A Simple Nonparametric Quality Control Chart for Monitoring Students’ GPAs

Abstract

The Shewhart sign control chart is a distribution-free (or nonparametric) chart that was proposed by Amin, Reynolds, and Bakir [1] to monitor a process median. However, those authors, neither supplied tables for the control limits, nor did they present a real-world application for the chart. As a result, practitioners have had no guidance on how to apply the chart to their real-world data. To remedy these discrepancies, the necessary control limits are generated and the chart is applied to real-world data related to education, in this paper. The Shewhart sign control chart is applicable to any process that has a continuous probability distribution; no assumption of symmetry or normality is required. In contrast, the traditional Shewhart XBar (or mean) chart requires the process to be normally distributed. If the process is not normally distributed, the XBar chart will lead to an incorrect specification of the control limits, the average run length and the false alarm rate. The sign chart has a very simple charting statistic which is the difference between the number of observations above and the number below a pre-specified target. As a real-world application, the Shewhart sign control chart is used to monitor students’ GPAs over time. The purpose is to detect any statistically significant shifts in students’ GPAs from a specified target GPA value.