A New EWMA Control Chart For Monitoring The Ratio Of Two Normal Variables

In many fields,there is the need to monitor quality characteristics defined as the ratio of two random variables.Therefore,on-line monitoring of quality characteristics become particularly important.Some production processes may include the following situations:the correct proportion of a property between two ingredients or elements within a product should be maintained under statistical control production conditions;implementation of quality control procedures where the performance of a product is measured as a ratio before and after some specific operation,for example a chemical reaction following the introduction of an additive in a product and monitoring of a chemical or physical property of a product,which is itself defined and computed as a ratio.Monitoring the ratio of random variables is widely used in many fields such as economics,biology,and transportation systems.Firstly,this paper analyzes the robustness of Exponentially Weighted Moving Average(EWMA)control chart,which is an existing control chart to monitor the ratio of two normal random variables.And consider the effect of parameter estimation on the performance of the EWMA control chart when different sample units are used to estimate the parameters under different sample units in the Phase I.Secondly,this paper proposes an improved one-side EWMA control chart of monitoring ratio,then analyzes the performance of the control chart,and compares it with the existing EWMA control chart of monitoring ratio.The simulation results show that the improved control chart proposed in this paper has better performance in the practical application of monitoring the ratio of two normal random variables.Finally,the practical application of the proposed control schemes is discussed with an illustrative.