A Synthetic Control Chart for Monitoring the Ratio of Two Normal Variables

Very recently, monitoring the ratio of two normal random variables by means of control charts has been investigated in statistical process control literature. The industrial implementation of these control charts involves monitoring of processes where the correct proportion of two ingredients or elements within a product should be maintained under statistical control, monitoring of quality characteristics measuring the performance of a product as the 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. This paper presents a Phase II synthetic control chart with each subgroup consisting of n > 1 sample units. Several tables are generated and commented to show the statistical performance of the investigated chart for known and random shift sizes affecting the in‐control ratio. A performance comparison with another control chart already proposed in literature shows the advantages associated to the implementation of the synthetic control chart. An illustrative example from the food industry is given for illustration.