A new lifetime distribution and its application in reliability

Author(s):  
Omid Kharazmi
Author(s):  
MINNIE H. PATEL ◽  
H.-S. JACOB TSAO

Empirical cumulative lifetime distribution function is often required for selecting lifetime distribution. When some test items are censored from testing before failure, this function needs to be estimated, often via the approach of discrete nonparametric maximum likelihood estimation (DN-MLE). In this approach, this empirical function is expressed as a discrete set of failure-probability estimates. Kaplan and Meier used this approach and obtained a product-limit estimate for the survivor function, in terms exclusively of the hazard probabilities, and the equivalent failure-probability estimates. They cleverly expressed the likelihood function as the product of terms each of which involves only one hazard probability ease of derivation, but the estimates for failure probabilities are complex functions of hazard probabilities. Because there are no closed-form expressions for the failure probabilities, the estimates have been calculated numerically. More importantly, it has been difficult to study the behavior of the failure probability estimates, e.g., the standard errors, particularly when the sample size is not very large. This paper first derives closed-form expressions for the failure probabilities. For the special case of no censoring, the DN-MLE estimates for the failure probabilities are in closed forms and have an obvious, intuitive interpretation. However, the Kaplan–Meier failure-probability estimates for cases involving censored data defy interpretation and intuition. This paper then develops a simple algorithm that not only produces these estimates but also provides a clear, intuitive justification for the estimates. We prove that the algorithm indeed produces the DN-MLE estimates and demonstrate numerically their equivalence to the Kaplan–Meier-based estimates. We also provide an alternative algorithm.


1978 ◽  
Vol 15 (3) ◽  
pp. 560-572 ◽  
Author(s):  
Toshiro Tango

Block replacement policy, under which items are replaced at constant intervals of time and at failure, is wasteful because sometimes almost new items are also replaced. In order to eliminate this kind of waste, the following replacement policy is suggested.(1) Items are exchanged for new items at time kT (k ··· 1, 2, …).(2) If items fail in [(k – 1) T, kT – v), they are replaced by new items, and if in [kT – v, kT), they are replaced by used items.The results of this ‘extended block replacement policy with used items' are studied for the Erlang lifetime distribution.


2000 ◽  
Vol 54 (4) ◽  
pp. 252 ◽  
Author(s):  
W. J. Owen ◽  
D. Sinha ◽  
M. H. Capozzoli

2012 ◽  
Vol 36 (11) ◽  
pp. 5380-5392 ◽  
Author(s):  
Ammar M. Sarhan ◽  
D.C. Hamilton ◽  
B. Smith

2007 ◽  
Vol 21 (23n24) ◽  
pp. 4048-4053
Author(s):  
C. H. YEUNG ◽  
Y. P. MA ◽  
K. Y. MICHAEL WONG

We propose a dynamical model of a competing population whose agents have a tendency to balance their decisions in time. The model is applicable to financial markets in which the agents trade with finite capital, or other multiagent systems such as routers in communication networks attempting to transmit multiclass traffic in a fair way. We find an oscillatory behavior due to the segregation of agents into two groups. Each group remains winning over epochs. The aggregation of smart agents is able to explain the lifetime distribution of epochs to 8 decades of probability. The existence of the super agents further refines the lifetime distribution of short epochs.


2017 ◽  
Vol 47 (13) ◽  
pp. 3052-3072 ◽  
Author(s):  
M. Goldoust ◽  
S. Rezaei ◽  
Y. Si ◽  
S. Nadarajah

Author(s):  
Michael Besel ◽  
Angelika Brueckner-Foit

The lifetime distribution of a component subjected to fatigue loading is calculated using a micro-mechanics model for crack initiation and a fracture mechanics model for crack growth. These models are implemented in a computer code which uses the local stress field obtained in a Finite Element analysis as input data. Elemental failure probabilities are defined which allow to identify critical regions and are independent of mesh refinement. An example is given to illustrate the capabilities of the code. Special emphasis is put on the effect of the initiation phase on the lifetime distribution.


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