A New Class with Decreasing Failure Rate Based on Countable Mixture and Its Application to Censored Data

2019 ◽  
Vol 48 (1) ◽  
pp. 20190376
Author(s):  
B. I. Mohammed ◽  
S. E. Abu-Youssef ◽  
M. G. Sief
Keyword(s):  
Failure Rate ◽  
Censored Data ◽  
New Class ◽  
Decreasing Failure Rate

scholarly journals Inference for the Exponential Distribution under Generalized Progressively Hybrid Censored Data from Partially Accelerated Life Tests with a Time Transformation Function

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1510
Author(s):  
Alaa H. Abdel-Hamid ◽  
Atef F. Hashem
Keyword(s):  
Exponential Distribution ◽  
Failure Rate ◽  
Censored Data ◽  
Sufficient Conditions ◽  
Transformation Function ◽  
Point Estimation ◽  
Estimation Methods ◽  
Time Transformation ◽  
Monte Carlo Simulation Study ◽  
Accelerated Life

In this article, the tampered failure rate model is used in partially accelerated life testing. A non-decreasing time function, often called a ‘‘time transformation function", is proposed to tamper the failure rate under design conditions. Different types of the proposed function, which have sufficient conditions in order to be accelerating functions, are investigated. A baseline failure rate of the exponential distribution is considered. Some point estimation methods, as well as approximate confidence intervals, for the parameters involved are discussed based on generalized progressively hybrid censored data. The determination of the optimal stress change time is discussed under two different criteria of optimality. A real dataset is employed to explain the theoretical outcomes discussed in this article. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

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.

Cluster shock models

1981 ◽  
Vol 18 (01) ◽  
pp. 104-111 ◽  
Author(s):  
Peter F. Thall
Keyword(s):  
Failure Rate ◽  
Present Note ◽  
Cluster Process ◽  
Completely Monotonic ◽  
Poisson Cluster Process ◽  
Preservation Theorem ◽  
Shock Models ◽  
Poisson Cluster ◽  
Decreasing Failure Rate ◽  
Over Time

The survival distribution of a device subject to a sequence of shocks occurring randomly over time is studied by Esary, Marshall and Proschan (1973) and by A-Hameed and Proschan (1973), (1975). The present note treats the case in which shocks occur according to a homogeneous Poisson cluster process. It is shown that if[the device surviveskshocks] =zk, 0 <z< 1, then the device exhibits a decreasing failure rate. A DFR preservation theorem is proved for completely monotonic. A counterexample to the IFR preservation theorem is given in whichis strictly IFR while the failure rate is initially decreasing and then increasing.

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