ESTIMATION OF THE CHANGE POINT OF THE GENERALIZED FAILURE RATE FUNCTION

1969 ◽  
Author(s):  
Subramani Arunkumar
Keyword(s):  
Failure Rate ◽  
Change Point ◽  
Rate Function ◽  
Failure Rate Function

ON THE BEHAVIORS OF THE PERCENTILE RESIDUAL LIFE FOR COMPONENTS AND FOR K-OUT-OF-N SYSTEMS

2015 ◽  
Vol 29 (2) ◽  
pp. 291-308
Author(s):  
Yan Shen ◽  
Zhisheng Ye
Keyword(s):  
Failure Rate ◽  
Change Point ◽  
Residual Life ◽  
Parallel Systems ◽  
Rate Function ◽  
Single Component ◽  
Failure Rate Function ◽  
Component Failure ◽  
Number Of Components ◽  
Intimate Relations

This paper investigates properties of the percentile residual life (PRL) function for a single component and for a k-out-of-n system. The shape of the component PRL function can be determined by the component failure rate function. The intimate relations between these two functions are studied first. Then we generalize the results to a k-out-of-n system by assuming independent and identical components. We show that the behavior of the PRL for a k-out-of-n system is quite different from the component PRL. We also find that for series and parallel systems, the location of the change point of the PRL is monotone in the number of components in a system.

REDEFINING FAILURE RATE FUNCTION FOR DISCRETE DISTRIBUTIONS

2002 ◽  
Vol 09 (03) ◽  
pp. 275-285 ◽  
Author(s):  
M. XIE ◽  
O. GAUDOIN ◽  
C. BRACQUEMOND
Keyword(s):  
Failure Rate ◽  
Rate Function ◽  
Monotonicity Property ◽  
Discrete Distributions ◽  
The Other ◽  
Continuous Case ◽  
Discrete Version ◽  
Series System ◽  
Failure Rate Function ◽  
Definition Of

For discrete distribution with reliability function R(k), k = 1, 2,…,[R(k - 1) - R(k)]/R(k - 1) has been used as the definition of the failure rate function in the literature. However, this is different from that of the continuous case. This discrete version has the interpretation of a probability while it is known that a failure rate is not a probability in the continuous case. This discrete failure rate is bounded, and hence cannot be convex, e.g., it cannot grow linearly. It is not additive for series system while the additivity for series system is a common understanding in practice. In the paper, another definition of discrete failure rate function as In[R(k - 1)/R(k)] is introduced, and the above-mentioned problems are resolved. On the other hand, it is shown that the two failure rate definitions have the same monotonicity property. That is, if one is increasing/decreasing, the other is also increasing/decreasing. For other aging concepts, the new failure rate definition is more appropriate. The failure rate functions according to this definition are given for a number of useful discrete reliability functions.

Initial and final behaviour of failure rate functions for mixtures and systems

2003 ◽  
Vol 40 (03) ◽  
pp. 721-740 ◽  
Author(s):  
Henry W. Block ◽  
Yulin Li ◽  
Thomas H. Savits
Keyword(s):  
Asymptotic Behaviour ◽  
Failure Rate ◽  
Rate Function ◽  
Coherent Systems ◽  
Failure Rate Function ◽  
Rate Functions ◽  
Limiting Behaviour

In this paper we consider the initial and asymptotic behaviour of the failure rate function resulting from mixtures of subpopulations and formation of coherent systems. In particular, it is shown that the failure rate of a mixture has the same limiting behaviour as the failure rate of the strongest subpopulation. A similar result holds for systems except the role of strongest subpopulation is replaced by strongest min path set.

scholarly journals Generalising Exponential Distributions Using an Extended Marshall–Olkin Procedure

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 464
Author(s):  
Victoriano García ◽  
María Martel-Escobar ◽  
F.J. Vázquez-Polo
Keyword(s):  
Failure Rate ◽  
Real Data ◽  
Rate Function ◽  
Exponential Distributions ◽  
Symmetric Distributions ◽  
Failure Rate Function ◽  
Numerical Examples ◽  
Special Cases ◽  
The Common ◽  
Family Of Distributions

This paper presents a three-parameter family of distributions which includes the common exponential and the Marshall–Olkin exponential as special cases. This distribution exhibits a monotone failure rate function, which makes it appealing for practitioners interested in reliability, and means it can be included in the catalogue of appropriate non-symmetric distributions to model these issues, such as the gamma and Weibull three-parameter families. Given the lack of symmetry of this kind of distribution, various statistical and reliability properties of this model are examined. Numerical examples based on real data reflect the suitable behaviour of this distribution for modelling purposes.

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