Estimation of Parameters of a Mixed Failure Time Distribution Which is a Mixture of Degenerate (Degenerate at Zero) and I. G. Distribution

2014 ◽  
Vol 43 (23) ◽  
pp. 5039-5051 ◽  
Author(s):  
V. U. Dixit ◽  
S. P. Nabar
Keyword(s):  
Time Distribution ◽  
Failure Time ◽  
Estimation Of Parameters ◽  
Failure Time Distribution

FAILURE TIME DISTRIBUTION UNDER A δ-SHOCK MODEL AND ITS APPLICATION TO ECONOMIC DESIGN OF SYSTEMS

1999 ◽  
Vol 06 (03) ◽  
pp. 237-247 ◽  
Author(s):  
ZEHUI LI ◽  
LING-YAU CHAN ◽  
ZHIXIN YUAN
Keyword(s):  
Poisson Distribution ◽  
Time Distribution ◽  
Failure Time ◽  
Time Lag ◽  
Economic Design ◽  
Point Of View ◽  
Shock Model ◽  
Failure Model ◽  
Failure Time Distribution ◽  
As If

Suppose that shocks arrive and act on a system according to a Poisson distribution with mean rate of arrival equal to λ shock(s) per unit time. A δ-shock failure model is proposed in this paper, which assumes that when a system is acted on by a shock, it will recover fully in time δ(>0), and after that it will function as if no shock had occurred before. If the time lag between two successive shocks is less than δ, the second shock will cause failure of the system. Theoretical expressions related to the distribution of the failure time of the system are derived. These results can be used to optimize the design of a system from a costing point of view.

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