}=ORxiwv "2"4"3

uO=O Q=Qk Q@=Q@ w lJwm Q=}U@ C=}�RH |=yxir-wt hPL '|}=ORxiwv OQm} wQ T=U=xO=iDU= =@ xm OwW|t s=Hv= xv=DU; OL l} R= xO=iDU= =@ Q=m u}= "CU= QiY =@ =yv;C=}�RH |xir-wt QY=va s=tD [16]"OwW|t x@U=Lt � = �

p2In(n) |x]@=Q R=?}=Q[ Q}=U =t= &OvwW|t xO=O Q=Qk QiY Q@=Q@ 'OvDUy xv=DU; OL R= QDlJwm xm5 |x]@=Q "OwW|t xDio CNU |R=Uxv=DU; Q=m u}= x@ "Ovv=t|t |k=@ Q}}eD uwO@

"OyO|t u=Wv =Q CNU |R=Uxv=DU;

fhard(�) =

8<:0 j�j � �� j�j > �

(5)

"2 |x} RHD K]U QO |rY= Q=OQ@ |R=UxOQWi "2 pmW

6

2 1|xQ

=tW'35

�1|xQwO

'�139

8u=DUt

R�h}QW

C}Q}Ot

w`}=vY

|UOvyt Cq=mW= RwQ@ =}|}=Q=m uDiQ u}@ R= x@ QHvt Ov=wD|t C=HwUvt K]U QOXkv xvwoQy

CqwYLt QO |vt}= Cq=mW= �|v=WvVD; C=R}yHD pFt� OQ=wt |NQ@ QO w |Qy=_u}= O}rwD Ov}=Qi '|Q=t; u} wv |=yVwQ R= xO=iDU= =@ OUQ|t Q_v x@ 'u}=Q@=v@ "OwW

"OwW |Q}owrH |Oa@ |r=tDL= Q]N wv Qy R= =D OwW V}=B O}=@ C=HwUvtp=ta= Q} wYD |wQ Q@ VR=OQBV}B pL=Qt '|R=Ux}@W C=ar=]t |=OD@= QOO};|t CUO x@ pwYLt R= 128 QO 128 R}=U =@ Q} wYD l} ?}DQD u}= x@ "OwW|t

"OwW|t xO=iDU= `HQt Q} wYD u=wva x@ Q} wYD u}= R= |Oa@ pL=Qt QO xmx@ sOYl} Q=}at h=QLv= w QiY u}ov=}t =@ p=tQv `} RwD =@ |iO=YD |=]Nu=wva x@ Q} wYD 1000 O=OaD ?}DQD u}= x@ w OwW|t xi=[= Q} wYD pUm}B Qyx@ '|R=UQ=OQ@ R= xO=iDU= =@ Q} w=YD u}= R= s=Om Qy "OvwW|t O}rwD 1 R=i |=yxO=Ow ?} QkD ?}=Q[ pt=W Q=OQ@ u}= xm OvwW|t p}O@D lHwt ?}=Q[ R= Q=OQ@ l}xQ=W= =yv; x@ p@k VN@ QO xm 'Oa@ Vy=m |=yVwQ wvD x@ xHwD =@ "CU= C=}�RHu} Ro}=H Qo}O QY=va =@ OQ=wt |NQ@ QO =} hPL Q=OQ@ u}= C=}�RH CtUk 'OW?} Q[ |O=OaD pt=W l} Qy xm Q=OQ@ 1000 '1 R=i u=}=B QO ?}DQD u}= x@ "OwW|txOW xO=iDU= 3 |x} RHD K]U R= xr=kt u}= |R=Ux}@W QO "s} Q=O Q=}DN= QO 'OvDUyu=tR u}vJty w hWm |=Q@ Q_v OQwt Q}}eD O=a@= |xv}tm x@ xHwD =@ K]U u}= "CU=|x}=B `@=wD u}vJty "CU= xOt; CUO x@ =]N w |aU R= xO=iDU= =@ C=@U=Lt s=Hv=QO "OvDUy: : : w uQ=kDt '|m} Rmt xqm 'Q=y xrtH R= |irDNt `=wv= |=Q=O lHwt'CU= x}=B `@=D wv u} QDG}=Q w u} QDOQ@ Q=mQB xm 'Q=y lHwt R= xr=kt u}= |R=Ux}@W

