The design of two-sided S2-chart with estimated in-control process variance based on conditional median run length

Abstract

ABSTRACTMonitoring 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 S2-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 S2-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.KEYWORDS: Average run lengthconditional and unconditional performanceexceedance probability criteriaconditional run lengthunbiasedness AcknowledgementsThe authors thank the anonymous referees and the editor for their valuable comments. First author’s work was supported by the Banaras Hindu University, India under the IoE Scheme (Grant Number 6031). The second author’s work was supported by a Research Fellowship from University Grant Commission (UGC), India within the scope of the doctoral program at the Department of Science and Technology-Centre for Interdisciplinary Mathematical Sciences (DST-CIMS), Banaras Hindu University, Varanasi.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe work was supported by the Banaras Hindu University with grant number IoE-6031.Notes on contributorsNirpeksh KumarNirpeksh Kumar is an associate professor at the Department of Statistics, Banaras Hindu University, Varanasi (BHU), India. He received his Master’s and PhD degree in Statistics from the University of Allahabad, India. He was awarded SARChi Postdoctoral fellowship at the Department of Statistics, University of Pretoria, South Africa. He has published in numerous accredited peer-reviewed journals and has presented his research at several national and international conferences. His research interests include statistical outlier detection, statistical process/quality control, and time series analysis.Sonam JaiswalSonam Jaiswal has an MSc degree in Statistics and Computing from the DST Center for interdisciplinary Mathematical Sciences (DST-CIMS) at BHU, India. She is currently a PhD student at DST-CIMS, BHU. Her main area of research interest is in statistical process/quality control.