Economic and Sustainable Design of X Control Chart with Measurement Errors

The effect of non-normality and measurement errors are usually overlooked when designing control charts. Measurement and inspection errors occur in many industrial situations and their effect was shown in many papers in the literature to be significant. To counteract the effect of measurement errors and strive for a sustainable design of X control charts, this paper proposes extending the model of Duncan (1956) for the economic design of X cotrol charts when measurement errors exist. To mitigate the impact of the measurement errors, repeat measurements is instituted. The proposed model finds the optimal chart design parameters which are the sample size (n), the sampling frequency (h) and the control chart width (k). In this case also the model determines the number of repeat inspections (m) for the measurements. A solution procedure is proposed for the model and the results show savings in the costs of maintaining the X control chart that ranges between 8.53% to 47.39% when compared to Duncan model which assumes no measurements errors. The results en hance the use and sustainability of the charts.