"CU= xOW xO=iDU=xOt; CUO x@ Q=OQ@ 1000 |=Q@ Q=}at h=QLv= w u}ov=}t '1 R=i |=yDv= QOxm O};|t CUO x@ ?}=Q[ Q=OQ@ pw] |xR=Ov=x@ Q=OQ@ wO u}=Q@=v@ "OwW|t x@U=Lt�2k u=wva x@ s=k ?} Q[ Q=}at h=QLv= R= w �0;k u=wva x@ s=k ?} Q[ u}ov=}t R=

"OwW|t xO=iDU= 7 |x]@=Q |xQ=t; C=@U=Lt QOq=@ pQDvm OL uDi=} |=Q@ C=@U=Lt ' �2 w �0 |=yQ=OQ@ uOt; CUO x@ =@pQDvm CLD Cr=L QO xQ=t; 10000 O=OaD '=yVwQ R= s=Om Qy |=Q@ "OwW|t R=e;u}t= 9950 =@ Q@=Q@ q=@ OL Q=Okt "OvwW|t ?DQt |OwaY ?}DQD x@ w xOW O}rwD|R=Uxv=DU; '|R=UxOQWi VwQ |=Q@ Q=Okt u}= "OwW|t xDiQo Q_v QO |@}DQD |xQ=t;39 7064 w 13 7861 '12 9635 =@ Q@=Q@ ?}DQD x@ CNU |R=Uxv=DU; w sQvs=tD= x@ |Q=t; Ov}=Qi pQDvm 1 R=i 'q=@ pQDvm OL uOQm =O}B =@ "O};|t CUO x@|w} Q=vU wO uDiQo Q_v QO =@ |O=yvW}B |=yVwQ OQmrta '2 R=i QO "OUQ|tx@ pmW `@ Qt Q}}eD l} 'pw= |w} Q=vU QO "OwW|t |@=} RQ= Q}}eD |=Q@ hrDNtQ}}eD l} 'swO |w} Q=vU QO "OwW|t p=ta= pwYLt Q} wYD |wQ 5 QO 5 O=a@=|=yVwQ |Ovtv=wD "OwW|t p=ta= Q} wYD |wQ pUm}B 3 Ct=N[ x@ ?Qwtxr=@vO pw] \UwDt |=yQ=}at R= xO=iDU= =@ C=Q}}eD `} QU hWm QO |O=yvW}B|x]kv p[=iD "OwW|t |@=} RQ= �STDRL� xr=@vO pw] Q=}at h=QLv= w �ARL�|@=} RQ= |=Q@ |YN=W u=wva x@ R}v (" = � � �) |ak=w R= |v}tND Q}}eD'u}ov=}t Q}O=kt "OwW|t xO=iDU= Q}}eD |x]kv j}kO u}tND QO VwQ OQmrtaxOW VQ=Ro |OQmrta |=yXN=W u=wva x@ =yp[=iD |xv=}t w 'Q=}at h=QLv=

"CU==D 1 R= (�) =]N |x}L=v QO Qwv COW Q}O=kt QO Q}}eD u=R}t u}vJty|xR=Ov= =@ pUm}B QO Qwv COW C=Q}}eD "CU= xOW xDiQo Q_v QO OL=w 10G}=Dv "OvDU}v xOy=Wt p@=k KrUtQ}e sWJ =@ (� � 10) 10 |w=Ut =} QDtm'CU= xOy=Wt p@=k pwOH QO xm Qw] u=ty "CU= xOt; 1 pwOH QO |R=Ux}@W\UwDt w xr=@vO pw] \UwDt '(�) C=Q}}eD COW V}=Ri= =@ VwQ xU Qy QO

