Asymmetry Considerations in Constructing Control Charts: When Symmetry Is Not the Norm

Abstract

Control charts (esp. X¯-chart) are proven and useful tools to preserve process alignment with its design mean. The control charts’ limits are designed symmetrically around the process’s mean. The assumption of symmetry is justifiable when assuming that the measurements are infinite. Typically, these assumptions are warranted since the measuring resolution is significantly (by orders of magnitude) lower than the deviation of the controlled process. However, when the measuring device has a resolution of the same order of magnitude as the standard deviation of the controlled process, the symmetrical nature is no longer justified. In low-resolution measurement process control, symmetry is not the norm and both these control limits should be built asymmetrically. To help remedy this issue, this article explores the asymmetrical nature of the low-resolution measurement and suggests a new (asymmetric) control limit based on false-alarm-required probabilities. This represents a novel approach to the problem