The Estimation of Reliability Function in Terms of the Catastrophe Theory

2014 ◽  
Vol 607 ◽  
pp. 817-820 ◽  
Author(s):  
Aleksandr Vasilyevich Pitukhin ◽  
Igor Skobtsov
Keyword(s):  
Probability Theory ◽  
Catastrophe Theory ◽  
Random Function ◽  
Stationary Process ◽  
Reliability Function ◽  
Random Processes ◽  
Cusp Catastrophe ◽  
Reliability Measures ◽  
Zero Crossings ◽  
Stationary Random Processes

The development of new catastrophe theory methods, coupled with probability theory is opening new possibilities to estimate the reliability measures. A brief review of the cusp catastrophe is presented in the introduction. The second part is devoted to probability approach. Manage variables are viewed as stationary random processes (functions) and a problem of overshoot of random function is formulated. Mean number of zero crossings by Gaussian random stationary process is evaluated; analytical equations to estimate the reliability function are obtained.

The Statement of Optimal Design Problem with the Cusp Catastrophe Theory Application

2014 ◽  
Vol 709 ◽  
pp. 530-533 ◽  
Author(s):  
Aleksandr Vasilyevich Pitukhin ◽  
Igor Skobtsov
Keyword(s):  
Optimal Design ◽  
Catastrophe Theory ◽  
Design Problem ◽  
Reliability Function ◽  
Function Evaluation ◽  
Statistical Linearization ◽  
Cusp Catastrophe ◽  
Optimal Design Problem ◽  
Linearization Methods ◽  
Theory Application

The purpose of this paper is to present the catastrophe theory method for the optimal design of machine components. A brief description of the cusp catastrophe is presented in the introduction. The statement of optimal design problem is given in the second part of the paper. A single criterion design is presented; the reliability function is used as the objective function. The last part is devoted to probability approach. Manage variables are viewed as stochastic quantities, analytical and statistical linearization methods are used for the reliability function evaluation.

A Bayesian Estimation of Reliability Measures of Stepwise Exponential Distribution System

1991 ◽  
Author(s):  
M. H. Hu
Keyword(s):  
Bayesian Estimation ◽  
Exponential Distribution ◽  
Distribution System ◽  
Failure Process ◽  
Reliability Function ◽  
Distribution Model ◽  
Time To Failure ◽  
Reliability Measures ◽  
In Series ◽  
Mean Time

Abstract This paper presents an analysis method for reliability measures of a system with step changes in failure and repair rates. Both failure and repair time have exponential function of time. Such a system is called a stepwise exponential distribution system. This kind of failure process can take place in various equipments. This paper deals with the system having components in series arrangement. Bayesian statistics is used in defining prior and posterior probability density functions of failure and repair rates. These functions provide information for the estimation of reliability measures: 1) failure and repair rates, 2) mean time to failure, 3) mean time to repair, 4) reliability function and 5) availability. A sample problem is given to illustrate the methodology. The Bayesian estimation of the stepwise exponential distribution model is useful in the planning of equipment predictive maintenance.

Sign in / Sign up

Export Citation Format

Share Document