KEYWORDS
System Availability, Confidence Interval, Shortest Length, Technique for Constructing, Hypotheses Testing.

ABSTRACT

Any estimate of system availability calculated from time-to-failure and time-to-repair test data will be subject to some degree of uncertainty due to uncertainty associated with the sample estimates of unknown parameters of the probability distributions of the test data. Although decisions about the true availability of the system should take this uncertainty into account, a point estimate of availability is usually the only statistic calculated. In this paper, we present an approach to constructing invariant confidence intervals for system availability that emphasizes pivotal quantities. The purpose of this paper is to give a technique for deriving confidence intervals with a minimum length property and for deciding if the true system availability differs significantly from a specified value when the true mean time between failures (MTBF) and the true mean time to restore the system to successful function (MTTR) are estimated from the sample data. Numerical examples illustrating the use of the technique are given.

Konstantin N. Nechval was born in Riga, Latvia, on March 5, 1975. He received the MS degree from the Aviation University of Riga, Latvia, in 1998. At present, he is a PhD Student in automatic control and systems engineering at the Riga Technical University. His research interests include stochastic processes, pattern recognition, operations research, statistical decision theory, and adaptive control.

Nicholas A. Nechval received the PhD degree in automatic control and systems engineering from the Riga Civil Aviation Engineers Institute (RCAEI) in June, 1969, and the DSc (Hab.) degree in radio engineering from the Riga Aviation University (RAU) in June, 1993. From 1987, Dr Nechval has been a member of the Scientific Society (on the problem of Protection from Biodeterioration) of the Russian Academy of Sciences. In 1992, he was awarded a Silver Medal of the Exhibition Committee (Moscow, Russia) in connection with research on the problem of Prevention of Collisions between Aircraft and Birds. He is the holder of several patents in this field. Dr Nechval was Professor of Applied Mathematics at RAU, from 1993 to 1999. At present, he is Professor of Mathematics and Computer Science and Head of the Mathematical Statistics Department at the University of Latvia, Riga, Latvia. His interests include mathematics, stochastic processes, pattern recognition, multidimensional statistical detection and estimation, multiresolution stochastic signal analysis, digital radar signal processing, operations research, statistical decision theory, and adaptive control. Professor Nechval is a professional member of the Latvian Statistical Association, the Institute of Mathematical Statistics, and CHAOS asbl (the Institute of Mathematics, based in Liege, Belgium). Dr. Nechval is also a member of the Latvian Association of Professors.

Eugene A. Kopytov was born in Lignica, Poland, on December 5, 1947. He received the PhD degree in automatic control and systems engineering from the Riga Civil Aviation Engineers Institute (RCAEI) in January, 1984, and the DSc (Hab.) degree in computer control at the Riga Aviation University (RAU) in December, 1997. At present, he is a Rector of the Transport and Telecommunication Institute, Riga, Latvia. His current research interests are centered in the areas of optimization, computer control, and application of functional analysis to engineering problems. Dr. Kopytov is a member of the Latvian Association of Professors and the Baltic Information Academy.

Edgars K. Vasermanis received the PhD degree in automatic control and systems engineering from the Riga Civil Aviation Engineers Institute (RCAEI) in June, 1974, and the DSc (Hab.) degree in economics and management at the Tallinn University in September, 1989. He is now a Dean of the Faculty of Economics and Management at the University of Latvia. His interests include economics and management, operations research, statistical decision theory, and adaptive control. Professor Vasermanis is a professional member of the Latvian Statistical Association, the Institute of Mathematical Statistics. He is a member of the Latvian Association of Professors.

Uldis Rozevskis received the PhD degree in computer science from the University of Latvia, Riga, Latvia, in September, 1980. He is now the Chairman of the Computer Science Department at the University of Latvia. His research interests include computer architecture, defect and fault-tolerant systems, testing and quality-assurance of digital systems, parallel and distributed computer systems, multichip module systems, and programmable digital systems. Dr. Rozevskis is a member of the Latvian Association of Professors.