A Note on the Mean Residual Life Function of a Parallel System

2005 ◽  
Vol 34 (2) ◽  
pp. 475-484 ◽  
Author(s):  
MAJID ASADI ◽  
ISMIHAN BAYRAMOGLU (BAIRAMOV)
Keyword(s):  
Residual Life ◽  
Parallel System ◽  
Mean Residual Life ◽  
Residual Life Function ◽  
Mean Residual Life Function ◽  
The Mean ◽  
Life Function

MEAN RESIDUAL LIFE FUNCTION FOR ADDITIVE AND MULTIPLICATIVE HAZARD RATE MODELS

2015 ◽  
Vol 30 (2) ◽  
pp. 281-297 ◽  
Author(s):  
Ramesh C. Gupta
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Turning Points ◽  
Sufficient Conditions ◽  
Mean Residual Life ◽  
Residual Life Function ◽  
Mean Residual Life Function ◽  
Hazard Rate Models ◽  
The Mean ◽  
Life Function

This paper deals with the mean residual life function (MRLF) and its monotonicity in the case of additive and multiplicative hazard rate models. It is shown that additive (multiplicative) hazard rate does not imply reduced (proportional) MRLF and vice versa. Necessary and sufficient conditions are obtained for the two models to hold simultaneously. In the case of non-monotonic failure rates, the location of the turning points of the MRLF is investigated in both the cases. The case of random additive and multiplicative hazard rate is also studied. The monotonicity of the mean residual life is studied along with the location of the turning points. Examples are provided to illustrate the results.

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