In this article we study profust reliability of non-repairable coherent systems through the concept of system signature. We obtain explicit expressions for the profust reliability and mean time to fuzzy failure of coherent systems. We compute and present mean time to failure and mean time to fuzzy failure of all coherent systems with three and four components. Finally, we illustrate the results for a well known class of coherent systems called m-consecutive-k-out-of-n:F.
GuanJWuY. Repairable consecutive-k-out-of-n:F system with fuzzy states. Fuzzy Sets Sys2006; 157: 121–142.
2.
CaiKYWenCYZhangML. Fuzzy states as a basis for a theory of fuzzy reliability. Microelectron Rel1993; 33: 253–263.
3.
WuH-C. Fuzzy reliability estimation using Bayesian approach. Computers Ind Engng2004; 46: 467–493.
4.
PandeyDTyagiSK. Profust reliability of a gracefully degradable system. Fuzzy Sets Sys2007; 158: 794–803.
5.
MirakbariMGanjiA. Reliability analysis of a rangeland system: the application of Profust theory. Stochastic Environ Res Risk Assessment2010; 24: 399–409.
6.
SamaniegoFJ. System signatures and their applications in engineering reliability. Springer, New York: 2007.
KocharSMukerjeeHSamaniegoFJ. The “signature”of a coherent system and its application to comparison among systems. Naval Res Log1999; 46: 507–523.
9.
NavarroJRuizJMSandovalCJ. A note on comparisons among coherent systems with dependent components using signatures. Stat Prob Letts2005; 72: 179–185.
10.
SamaniegoFJBalakrishnanNNavarroJ. Dynamic signatures and their use in comparing the reliability of new and used systems. Naval Res Log2009; 56: 577–591.
11.
NavarroJRychlikT. Comparisons and bounds for expected lifetimes of reliability systems. Eur J Operl Res2010; 207: 309–317.
12.
NavarroJSamaniegoFJBalakrishnanN. Joint signature of coherent systems with shared components. J App Prob2010; 47: 235–253.
13.
TriantafyllouISKoutrasMV. Signature and IFR preservation of 2-within-consecutive-k-out-of-n:F systems. IEEE Trans Rel2011; 60: 315–322.
14.
EryilmazSKoutrasMVTriantafyllouIS. Signature based analysis of m-consecutive-k-out-of-n:F system with exchangeable components. Naval Res Log2011; 58: 344–354.
15.
MahmoudiMAsadiM. The dynamic signature of coherent systems. IEEE Trans Rel2011; 60: 817–822.
16.
EryilmazS. The number of failed components in a coherent system with exchangeable components. IEEE Trans Rel2012; 61: 203–207.
