SEQUENTIAL ESTIMATION OF THE MAXIMUM IN A MODEL FOR CORROSION DATA

ADAM T. MARTINSEK

Department of Statistics, University of Illinois at Urbana-Champaign, 101 Illini Hall, 725 S. Wright Street, Champaign, IL 61820, U.S.A.

(Received January 4, 1999; revised May 24, 1999)

Abstract. One method of monitoring corrosion in an underground storage tank involves placing a sensor in the tank and running it around the tank’s interior. As it runs, the sensor records the local thickness of the tank. In this paper we consider the problem of estimating the maximum pit depth by providing a confidence interval that achieves both a specified confidence level and a specified degree of precision. A particular model, the three-parameter beta, is considered, and a stopping rule for determining the sample size is proposed. It is shown that the stopping rule achieves the desired confidence level and precision, asymptotically as the precision requirement becomes increasingly stringent. Moreover, the stopping rule is asymptotically efficient in terms of sample size. The limiting distribution of the stopping rule is derived, and simulation results are presented to supplement the asymptotics with finite sample size behavior.

Key words and phrases: Corrosion data, precise estimation, extreme value theory, stopping rule.