Improved EWMA schemes for monitoring the ratio of two normal random variables

Monitoring the ratio of two normal random variables, which is usually denoted as RZ, is one of the most important directions in statistical process control (SPC). In production scenarios, when the product specification is related to the relative ratio of two components in a mixture, or when the ratio represents a property of the product, or the difference between a product's quality measurement before and after an operation (such as a chemical reaction), the product quality can be improved by applying monitoring schemes for RZ. To further enhance the sensitivity of traditional RZ schemes in detecting process changes, especially small and moderate ones, this paper proposes an improved exponentially weighted moving average (IEWMA) monitoring scheme. The run length (RL) distribution of the proposed IEWMA-RZ scheme is obtained by using the Monte-Carlo (MC) simulation. The superiority of the proposed monitoring scheme is shown by comparing with the existing EWMA-RZ scheme.