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 beeninvestigated in literature. The industrial implementation of these control charts involves: monitoringof processes where the correct proportion of two ingredients or elements within a product should bemaintained under statistical control; monitoring of quality characteristics measuring the performance of aproduct as the ratio before and after some specific operation, for example a chemical reaction followingthe introduction of an additive in a product; 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 witheach subgroup consisting of > 1 sample units. Several tables are generated and commented to show thestatistical performance of the investigated chart for known and random shift sizes affecting the in-controlratio. A performance comparison with another control chart already proposed in literature shows theadvantages associated to the implementation of the Synthetic control chart. An illustrative example fromthe food industry is given for illustration.