Economic <i>X</i> Charts with Asymmetric Control Limits

Abstract

When assumptions such as equal probability of shift of process mean upwards or downwards, perfect measurement, and constant process variability are relaxed, a reasonable alternative to traditional single assignable cause variables control charts seems to be X̄ charts with control limits at unequal distances from the central line. The statistical properties and the economic design of X̄ charts with asymmetric control limits are studied and compared to those of traditional charts. It is found that while the assumptions of equal probability of upward or downward shift and of perfect measurement are critical to the estimation of operational characteristics and the optimal choice of control limits location, the assumption of constant variability does not have as noticeable an effect.