X-bar control chart design with asymmetric control limits and triple sampling

Abstract

The aim of the present study is to propose a control chart with asymmetric limits and triple sampling. Two topics have deserved closer attention of researchers in the process control field. The parameter variation is a construction approach for the most economic and robust control chart in the statistical control process. The present study has contributed to these two topics, since it focused on using the statistical control chart with asymmetric limits through a non-linear sampling procedure (non-fixed), with three possible decision regions. The proposition of asymmetric limits is justified by the fact that the criticity of a non-conform item, in some cases, is higher or lower depending on whether the monitored parameter deviation is positive or negative. The sampling cost is another aspect to be taken into consideration. Thus, the possibility of re-sampling the process was suggested and a new chart design was proposed when the conditions “criticity depending on the deviation sign” and “control process cost” were considered. The effects of estimating the statistical parameters were also taken into account in the analysis. The chart design was assessed through the mathematical expectation of the mean number of samples collected until a point out of control was detected. Numerical methods were adopted in the calculation of the control limit so that we could find a false positive of 0.27%. The main result of this work was to propose a structure for the use of this type of control chart.