IN THIS PAPER, WE STUDY THE RESIDUAL LIFETIME OF Coherent System WITH POSSIBLY DE- PENDENT IDENTICALLY DISTRIBUTED COMPONENT LIFETIMES. THESE RESULTS ARE BASED ON THE REPRESENTATION OF System RELIABILITY FUNCTION AS A DISTORTED FUNCTION OF COMMON RELIA BILITY FUNCTION OF COMPONENTS. ...

IN THIS PAPER, WE PROVIDE AN EXPRESSION FOR THE ENTROPY OF THE RESIDUAL LIFETIME OF ACoherent System, ESPECIALLY AN I -OUT-OF- N System, WHEN ALL COMPONENTS OF THE SystemARE ALIVE AT TIME T. VARIOUS PROPERTIES OF THE PROPOSED ENTROPY ARE DISCUSSED. SOMEPARTIAL ORDERING RESULTS AMONG THE System RESIDUAL LIFETIMES IN TERMS OF THEIR ENTROPIESARE ALSO OBTAINED.

IN THIS PAPER, WE CONSIDER SOME RELIABILITY PROPERTIES OF A Coherent System WITH A SINGLE COLD STANDBY COMPONENT. IT IS ASSUMED THAT THE COMPONENTS LIFETIMES OF THE System ARE INDEPENDENT AND IDENTICALLY DISTRIBUTED (I.I.D.) RANDOM VARIABLES. WE ALSO ASSUME THAT THE STANDBY COMPONENT IS INDEPENDENT OF THE ACTIVE COMPONENTS OF THE System. USING THE CONCEPT OF System SIGNATURE DEFINED BY SAMANIEGO (1985), SOME EXPRESSIONS FOR THE RELIABILITY AND THE MEAN RESIDUAL LIFE (MRL) FUNCTIONS OF THE System ARE GIVEN.ALSO SOME STOCHASTIC ORDERING RESULTS AND ILLUSTRATIVE EXAMPLES ARE PROVIDED. THESE EXTEND SOME RESULTS IN ERYILMAZ (2012) FOR A K -OUT-OF- N System.

IN THIS PAPER WE INTRODUCE A CLASS OF CONTINUOUS FRAMES IN A HILBERT SPACE H WHICH IS INDEXED BY SOME LOCALLY COMPACT GROUP G, EQUIPPED WITH ITS LEFT HAAR MEASURE. THESE FRAMES ARE OBTAINED AS THE ORBITS OF A SINGLE ELEMENT OF HILBERT SPACE H UNDER SOME UNITARY REPRESENTATION P OF G ON H.

IN THIS PAPER WE CONSIDER STRESS-STRENGTH MODELING FOR CALCULATING OF THE STRESSSTRENGTH RELIABILITY OF A Coherent System WHICH IS REPRESENTED AS A FUNCTION OF THESTRESS-STRENGTH RELIABILITIES OF ITS COMPONENTS. THE System COMPONENTS MAY EXPERIENCE THE SAME OR DIFFERENT STRESS LEVELS. WE ALSO POINT OUT A MISTAKE RESULT GIVEN BYBHATTACHARYA AND ROYCHOWDHURY (2013) WHEN THE COMPONENTS OF THE System ARE SUBJECTED TO A COMMON STRESS LEVEL.

THIS ARTICLE CONSIDERS THE MEAN RESIDUAL LIFE (MRL) FUNCTION OF A Coherent SystemWHEN THE NUMBER OF FAILED COMPONENTS OF THE System IS KNOWN. WE ASSUME THAT THELIFETIMES OF THE System COMPONENTS ARE INDEPENDENT AND IDENTICALLY DISTRIBUTED (IID)RANDOM VARIABLES AND SHOW THAT WHEN THE COMPONENTS OF THE System HAVE INCREASING(DECREASING) FAILURE RATE, THAT IS IFR (DFR), THE MRL FUNCTION OF THE System IS DECREASING (INCREASING) IN TIME. SAME PROPERTY FOR K -OUT-OF- N SystemS WITH INDEPENDENTBUT NOT IDENTICAL (INID) COMPONENTS IS ALSO SHOWN WHEN THE FAILED COMPONENTS OF THESystem ARE KNOWN, EXTENDING SOME RESULTS IN LITERATURES.