The design of two-sided S 2-chart with estimated in-control process variance based on conditional median run length

Abstract

ABSTRACT Monitoring both decrease and increase in the process variance has a significant value in effectively implementing any quality improvement program. This paper considers the Phase II two-sided -chart with estimated in-control (IC) process variance and evaluates its performance under the conditional perspective. The conditional perspective focuses on the conditional (given parameter estimates) IC run length distribution and its associated properties to evaluate chart’s performance with estimated parameters. Thus, it accounts for the practitioner-to-practitioner variability and, hence, provides a comprehensive understanding of the chart’s performance. To guard against unnecessary false alarms, we design the chart using the exceedance probability criterion under the conditional perspective, which ensures the desired IC performance with a high probability. Furthermore, because the median run length (MRL) is a more suitable representative of run length (RL) distribution, we examine the chart’s performance in terms of the median of the conditional RL distribution. We also discuss the biasedness property of the two-sided -chart, which is an outcome of the skewed nature of the charting statistic. It is shown that the proposed MRL-unbiased chart requires about within 500 Phase I observations to achieve a reasonably good IC and OOC performance.