Research Article Open Access

Nonparametric Analysis on System Availability: Confidence Bound and Power Function

Jau-Chuan Ke and Yunn-Kuang Chu

Abstract

In this study we consider the steady-state availability, denoted A, of a system with distribution-free failure and repair time. In particular, we are interested in constructing a lower confidence bound and a testing framework for A. We first show that the natural estimator  of A, defined as the ratio of the failure time sample mean to the sum of the failure time sample mean and the repair time sample mean, is strongly consistent and asymptotically normal. Then using the asymptotic distribution of Â, we develop a lower confidence bound and a hypothesis test for A. Finally, a numerical simulation study is conducted in order to illustrate the performance of  in applied inference about A.

Journal of Mathematics and Statistics
Volume 3 No. 4, 2007, 181-187

DOI: https://doi.org/10.3844/jmssp.2007.181.187

Published On: 31 December 2007

How to Cite: Ke, J. & Chu, Y. (2007). Nonparametric Analysis on System Availability: Confidence Bound and Power Function. Journal of Mathematics and Statistics, 3(4), 181-187. https://doi.org/10.3844/jmssp.2007.181.187

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Keywords

  • Availability
  • hypothesis test
  • lower confidence bound
  • power function
  • repairable system
  • simulation
  • Slutsky’s theorem