Steady-state ARL analysis of ARL-unbiased EWMA-RZ control chart monitoring the ratio of two normal variables

摘要

Very recently, control charts for monitoring the ratio of 2 normal variables have been investigated in statistical process control. In the two-sided case, however, these control charts tend to be average run length (ARL) biased, in the sense that some out-of-control ARL values are larger than the in-control ARL. This paper proposes an ARL-unbiased EWMA control chart for monitoring of this kind of ratio with each subgroup consisting of n1 sample units. Also, to study the long-term properties of ARL-unbiased EWMA-RZ control chart, we investigate the steady-state ARL. Several tables and figures are given to show the statistical properties of the proposed control charts. The comparison results show that the proposed ARL-unbiased chart outperforms other two-sided control charts in terms of the zero-state and steady-state ARL. An example illustrates the use of this chart on a real quality control problem from the food industry.