38 ZACHARY G.STOUMBOS AND MARION R.REYNOLDS.JR substituting in (A2).we obtair 6=-2+. (A4 the control statistic for this SPRT is.Similarly to atistrdltiona on the starting vaie Thus.for=+2 (or equivalently.=( n)/(2a.the contr iof the SPR OC(u)=p(glu)+ oc(u')f(u'lu)du' a factor of2）,and for =(g-u-+） -2 (or equivalently of th +厂ocfu-uaw (B2) (Al)(apart from the starting value o of the contro statistic and a factor of (-2%)). endix B.Ex geometric distribution with mean 1/(1-OC(0)) conditional on the starting value uo dfo the ARL.ATS.ANOS,and SSATS ARL(to)=1+ARL(0)OC(uo) of the SPRT chart.The dependence of these expres ss parameter (or equivalently8 -1+(98) qual to one sprt with sta pected addi Given i,let f(u'lu)denote the one-step transition density of the ional numbe rof SPRT's with starting values 0,whe contr om any poin e rst SPR Ocd the fir rst SPR th density of the ATS of the SPRT chart.conditional on the starting (th value uo of the control statistic.ATS(uo),is given by ote the ATS(uo)=do+(ARL(uo)-1)d and p( =6+(9)4 (B3) At the ith SPRT,if the first observation is= ith sta ANOS()=ASN(uo)+ANOS(0)OC(u) the ASN of a SPRT whe ASN(uo)+(ARL(0)-ASN(O))OC(wo) this SP -ASN()+(AS((B) Oc(o) the control statistic.satisfies the integral quation That ASN(u)=1+ ASN(u)f(uju)du' additional number of o =1+ASN(u)f(u'-u)du'.(B1) ity OC(u)). Note that ASN(u)=E(Nlu),for all i. Journal of Quality Technology Vol.29.No.1.January 1997 Reproduced with permission of the copyright owner.Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission