One important tool of statistical process control (SPC) is control chart . The occurrence of non-conforming items or defects in a manufacturing process has been widely monitored by the time between events (TBE) control chart which is based on the inter-arrival times of non-conforming items . It is often assumed that the occurrence of defects is modelled by a homogeneous Poisson process and then the TBEs follow independent and identically distributed (i.i.d.) exponential variables . The average run length (ARL( is widely used to evaluate the performance of control charts . The ARL is de?ned as the average number of samples to be collected until the control chart issues an out-of-control signal .