QY=va u}ov=}t �1;�;S(k) w Q}}eD |x]kv � 'Q} wYD |xOvQ=tW S 'x]@=Q u}= QO"OwW|t x@U=Lt Q} R CQwY x@ xm CU= Q}}eD |x]kv R= Oa@ ?}=Q[ Q=OQ@ s=k

(s� �)�1SX

t=�+1�t(k) (8)

1 R=i QO xOW xOR u}tND ?} Q[ u}t=k Q=}at h=QLv= w u}ov=}t �2k w�0;k

Cr=L R= Ov}=Qi GwQN X}NWD C}r@=k u=tRsy CQwY x@ xQ=t; u}= "OvDUyCr=L X}NWD |=Q@ "OQ=O =Q 32Q}}eD |x]kv u}tND Qw] u}ty w pQDvm CLDx=oQy "OwW|t xO=iDU= 33 �UCL� q=@ |xv=DU; OL l} R= pQDvm R= GQ=N|LqY= s=Ok= w OwW|t hkwDt O}rwD Ov}=Qi 'OQm Rw=HD UCL u=R}t R= xQ=t;|}=Hu; R= u}vJty "OQ}o|t CQwY pQDvm CLD Cr=L x@ Ov}=Qi CWoR=@ |=Q@'CU= xOW |L=Q] |}=tvCUQO |xv}W}@ OQm} wQ T=U= Q@ |rQDvm |xQ=t; xmw OQ}PB|t CQwY |r@k |xvwtv m w xvwtv u; u}@ |}xU}=kt xvwtv Qy |=R= x@VQ=Ro |}=yv |xQ=t; u=wva x@ C=U}=kt u}= |=Q@ xOt; CUO x@ u=R}t |xv}W}@xQ=t; |=Q@ Q=Okt u}= O=H}= x@ QHvt xm |}x]kv |UQQ@ =@ '?}DQD u}= x@ "OwW|t|xQHvB l} m "Ci=} CUO (�) Q}}eD |x]kv u}tND x@ u=wD|t 'CU= xOWOwW|t xDiQo Q_v QO C=@U=Lt sHL V}=Ri= R= |Q}owrH |=Q@ xm CU= lQLDts}_vD p@=k O}rwD |xNQJ u=tR w |D=@U=Lt |=yC}r@=k x@ xDU@ u; |xR=Ov= w

"CU=|=Q@ sRq |=yxvwtv O=OaD 'Ov}=Qi QO Q}}eD Qy RwQ@ R= Oa@ 'xQ=t; u}= R= xO=iDU= =@Q}}eD |x]kv w |ak=w Q}}eD |x]kv p[=iD u}vJty w xr=@vO pw] =} Q}}eD hWmO=OaD u}ov=}t "OwW|t C@F Ov}=Qi \UwD |O=yvW}B |rQDvm |x} wQ \UwD |v}tNDhWm =D sRq |xvwtv O=OaD Q=}at h=QLv= w (ARL) 34 Q}}eD hWm =D sRq |xvwtvp[=iD |=Q@ xv=}t w 'Q=}at h=QLv= 'u}ov=}t u}vJty w (STDRL) 35 Ci}W|=Q@ |}=yXN=W u=wva x@ (� � �) |ak=w Q}}eD |x]kv w |v}tND Q}}eD |x]kv

"CU= xOW xO=iDU= |O=yvW}B |=yVwQ |}=Q=m |xU}=kt w |@=} RQ=

|R=Ux}@W C=ar=]t "4|Q} wYD |wQ|R=Ux}@W|xar=]t 'xr=ktu}= |O=yvW}B |=yVwQ|}=Q=m|@=} RQ= |=Q@u=Wv =Q xJQ=B l} Ci=@ R= |}xvwtv 5 pmW "CU= xDiQo CQwY xJQ=B wv l} R=

"OyO|tCU= |y}O@ "OvQ}o Q=Qk xO=iDU= OQwt |}xOQDUo OQ=wt QO Ovv=wD|t =yxJQ=B

"xJQ=B Ci=@ R= |}xvwtv "5 pmW

7

"""pwYL

tQ}wYD

|Q}oQ=m

x@|=Q@|

}=yVwQ|

xaUwD"hrDNt C=Q}}eD |=Q@ |R=Ux}@W G}=Dv "1 pwOH

|R=UxOQWi CNU |R=Uxv=DU; sQv |R=Uxv=DU;UCL = 12=9635 UCL = 39=7064 UCL = 13=7861

pmW `@ Qt Q}}eD� ARL STDRL E(") std(") med(") ARL STDRL E(") std(") med(") ARL STDRL E(") std(") med(")

�1 105 56 115 98 98 93 116 12 65 00 218 19 220 09 210 58220 43171 50 69 01 57 26 63 06 57 43 46 00�2 8 22 3 48 0 90 2 51 0 00 188 36 196 57 181 31196 32114 00 7 88 2 87 0 64 2 11 0 00�3 4 03 1 18 �0 09 0 93 00 56 04 44 27 46 99 44 04 38 00 4 29 1 27 �0 04 0 85 0 00�4 2 53 0 69 �0 9 0 45 0 00 8 75 1 63 0 25 0 77 0 00 2 61 0 75 �0 09 0 47 0 00�5 1 86 0 55 �0 03 0 26 0 00 5 55 1 04 0 01 0 33 0 00 1 91 0 47 �0 07 0 36 0 00�6 1 34 0 49 �0 10 0 44 0 00 3 95 0 73 �0 02 0 14 0 00 1 49 0 52 �0 03 0 30 0 00�7 1 06 0 24 0 00 0 00 0 00 3 10 0 46 �0 01 0 10 0 00 1 08 0 27 �0 01 0 10 0 00�8 1 00 0 00 �0 01 0 10 0 00 2 45 0 50 0 00 0 00 0 00 1 01 0 10 0 00 0 00 0 00�9 1 00 0 00 �0 01 10 0 00 2 05 0 26 0 00 0 00 0 00 1 00 0 00 0 00 0 00 0 00�10 1 00 0 00 0 00 0 00 0 00 1 90 0 30 0 00 0 00 0 00 1 00 0 00 0 00 0 00 0 00

?Qwt Q}}eD� ARL STDRL E(") std(") med(") ARL STDRL E(") std(") med(") ARL STDRL E(") std(") med(")

�1 175 74 174 09 170 67174 69127 00 231 98 216 64 224 85216 43 170 5 100 48 107 14 95 64106 59 59 50�2 54 31 45 61 46 95 46 15 39 00 219 05 208 32 214 69210 21 14 00 35 49 31 99 28 68 31 58 19 50�3 12 03 6 54 4 01 5 83 2 00 81 160 72 22 70 28 68 65 12 50 9 03 3 30 1 43 2 79 1 00�4 5 78 1 83 0 24 1 29 0 00 45 59 48 49 40 44 45 01 12 00 5 30 1 56 �0 07 1 17 0 00�5 4 14 1 29 0 02 0 85 0 00 28 28 22 33 19 02 22 51 9 50 3 56 0 99 �0 15 0 73 0 00�6 2 93 0 93 �0 15 0 78 0 00 9 61 2 34 0 74 1 79 0 00 2 81 0 69 �0 09 0 62 0 00�7 2 39 0 76 �0 02 0 32 0 00 6 75 0 31 0 01 0 44 0 00 2 13 0 56 �0 10 0 39 0 00�8 1 99 0 58 �0 05 0 39 0 00 5 35 0 95 0 03 0 54 0 00 1 74 0 52 �0 07 0 36 0 00�9 1 71 0 48 �0 01 0 10 0 00 4 20 0 93 0 05 0 33 0 00 1 59 0 49 �0 01 0 10 0 00�10 1 4 0 49 �0 01 0 10 0 00 3 45 0 72 0 03 0 33 0 00 1 22 0 42 �0 02 0 14 0 00

