In the present paper, we introduce a partially sequential nonparametric test for Phase-II monitoring of location Parameter. Unlike previous communications, we introduce a partially sequential test for naturally censored data. In the present context, we consider right censored observations from both the phases. Existing partially sequential or semi-sequential procedures based on inverse sampling schemes, pioneered by Wolfe (1977) and Orban and Wolfe (1980), are modified to accommodate the effect of censoring. We use the typical score function proposed by Gehan (1965) and Mantel (1967), in their generalization of Wilcoxon's rank statistic for censored data. Such a score function is also used by Gombay (1999) in connection to at most one change point detection problem.
Our proposed modification is motivated from a practical problem of statistical monitoring when a sample of prefixed size is available a-priori. We discuss in detail the statistical methodologies and some asymptotic results. Numerical results based on Monte-Carlo are provided to justify the asymptotic theory. Some power performances against fixed alternatives are discussed to verify the robustness of the proposed test. We also provide an illustrative example with real data.
Keywords: Censored data; Modified Wilcoxon score; Partially sequential; Test for location
Biography: Dr. Amitava Mukherjee is an independent researcher at the department of Mathematics and System Analysis in Aalto University, School of Science and Technology (Formerly Helsinki University of Technology), in Finland. He obtained his doctoral degree in Statistics from Calcutta University, India. His dissertation covers several sequential-type nonparametric tests and their applications which leads to seven international publications. He spent couple of years in Umeå University, Sweden before moving to Finland. Other than Sequential Analysis and works on water quality, his research interest includes the area of Statistical Process Control, Geostatistics and Financial Statistics. He has made several academic visits to various parts of the world and is keen in developing research collaborations. Dr. Mukherjee is promising statistician and has received several awards including U.S. Nair memorial award for Young Statisticians from Indian Society for Probability and Statistics.