Extreme Points of the Class of Discrete Decreasing Failure Rate Life Distributions.

1978 ◽  
Author(s):  
Naftali A. Langberg ◽  
Ramon V. Leon ◽  
Frank Proschan ◽  
James Lynch
Keyword(s):  
Failure Rate ◽  
Extreme Points ◽  
Life Distributions ◽  
Decreasing Failure Rate

Extreme Points of the Class of Discrete Decreasing Failure Rate Life Distributions

1980 ◽  
Vol 5 (1) ◽  
pp. 35-42 ◽  
Author(s):  
Naftali A. Langberg ◽  
Ramón V. León ◽  
James Lynch ◽  
Frank Proschan
Keyword(s):  
Failure Rate ◽  
Extreme Points ◽  
Life Distributions ◽  
Decreasing Failure Rate

The extreme points of the set of decreasing failure rate distributions

1981 ◽  
Vol 57 (3) ◽  
pp. 303-310 ◽  
Author(s):  
Naftali A. Langberg ◽  
Ram�n V. Le�n ◽  
James Lynch ◽  
Frank Proschan
Keyword(s):  
Failure Rate ◽  
Extreme Points ◽  
Decreasing Failure Rate

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.

ON THE PROXIMITY OF WEIGHTED AND EXPONENTIAL DISTRIBUTIONS

2010 ◽  
Vol 17 (01) ◽  
pp. 1-14 ◽  
Author(s):  
BRODERICK O. OLUYEDE
Keyword(s):  
Failure Rate ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Weight Functions ◽  
Exponential Distributions ◽  
Increasing Failure Rate ◽  
Hazards Model ◽  
Life Distributions ◽  
Decreasing Failure Rate ◽  
Transformed Distributions

In this paper stochastic relations and closure results for weighted and transformed distributions including the proportional hazards model are presented. Exponential approximations to the class of increasing failure rate (IFR) and decreasing failure rate (DFR) weighted distributions including transformed distributions with monotone weight functions are obtained. These include approximations via the proportional hazards and length-biased exponential distributions. Also, bounds and moment-type inequalities for weighted life distributions including proportional hazards models and some applications are presented.

The Extreme Points of the Set of Decreasing Failure Rate Distributions.

1979 ◽  
Author(s):  
Naftali A. Langberg ◽  
Ramon V. Leon ◽  
James Lynch ◽  
Frank Proschan
Keyword(s):  
Failure Rate ◽  
Extreme Points ◽  
Decreasing Failure Rate

Is high-altitude mountaineering Russian roulette?

2013 ◽  
Vol 9 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Edward K. Cheng
Keyword(s):  
High Altitude ◽  
Failure Rate ◽  
Rate Model ◽  
Reliability Engineering ◽  
Significant Difference ◽  
Inference Techniques ◽  
Decreasing Failure Rate

AbstractWhether the nature of the risks associated with climbing high-altitude (8000 m) peaks is in some sense “controllable” is a longstanding debate in the mountaineering community. Well-known mountaineers David Roberts and Ed Viesturs explore this issue in their recent memoirs. Roberts views the primary risks as “objective” or uncontrollable, whereas Viesturs maintains that experience and attention to safety can make a significant difference. This study sheds light on the Roberts-Viesturs debate using a comprehensive dataset of climbing on Nepalese Himalayan peaks. To test whether the data is consistent with a constant failure rate model (Roberts) or a decreasing failure rate model (Viesturs), it draws on Total Time on Test (TTT) plots from the reliability engineering literature and applies graphical inference techniques to them.

Stochastic inequalities for an overflow model

1987 ◽  
Vol 24 (3) ◽  
pp. 696-708 ◽  
Author(s):  
Arie Hordijk ◽  
Ad Ridder
Keyword(s):  
Failure Rate ◽  
Lower Bounds ◽  
Approximation Method ◽  
Queueing Networks ◽  
Upper And Lower Bounds ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Decreasing Failure Rate ◽  
General Method

A general method to obtain insensitive upper and lower bounds for the stationary distribution of queueing networks is sketched. It is applied to an overflow model. The bounds are shown to be valid for service distributions with decreasing failure rate. A characterization of phase-type distributions with decreasing failure rate is given. An approximation method is proposed. The methods are illustrated with numerical results.

CLASSIFICATION OF MULTIVARIATE LIFE DISTRIBUTIONS BASED ON PARTIAL ORDERING

2002 ◽  
Vol 16 (1) ◽  
pp. 129-137 ◽  
Author(s):  
Dilip Roy
Keyword(s):  
Present Article ◽  
Failure Rate ◽  
Partial Ordering ◽  
Increasing Failure Rate ◽  
Multivariate Generalization ◽  
Partial Orderings ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

Barlow and Proschan presented some interesting connections between univariate classifications of life distributions and partial orderings where equivalent definitions for increasing failure rate (IFR), increasing failure rate average (IFRA), and new better than used (NBU) classes were given in terms of convex, star-shaped, and superadditive orderings. Some related results are given by Ross and Shaked and Shanthikumar. The introduction of a multivariate generalization of partial orderings is the object of the present article. Based on that concept of multivariate partial orderings, we also propose multivariate classifications of life distributions and present a study on more IFR-ness.

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