Control chart limits based on true process capability with consideration of measurement system error

Abstract

Shewhart X-and R control charts and process capability indices, proven to be effective tools in statistical process control are widely used under the assumption that the measurement system is free from errors. However, measurement variability is unavoidable and may be evaluated by the measurement system discrimination ratio (DR). This paper investigates the effects of measurement system variability evaluated by DR on the process capability indices Cp and Cpm, on the expected non conforming units of product per million (ppm), on the expected mean value of the Taguchi loss function (E(Loss)) and on the Shewhart charts properties. It is shown that when measurement system variability is neglected, an overestimation of ppm and underestimation of E(Loss) are induced. Moreover, significant effects of the measurement variability on the control chart properties were made in evidence. Therefore, control charts limits calculation methods based on process real state were developed. An example is provided in order to compare the proposed limits with those traditionally calculated for Shewhart X-, R charts.