ON AGING PROPERTIES BASED ON THE RESIDUAL LIFE OF k-OUT-OF-n SYSTEMS

1999 ◽  
Vol 13 (2) ◽  
pp. 193-199 ◽  
Author(s):  
Félix Belzunce ◽  
Manuel Franco ◽  
José M. Ruiz
Keyword(s):  
Failure Rate ◽  
Residual Life ◽  
Mean Residual Life ◽  
Aging Properties ◽  
Life Distributions ◽  
Decreasing Failure Rate

In this paper, we give characterizations of nonparametric families of life distributions based on aging and variability orderings of the residual life of k-out-of-n systems. We obtain some results of increasing (decreasing) failure rate classes as well as of new classes decreasing (increasing) mean residual life of the system and new better (worse) than used in expectations of the system. Relationships among themselves and others such as new better (worse) than used, new better (worse) than used expectations, and decreasing (increasing) mean residual life are also given.

Some Characterizations of the Exponential and Related Life Distributions

1986 ◽  
Vol 35 (3-4) ◽  
pp. 189-198 ◽  
Author(s):  
S. P. Mukherjee ◽  
Dilip Roy
Keyword(s):  
Order Statistics ◽  
Failure Rate ◽  
Residual Life ◽  
Mean Residual Life ◽  
Finite Range ◽  
Conditional Expectations ◽  
Coefficients Of Variation ◽  
Constant Coefficients ◽  
Life Distributions ◽  
Pearsonian Type

Characterizations of the exponential, the Pearsonian Type XI and a finite range distributions have been obtained in terms of different constant coefficients of variation of residual life. These results have also been stated in terms of conditional expectations of suitably chosen functions of order statistics. A few earlier results have been generalised. Some related results in IMRL and DMRL. classes of distributions have been presented . Also characterizations involving the product of failure rate and mean residual life are aiven.

scholarly journals Reversed Preservation Properties for Series and Parallel Systems

2007 ◽  
Vol 44 (4) ◽  
pp. 928-937 ◽  
Author(s):  
Félix Belzunce ◽  
Helena Martínez-Puertas ◽  
José M. Ruiz
Keyword(s):  
Failure Rate ◽  
Residual Life ◽  
Parallel Systems ◽  
Mean Residual Life ◽  
Convex Order ◽  
Increasing Failure Rate ◽  
Decreasing Failure Rate ◽  
New Better Than Used ◽  
Better Than

Recently Li and Yam (2005) studied which ageing properties for series and parallel systems are inherited for the components. In this paper we provide new results for the increasing convex and concave orders, the increasing mean residual life (IMRL), decreasing failure rate (DFR), the new worse than used in expectation (NWUE), the increasing failure rate in average (IFRA), the decreasing failure rate in average (DFRA), and the new better than used in the convex order (NBUC) ageing classes.

Preservation results for life distributions based on comparisons with asymptotic remaining life under replacements

2000 ◽  
Vol 37 (4) ◽  
pp. 999-1009 ◽  
Author(s):  
M. C. Bhattacharjee ◽  
A. M. Abouammoh ◽  
A. N. Ahmed ◽  
A. M. Barry
Keyword(s):  
Residual Life ◽  
Point Of View ◽  
Mean Residual Life ◽  
Remaining Life ◽  
Repairable Systems ◽  
Repair Strategy ◽  
Aging Properties ◽  
Life Distributions ◽  
The Mean ◽  
Life Function

We investigate some preservation properties of two nonparametric classes of survival distributions and their duals, under appropriate reliability operations. The aging properties defining these nonparametric classes are based on comparing the mean life of a new unit to the mean residual life function of the asymptotic remaining survival time of the unit under repeated perfect repairs. They are motivated from a point of view that realistic notions of degradation, applicable to repairable systems, should be based on contrasting some aspect of the remaining life of a repairable unit (under a given repair strategy, such as renewals) to the life of a new unit.

