44 SUSAN L.ALBIN.LAN KANG.AND GERALD SHEA run rules.that is:(1)no run rules:(2)2/3 Sam Here.simulation is used to estimate Aris for all Side rule only:(3)2/3 Opposite Side rule the pro s control procedures,except the chart one ativewould have been to mpe simulate the X and MR te X Chart with and without Run Rules:Thes runs rules.We choose to use simulation.Essentially (with less htty lines of code) and MR Charts with Rules alternatives and without Rur graphs. The X en 110 X and EWMA Chart with and without Run se published results and numerical calculations to Rules:These alternatives are convenient,again, that there is ony one grapl For the simulation.the in-control process has interpretation and standard deviation 1,without loss of shina shift 3,and 4.The 品0A222 Each ARL is estimated by simulating n indepen The arls for an x chart a replicates of the process The replicates yield a outside of the false-alarm is 1/a=370 where a =0.0027 is the fals The estimate o s standard error are detection is 1/3 whereis the probability a specified i=∑ shift is detected on one observation run rules the MR chart,an () the where etween 8=n-1 dramdM procedure to solve integ quations to find ARLs ias in the To find ARLs for the EWMA Crowder (1987a)use first observation an alarm can occur only if the ob EWMA d EWMA n A ion is outside the art control l if the oh c)nd acccei and Lucas (use the ervation is outside the x chart or Mr chart control imits.For the third and remaining observatio with run rules by applying concepts in Champ and r MR chart control limits o 1 Voodal1(1987. Thus the control procedure does not reach a"steady ournal 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