XwYN x@ 'C=@U=Lt |=Q@ R=}v OQwt sHL w u=tR Cw=iD u}= "CU= |R=UxOQWi=@ |}=yOv}=Qi u}vJty w OvDUy �100 |UQR=@ OvtR=}v xm T=UL `}=vY QOw CaQU x@ xHwD =@ O}=@ u=YYNDt w CU= x_Lqt p@=k 'q=@ O}rwD CaQU?=NDv= =Q Q_v OQwt VwQ |O=} R C}U=UL w CkO =@ 'Ov}=Qi C=YNWt Q}=U

"Ovvm

|Q}oxH}Dv "5xHwD OQwt Q}N= |=yp=U QO xm '|Q=t; Ov}=Qi pQDvm u} wv |=yOQm} wQ R= |m}"CU= |Q=t; Ov}=Qi pQDvm QO Q} w=YD VR=OQB R= xO=iDU= 'CU= xDiQo Q=Qk |v=w=Qi

|R=UxOQWi |=yVwQ u}vJty "CU= xDi=} Vy=m Q}}eD |x]kv hWm QO C=i=QLv=|}=ORxiwv VwQ x@ C@Uv =Q |QDy@ ?D=Qt x@ OQmrta sQv |R=Uxv=DU; =@ |}=ORxiwv wQ_vt R= w C=Q}}eD |=yCOW s=tD hWm QO CNU |R=Uxv=DU; R= xO=iDU= =@x@ 'pmW `@ Qt C=Q}}eD QO "OvyO|t u=Wv OwN R= |OQmrta |=yXN=W s=tDVwQ 'Q}}eD COW Q}O=kt s=tD |=R= x@ ?Qwt C=Q}}eD QO w (� � 2) |=R=u}= "OQ=O C=Q}}eD hWm QO |QDy@ OQmrta sQv |R=Uxv=DU; R= xO=iDU= =@ |}=ORxiwvCW=O xHwD O}=@ =t= CU= x_Lqt p@=k lJwm C=Q}}eD QO XwYN x@ Cw=iDQ@=Q@ |R=UxOQWi VwQ QO Q} wYD l} |=Q@ xQ=t; |x@U=Lt w VR=OQB u=tR xm|=[i u}vJty "CU= x}v=F 4 56 Q@=Q@ |}=ORxiwv |=yVwQ QO w x}v=F 1 108VwQ R= QDW}@ ?D=Qt x@ x} RHD K]U x@ xDU@ |}=ORxiwv |=yVwQ |=Q@ |D=@U=Lt

8

2 1|xQ

=tW'35

�1|xQwO

'�139

8u=DUt

R�h}QW

C}Q}Ot

w`}=vY

|UOvyt CLD Cr=L x@ Ov}=Qi `} QU uOv=OQoR=@ |=Q@ Q}}eD |x]kv hWm u}vJty w Ov}=Qi

|=yQ=Owtv Q}=U u}vJty w lHwt |x}=B `@=wD Q}=U R= xO=iDU= "CU= pQDvmxDiQo Q_v QO |D; C=ar=]t QO Ovv=wD|t xm OvDUy |r�=Ut xrtH R= pQDvm

"OvwW

'CNU |R=Uxv=DU; R= xO=iDU= =@ |}=ORxiwv '|R=UxOQWi VwQ xU 'xr=kt u}= QO|=ylHwt |=v@t Q@ xU Qy xm - sQv |R=Uxv=DU; R= xO=iDU= =@ |}=ORxiwv w|UQQ@ C=HwUvt |wQ |O=yvW}B |=yVwQ OQmrta "OW x�=Q= - Ov=|Oa@ l}QO C=Q}}eD hWm QO =yVwQ ?U=vt OQmrta Qou=Wv |R=Ux}@W C=ar=]t w OW

