Setting process control chart limits for rounded-off measurements

Measurements can often be imprecise and subjected to rounding-off. Typically, this rounding-off is ignored and assumed to have little to no effect. However, when the measuring scale step is not negligible, it may affect statistical control tools such as $$ -chart. Designing statistical process controls without considering the effects of rounding leads to high exposure to false negative results. This study illustrates the effects of rounding on the X-chart and shows that the result may further deteriorate due to asymmetry (incompatibility of the process and the measuring device parameters). A new simple method to design control limits is proposed, based on maintaining the original characteristics of the chart as devised by Shewhart.