Nested Plans as Sequential Quality Control Schemes for Detecting a Change in a Multivariate Normal Distribution

Abstract

In the present paper we consider the problem of sequential quality control and propose nested plans for the quick detection, with low false alarm rate, of a change in a stochastic system. The nested plan includes two phases: a variable plan and an attributes plan. For the proposed nested plans we evaluate the exact (non-asymptotic) expressions for the in-control and out-of-control mean and the standard deviation of the run length. We especially consider the example where the initial and the final distributions are multivariate normal with different parameters and show that for many practical situations the speed of detection of a change using our proposed procedure is comparable with that of CUSUM detection schemes.

Key Words:

• Average run length
• CUSUM
• multivariate normal distribution
• nested plan
• sequential quality control

Additional information

Notes on contributors

Yan Lumelskii

Yan Lumelskii is Research Associate at the Statistics Laboratory, Faculty of Industrial Engineering and Management, Technion — Israel Institute of Technology. He has Professor and Head of the Department Probability Theory and Mathematical Statistics, Perm State University, Russia. His research interests include sequential plans of random walks, unbiased estimations and estimations minimizing the bias, statistical classification problems in the case of multidimensional normal and Wishart distributions, statistical quality control and reliability.

Gregory Gurevich

Gregory Gurevich is a Lecturer in the Department of Industrial Engineering and Management, Sami Shamoon College of Engineering. His main research interests include: change point problems; optimal sequential plans; statistical methods in occupational medicine; and statistical planning and inference. Dr. Gurevich is a member of the Israel Statistical Association. His publications have appeared in the statistical and engineering literature.

Paul D. Feigin

Paul D. Feigin is Professor of Statistics in the Faculty of Industrial Engineering and Management at the Technion, which he joined in 1976. His main research interests include: inference for stochastic processes; design and analysis of experiments; modern methods of data-mining and forecasting; statistics in genetics; and statistical analysis of call-level data from Call Centers. Dr. Feigin is a past-president of the Israel Statistical Association, is an elected fellow of the Institute of Mathematical Statistics and of the International Statistical Institute.