Performance Analysis of Interval Type-2 Fuzzy <inline-formula><math display="inline"><semantics><mrow><mover><mi mathvariant="bold">X</mi><mo>¯</mo></mover></mrow></semantics></math></inline-formula> and R Control Charts

Statistical process control (SPC) is one of the most powerful techniques for improving quality, as it is able to detect special causes of problems in processes, products and services with a remarkable degree of accuracy. Among SPC tools, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mi mathvariant="normal">X</mi><mo>¯</mo></mover></mrow></semantics></math></inline-formula> and R control charts are widely employed in process monitoring. However, scenarios involving vague, imprecise and even subjective data require a type-2 fuzzy set approach. Thus, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mi mathvariant="normal">X</mi><mo>¯</mo></mover></mrow></semantics></math></inline-formula> and R control charts should be coupled with interval type-2 triangular fuzzy numbers (IT2TFN) in order to add further information to traditional control charts. This paper proposes a performance analysis of IT2TFN and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mover><mi mathvariant="normal">X</mi><mo>¯</mo></mover></mrow></mrow></semantics></math></inline-formula> and R control charts by means of average run length (ARL), standard deviation of the run length (SDRL) and RL percentile. Computer simulations were carried out considering 10,000 runs to obtain ARL, SDRL and the 5th, 25th, 50th, 75th and 95th RL percentiles. Simulation results reveal that the proposed control charts increased fault detection capability (speed of response) and slightly reduced the number of false alarms in processes under control. Moreover, it was observed that, in addition to superior performance, IT2TFN <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mi mathvariant="normal">X</mi><mo>¯</mo></mover></mrow></semantics></math></inline-formula>-R control charts proved to be more robust and flexible when compared to traditional control charts.