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Journal of Information Science and Engineering, Vol. 24 No. 5, pp. 1521-1535 (September 2008)

Fuzzy System Reliability Analysis Using Triangular Fuzzy Numbers Based on Statistical Data

Jing-Shing Yao, Jin-Shieh Su* and Teng-San Shih*
 Department of Mathematics
National Taiwan University
Taipei, 106 Taiwan
*Department of Applied Mathematics
Chinese Culture University
Taipei, 111 Taiwan
E-mail: suston@tpts8.seed.net.tw

In this article, we use the fuzzy concept to consider the reliability of serial system and the reliability of parallel system. Since the population reliability Rj of the subsystem Pj(j = 1, 2, ..., n) is unknown, if we use the point estimate Rj to estimate Rj from the statistical data in the past, we don't know the probability of the error Rj - Rj. Moreover, the reliability of the system may fluctuate around the point estimate Rj during a time interval. It follows that to use the point estimate Rj to estimate the population reliability Rj is not suitable for the real cases. Therefore, it is more desirable to use the statistical confidence interval. Moreover, the probability of the error Rj - Rj can also be solved. In this paper, we use the statistical confidence interval instead of the point estimate. We transfer the statistical confidence interval into the triangular fuzzy number. Through these triangular fuzzy numbers, we consider the fuzzy reliability system. We fuzzify the reliability of both the serial and parallel systems. Through defuzzifying the fuzzy reliability using the signed distance method; we get a fuzzy estimate of reliability in the two systems.

Keywords: fuzzy reliability, statistical data, signed distance, i-v fuzzy number, triangular fuzzy number

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Received October 31, 2006; revised March 6 & May 18, 2007; accepted June 27, 2007.
Communicated by Chin-Teng Lin.