By Mangey Ram, J. Paulo Davim

This publication provides unique reviews describing the newest examine and advancements within the sector of reliability and platforms engineering. It is helping the reader deciding upon gaps within the present wisdom and offers fruitful components for additional study within the box. between others, this publication covers reliability measures, reliability review of multi-state platforms, optimization of multi-state structures, non-stop multi-state structures, new computational ideas utilized to multi-state structures and probabilistic and non-probabilistic protection assessment.

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Therefore, the system failure probability at time t can be estimated as follows. FðtÞ ¼ P X pj Á F j ðtÞ j¼1 ¼1À j À1 P N X X ð6Þ pj Aji e Àaji t j¼1 i¼0 Note that p is the reduced number of system failure paths in the systems with circular type. For the system with circular type, the probability of the system failure F(t) can be estimated by FðtÞ ¼ n p X pj Á F j ðtÞ j¼1 ¼1Àn p N j À1 X X ð7Þ pj Aji e Àaji t j¼1 i¼0 Thus, the system failure probabilities of consecutive-k-out-of-n: F systems can be calculated by Eqs.

A spreadsheet table was utilized in deriving N(j, k, n) by Bollinger [3]. A closed form of general N(j, k, n) has been also derived [21, 23, 31]. Circular structure of this system was introduced and the system reliability was provided by Derman et al. [10]. A recursive model to estimate the reliability of circular-type systems was developed by Du and Hwang [13]. A closed-form expression of the reliability of circular consecutive-k-out-of-n: F systems for n ≤ 2k + 1 and when the components were identical with constant failure probability has been derived by Zuo and Kuo [48].

References 1. Rausand, M. and Høyland, A. (2004). System reliability theory; models, statistical methods, and applications, 2nd ed. Hoboken, NJ: Wiley. 2. Rausand, M. (2014). Reliability of Safety-Critical Systems: Theory and Applications. NJ: John Wiley & Sons. 3. IEC 60050-191. (1990). International Electrotechnical Vocabulary - Chapter 191: Dependability and quality of service, International Electrotechnical Commission. 4. Downer, J. (2011). On audits and airplanes: Redundancy and reliability-assessment in high technologies, Accounting, Organizations and Society, vol.

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