=yCWwv=B1. multivariate exponentially weighted moving average(MEWA)2. multivariate cumulative sum3. geometric pro�les4. machine vision systems5. Jig and Fixture6. pixel7. spatial domain8. frequency domain9. Tico10. Sari-Sarraf11. Goddard12. Ngan13. surface barrier layer14. machine learning15. generalized likelihood ratio test16. quantile-quantile plot17. low rank tensor decomposition18. functional principle component analysis19. sharp changes20. orthonormal21. contrast22. alignment23. signal to noise ratio24. vectorization25. approximation26. detail27. compression28. denoising29. hard threshold DE noising30. soft threshold dnoising31. generalized likelihood ratio32. change point33. upper control limit34. average run length35. standard deviation of run length

�References� `@=vt1. Montgomery, D.C., Introduction to statistical quality

control, John Wiley & Sons, 6th Edition, Wiley seriesin probability and statistics (2008).

2. Noorossana, R., Saghaei, A. and Amiri, A., Statisticalanalysis of pro�le monitoring, John Wiley & Sons, 1stEdition, Wiley series in probability and statistics (2011).

3. Siew, L.H., Hodgson, R.M. and Wood, E.J., \Texturemeasures for carpet wear assessment", Pattern Analy-sis and Machine Intelligence, IEEE Transactions, 10(1),pp.92-105 (1988).

4. Latif-Amet, A., Ert�uz�un, A. and Ercil, \A. An e�cientmethod for texture defect detection: Sub-band domainco-occurrence matrices", Image and Vision computing,18(6), pp.543-553 (2000).

5. Tico, M., Kuosmanen, P. and Saarinen, J., \Waveletdomain features for �ngerprint recognition", ElectronicsLetters, 37(1), pp.1-12 (2001).

6. Sari-Sarraf, H. and Goddard, J.S., \Robust defect seg-mentation in woven fabrics", Computer Vision and Pat-tern Recognition", IEEE Conference on Computer Soci-ety, CA, USA, pp. 938-944 (1998).

7. Ngan, H.Y., Pang, G.K., Yung, S.P. and et al. \Waveletbased methods on patterned fabric defect detection",Pattern recognition, 38(4), pp.559-576 (2005).

8. Lin, H.D., \Computer-aided visual ispection of surfacedefects in ceramic capacitor chips", Journal of MaterialsProcessing Technology, 189(1), pp.19-25 (2007).

9. Megahed, F.M., Woodall, W.H. and Camelio, J.A., \Areview and perspective Journal of Quality Technology,on control charting with image data", 43(2), pp.83-98(2011).

10. Megahed, F.M., Wells, L.J., Camelio, J.A. and et al.\A spatiotemporal method for the monitoring of imagedata", Quality and Reliability Engineering International,28(8), pp.967-980 (2012).

11. He, Z., Zuo, L., Zhang, M. and et al. \An image-basedmultivariate generalized likelihood ratio control chart fordetecting and diagnosing multiple faults in manufactur-ing products", International Journal of Production Re-search, 54(6), pp.1771-1784 (2016).

12. Wells, L.J., Megahed, F.M., Niziolek, C.B. and et al.\Statistical process monitoring approach for high den-sity point clouds", Journal of Intelligent Manufacturing,24(6), pp.1267-1279 (2013).

13. Yan, H., Paynabar, K. and Shi, J., \Image-based pro-cess monitoring using low-rank tensor decomposition",IEEE Transactions on automation science and engineer-ing, 12(1), pp.216-227 (2015).

14. Colosimo, B.M. \Modeling and monitoring methods forspatial and image data", Quality Enginnering, 30(1),pp.94-111 (2018).

15. Menafoglio, A., Grasso, M., Secchi, P. and et al. Pro�lemonitoring of probability density functions via Simplicialfunctional PCA with application to image data, Techno-metrics, Published online, (2018).

16. Ogden, R.T. Essential wavelets for statistical applica-tions and data analysis, Birkhauser (1997).

17. Gonzalez, R.C. and Woods, R.E., Digital image process-ing, Prentice Hall (2007).

18. Shamos, M.I. \Geometric Intersection Problems", 17thIEEE Symposium on Foundations of Computer Science,TX, USA, pp.208-215 (1976).

9