Semi-Sequential One-Shot Monitoring of Small Disorders With Controlled Type I Error Rate

Abstract

We propose a simple two-stage monitoring rule for detecting small disorders in a two-sample location problem. The proposed rule is based on ranks and hence is nonparametric in nature. In the first stage, we use a sequential monitoring scheme to decide the necessity of employing a location test at some point of time. If there is urgency, we simply use a two-sample Wilcoxon rank sum test in the second stage. This leads to a semi sequential one-shot monitoring procedure. We study some asymptotic performance of the proposed rule. We also present some numerical findings obtained through Monte Carlo studies. The proposed rule meets the challenge of controlling type I error rate in sequential monitoring of an incoming series of observations.

Keywords:

• Controlling Type I error rate
• Curved stopping boundaries
• Monitoring structural changes
• One-shot test
• Rank sum statistic
• Semi-sequential monitoring
• Sequential Monte Carlo

Mathematics Subject Classification:

• 62G10
• 62L05

Acknowledgments

The author is grateful to the Associate Editor and two unknown reviewers for their critical suggestions to improve the article. Thanks are due to Council of Scientific and Industrial Research, India for providing necessary financial support under the sanction: F. No. 9/28 (697)/2008-EMR-I during his stay in Calcutta University, Kolkata, India at the time of major part of this work.