QS系列培训课程--统计过程控制ＳＰＣ学习与理解（PDF 151页）(2)

QSStudyandUnderstandingofStatisticalProcessControlSPCSPC-1StudyandUnderstandingofStatisticalProcessControl(SPC)来自[1]1-3125[2]X+∞∞−=−−xexfx,21)(222)(σµσπ(1-1),µ,σ2,σXµσX~N(µσ,2)f(x)1-4,:(1)x=µ,0h,fhfh()()µµ−=+(1-2)(2)x=µ,f(x):f()µπσ=12(1-3)xµ,f(x)来自[2]来自(3)σ,µ,f(x)ox,,1-5f(x)µ(4)µ,σ,f(x)1-6σ,;,(5)XF(x)Xx来自(Xx)FxPXxftdtedtxxt()()()()===−∞−∞−−∫∫12222πσµσ(1-4)F(x)1-7x→+∞,F(x)→1,f(x)1,−∞+∞−∞+∞−−∫∫==fxdxedxx()()121222πσµσF(x)1-8x=µF(µ)=0.5(6)µ=0,σ=1,φ(z)Φ(z),φπ()zez=−1222(1-5)dteztz2221)(−∞−∫=Φπ(1-6)Φ(z),(1:),X~N(µσ,2),Xdteσ2π1F(x)222σµ)(tx−−∞−∫=(1-7),F(x)(1-6),(1),F(x):Zx=−µσ(1-8)ZN~(,)01ut=−µσ(1-9)(1-7):)()(2121)(2222σµππσµ−Φ=Φ===−∞−−∞−−∫∫xZdueduexFuZux(1-10)来自~N(10.04,0.01),==2,04.10σµ001.,=0.1σ,10.000.151-10P=P(X9.85)+P(X10.15),1-10P,(1-8)ZxN=−µσ~(,)01Z,1-11φ()Z,LSLUSLZZLZu9.11.004.1085.9σµLSL−=−=−=LZ1.11.004.1015.10σµUSL=−=−=uZ来自(x9.85)PZl=P(ZZL)=P(Z-1.9)=P(x9.85),P(x10.15)PZu=P(ZZu)=P(Z1.1)=P(x10.15),(1)PZlPZu(7)XNNXNnnn111222222~(,),~(,),,~(,)µσµσµσXL,,YXXXNnnn=++++++++121212222LLL~(,)µµµσσσ(8)E(X)D(X)EXxfxdxxedxx()()()===−∞∞−∞+∞−−∫∫12222πσµµσ(1-11),Xdx)f()(dx)(f))(()(]))([()(222xxxXExXDXEXEXDµ−=−==−=∫∫∞∞−∞∞−=−=−∞∞−−∫1222222πσµσµσ()()xedxx(1-12)XE(X)D(X)DXX()()=σσ:a)C,E(C)=C(1-13)来自)X,C,ECXCEX()()=⋅(1-14)c)X,Y,EXYEXEY()()()+=+(1-15)EXXEXEXnn()()()11++=++LL(1-16)d)X,Y,E(Y)E(X)E(XY)=(1-17):a)C,D(C)=0(1-18)b)X,C,DCXCDX()()=⋅2(1-19)c)X,Y,DXYDXDY()()()+=+(1-20)DXXDXDXnn()()()11++=++LL(1-21)1.4[1](1)1-1,(2)1-1(3)(4)X,ixi,n:xxxn12,,,L,X1-1,X,n,nxxn1,,L,XX(5)xxxn12,,,LX,,xiXini(,,,)=12LXXXn12,,,L,XiX,Xn,xxxn12,,,L来自(6)XXXn12,,,LX,gXXn(,,)1L,g,gXXXn(,,,)12Lxxxn12,,,LXXXn12,,,L,gxxxn(,,,)12LgXXXn(,,,)12L,X~N(µσ,2),XXXn12,,,LX,XnXini==∑11,X(7)X~N(µσ,2),XXXn12,,,L,()XnXini==∑11,EX()=µ(1-22)DXn()=σ2(1-23)XNn~(,)µσ2(1-24),EX()µ,DX()σ2n,n,Xµ(8)X~N(µσ,2),XXXn12,,,LX,X()S2()µ2σin1iXn1Xµ∑=∧==(1-25)2in1i22)X(X1n1Sσ−−==∑=∧(1-26)XS2XXXn12,,,Lxxxn12,,,L,xnxini==∑11(1-27)snxxini21211=−−=∑()(1-28)来自(x),P(Xx):XNZXN~(,),~(,)µσµσ201=−XOZZX,ZX,1-13baXσµXσ1Z+=−=(1-29)a=1σ(1-30)b=−µσ(1-31),Z,Φ(Z)(1,Φ(Z))1-13,ZΦ(Z),1-12F(x)=Φ(Z)来自[1]来自()100(n=100),():来自[]:,()xii(,,)=1100L,Fxi()xii(,,)=1100LFxii()(,,)=1100LFxi():,,100,,50,10-25,,1.27,1.551.265~1.55551.555-1.265=0.29,0.03(),101-1F(x)x,x(,)−∞+∞,1.265~1.295−∞~.1295,1.265,1.565,01,1.295,1.325,,1.535,1-14来自µσ1-15x=µ,F(µ)=0.5;σµx−=,15.9%σ)F(µ=−µσF(x)=50%1.405µ=∧F(x)=15.9%1.358σµ=−∧∧,=−=∧∧1.358µσ140513580047...−=1-151.6[1](1)nEn,,,n,E,,1-1,n,,nn来自(2)nE:AA,ApP(A)=,Aqp1)AP(=−=;En,n(Bernoulli),(3)XnA,X,0,1,,n,PXknkPPnknk()(),,,,,==−=−1012kL(1-32)nknknk=−!!()!(1-33)Xn,P,X~B(n,p)X1-16X~B(15,0.10)p(X=k)n10,p0.1,np)(λk!eλλk=−nkppknk−−()1,PXknkppekknkk()()!==−≈−−1λλ(1-34),λ=npFxPXxnkppekkxknkkxk()()()!==−≈=−=−∑∑001λλ(1-35)npp)(1pknkE(X)knkn0k=−=−=∑(1-36)DXkEXnkppnppknknk()(())()()=−−=−=−∑0211(1-37)来自~B(15,0.10)p(X=k)pnp1.7[1]X0,1,2,L0,1,2,=k,k!eλk)P(Xλk−==(1-38)λ0XλX~()πλ1-17P(X=k)FxPXxekkxk()()!===−∑0λλ(1-39)F(x)(2)cu来自(X=k)EXkekkk()!===∞−∑0λλλ(1-40)DXkEXekkk()(())!=−==∞−∑02λλλ(1-41)1.8,1-1(),,来自(1-18)(1)()(2)()(3)()1-18[3](1)()(2)()(3)()1-19来自来自[3](a)();(b)来自[3]a,b,,,来自