Preservation results for life distributions based on comparisons with asymptotic remaining life under replacements

2000 ◽  
Vol 37 (04) ◽  
pp. 999-1009 ◽  
Author(s):  
M. C. Bhattacharjee ◽  
A. M. Abouammoh ◽  
A. N. Ahmed ◽  
A. M. Barry
Keyword(s):  
Residual Life ◽  
Point Of View ◽  
Mean Residual Life ◽  
Remaining Life ◽  
Repairable Systems ◽  
Repair Strategy ◽  
Aging Properties ◽  
Life Distributions ◽  
The Mean ◽  
Life Function

We investigate some preservation properties of two nonparametric classes of survival distributions and their duals, under appropriate reliability operations. The aging properties defining these nonparametric classes are based on comparing the mean life of a new unit to the mean residual life function of the asymptotic remaining survival time of the unit under repeated perfect repairs. They are motivated from a point of view that realistic notions of degradation, applicable to repairable systems, should be based on contrasting some aspect of the remaining life of a repairable unit (under a given repair strategy, such as renewals) to the life of a new unit.

MEAN RESIDUAL LIFE AND OTHER PROPERTIES OF WEIBULL RELATED BATHTUB SHAPE FAILURE RATE DISTRIBUTIONS

2004 ◽  
Vol 11 (02) ◽  
pp. 113-132 ◽  
Author(s):  
C. D. LAI ◽  
LINGYUN ZHANG ◽  
M. XIE
Keyword(s):  
Failure Rate ◽  
Residual Life ◽  
Weibull Model ◽  
Parameters Estimation ◽  
Mean Residual Life ◽  
Bathtub Shape ◽  
Reliability Characteristics ◽  
Rate Functions ◽  
Life Distributions ◽  
The Relationship

The two-parameter Weibull distribution is widely used in reliability analysis. Because of its monotonic ageing behaviour, its applicability is hampered in certain reliability situations. Several generalizations and extensions of the Weibull model have been proposed in the literature to overcome this limitation but their properties have not yet been described in a unified manner. In this paper, graphical displays of the mean residual life curves of several families of Weibull related life distributions are given together with their corresponding failure rate functions. The relationship between these two functions are visibly demonstrated. We focus our attention on the Weibull related families that have bathtub or modified bathtub shape failure rates. Important reliability characteristics such as burn-in, change point and flatness of bathtub of these families are examined. Model selection and parameters estimation are also discussed.

Ageing Characteristics of the Weibull Mixtures

1996 ◽  
Vol 10 (4) ◽  
pp. 591-600 ◽  
Author(s):  
Pushpa L. Gupta ◽  
Ramesh C. Gupta
Keyword(s):  
Failure Rate ◽  
Residual Life ◽  
Mean Residual Life ◽  
Conditional Distributions ◽  
Property A ◽  
Mixtures Of Distributions ◽  
The Mean ◽  
Decreasing Failure Rate ◽  
Monotonic Properties ◽  
Life Function

It is well known that mixtures of decreasing failure rate (DFR) distributions have the DFR property. A similar result is, of course, not true for increasing failure rate (IFR) distributions. In a recent note, Gurland and Sethuraman (1994, Technometrks36(4): 416–418) presented two examples where mixtures of IFR distributions show DFR property. In this paper, we present a general approach to study the mixtures of distributions and show that the failure rates of the unconditional and conditional distributions cross at most at one point. Mixtures of Weibull distribution with a shape parameter greater than 1 are examined in detail. This also enables us to study the monotonic properties of the mean residual life function of the mixture. Some examples are provided to illustrate the results.

scholarly journals Reversed Preservation Properties for Series and Parallel Systems

2007 ◽  
Vol 44 (04) ◽  
pp. 928-937
Author(s):  
Félix Belzunce ◽  
Helena Martínez-Puertas ◽  
José M. Ruiz
Keyword(s):  
Failure Rate ◽  
Residual Life ◽  
Parallel Systems ◽  
Mean Residual Life ◽  
Convex Order ◽  
Increasing Failure Rate ◽  
Decreasing Failure Rate ◽  
New Better Than Used ◽  
Better Than

Recently Li and Yam (2005) studied which ageing properties for series and parallel systems are inherited for the components. In this paper we provide new results for the increasing convex and concave orders, the increasing mean residual life (IMRL), decreasing failure rate (DFR), the new worse than used in expectation (NWUE), the increasing failure rate in average (IFRA), the decreasing failure rate in average (DFRA), and the new better than used in the convex order (NBUC) ageing classes.

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