Some new results on bathtub-shaped hazard rate models

<abstract><p>The most common non-monotonic hazard rate situations in life sciences and engineering involves bathtub shapes. This paper focuses on the quantile residual life function in the class of lifetime distributions that have bathtub-shaped hazard rate functions. For this class of distributions, the shape of the $ \alpha $-quantile residual lifetime function was studied. Then, the change points of the $ \alpha $-quantile residual life function of a general weighted hazard rate model were compared with the corresponding change points of the basic model in terms of their location. As a special weighted model, the order statistics were considered and the change points related to the order statistics were compared with the change points of the baseline distribution. Moreover, some comparisons of the change points of two different order statistics were presented.</p></abstract>

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Dynamic Multivariate Quantile Residual Life in Reliability Theory

Mathematical Problems in Engineering ◽

10.1155/2018/1245656 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10

Author(s):

M. Shafaei Noughabi ◽

M. Kayid ◽

A. M. Abouammoh

Keyword(s):

Hazard Rate ◽

Residual Life ◽

Rate Function ◽

Reliability Theory ◽

Dynamic Feature ◽

Hazard Rate Function ◽

Residual Life Function ◽

Quantile Residual Life ◽

Multivariate Quantile ◽

Life Function

We extend the univariate α-quantile residual life function to multivariate setting preserving its dynamic feature. Principal attributes of this function are derived and their relationship to the dynamic multivariate hazard rate function is discussed. A corresponding ordering, namely, α-quantile residual life order, for random vectors of lifetimes is introduced and studied. Based on the proposed ordering, a notion of positive dependency is presented. Finally, a discussion about conditions characterizing the class of decreasing multivariate α-quantile residual life functions is pointed out.

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MEAN RESIDUAL LIFE FUNCTION FOR ADDITIVE AND MULTIPLICATIVE HAZARD RATE MODELS

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964815000388 ◽

2015 ◽

Vol 30 (2) ◽

pp. 281-297 ◽

Cited By ~ 1

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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A GENERALIZED ENTROPY-BASED RESIDUAL LIFETIME DISTRIBUTIONS

International Journal of Biomathematics ◽

10.1142/s1793524511001416 ◽

2011 ◽

Vol 04 (02) ◽

pp. 171-184 ◽

Cited By ~ 10

Author(s):

VIKAS KUMAR ◽

H. C. TANEJA

Keyword(s):

Residual Life ◽

Survival Function ◽

Monotonicity Property ◽

Entropy Measure ◽

Residual Lifetime ◽

Mean Residual Life ◽

Present Communication ◽

Dynamic Information ◽

Lifetime Distributions ◽

Life Function

The present communication considers Havrda and Charvat entropy measure to propose a generalized dynamic information measure. It is shown that the proposed measure determines the survival function uniquely. The residual lifetime distributions have been characterized. A bound for the dynamic entropy measure in terms of mean residual life function has been derived, and its monotonicity property is studied.

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