Quality degradation due to shipment of nonconforming product under statistical process control in the absence of quarantining

In a statistical process control regime using control charts, the question is addressed of the amount of nonconforming product shipped if quarantining is not employed back to the beginning of the run rule detecting an out-of-control condition. The approach is a Monte Carlo calculation by computer using a random number generator to assign the variation in the variable about a process mean value X deviating from the design mean X[sub o] while the process is set out of control numerically (X [ne] X[sub o]). A subroutine analyzes the resulting [bar X] values as batches are created mathematically. Outputs are the fraction of batches shipped, the average time interval before detection, the fraction of batches shipped, the average time interval before detection, the fraction of nonconforming parts in shipped batches, the number of nonconforming parts shipped per 1,000 parts produced, and the number of nonconforming batches detected by each run rule as a function of time after the initiation of the out-of-control condition. It is found that the number of nonconforming parts shipped per 1,000 parts produced peaks at an error value of [vert bar] X [minus] X[sub o] [vert bar] = 3.0[sigma][sub [bar X]] to 3.5[sigma][sub [bar X]]. Implications formore » quarantining and Just In Time inventory are discussed. The reduction of nonconforming material shipped if NDT with a known probability of detection is employed is also discussed.« less