Bayesian estimation of the parameters in two non-independent component series system with dependent time failure rate

2004 ◽  
Vol 154 (1) ◽  
pp. 41-51 ◽  
Author(s):  
Awad El-Gohary
Keyword(s):  
Bayesian Estimation ◽  
Failure Rate ◽  
Independent Component ◽  
Series System

REDEFINING FAILURE RATE FUNCTION FOR DISCRETE DISTRIBUTIONS

2002 ◽  
Vol 09 (03) ◽  
pp. 275-285 ◽  
Author(s):  
M. XIE ◽  
O. GAUDOIN ◽  
C. BRACQUEMOND
Keyword(s):  
Failure Rate ◽  
Rate Function ◽  
Monotonicity Property ◽  
Discrete Distributions ◽  
The Other ◽  
Continuous Case ◽  
Discrete Version ◽  
Series System ◽  
Failure Rate Function ◽  
Definition Of

For discrete distribution with reliability function R(k), k = 1, 2,…,[R(k - 1) - R(k)]/R(k - 1) has been used as the definition of the failure rate function in the literature. However, this is different from that of the continuous case. This discrete version has the interpretation of a probability while it is known that a failure rate is not a probability in the continuous case. This discrete failure rate is bounded, and hence cannot be convex, e.g., it cannot grow linearly. It is not additive for series system while the additivity for series system is a common understanding in practice. In the paper, another definition of discrete failure rate function as In[R(k - 1)/R(k)] is introduced, and the above-mentioned problems are resolved. On the other hand, it is shown that the two failure rate definitions have the same monotonicity property. That is, if one is increasing/decreasing, the other is also increasing/decreasing. For other aging concepts, the new failure rate definition is more appropriate. The failure rate functions according to this definition are given for a number of useful discrete reliability functions.

Reliability Estimation for Cold Standby Series System Based on General Progressive Type II Censored Samples

2013 ◽  
Vol 321-324 ◽  
pp. 2460-2463 ◽  
Author(s):  
Yi Min Shi ◽  
Xiao Lin Shi
Keyword(s):  
Bayesian Estimation ◽  
Reliability Function ◽  
Reliability Estimation ◽  
Likelihood Method ◽  
Series System ◽  
Type Ii ◽  
Censored Samples ◽  
Progressive Type ◽  
Cold Standby ◽  
Two Parameter

Suppose that the life of unit is distributed as two-parameter exponential distribution. The Bayesian estimation for cold standby series system is studied based on general Progressive type II censored samples. Under the different error loss, the Bayesian estimation of the unknown parameter and reliability function are derived where hyper-parameters are estimated by using Maximum likelihood method. At last, a numerical example is given by means of the Monte-Carlo simulation to illustrate the correctness and feasibility for the method proposed in this paper.

Estimation of Failure Rate and its Applications in the Case of Zero-Failure Data

2014 ◽  
Vol 945-949 ◽  
pp. 1046-1049
Author(s):  
Ming Han
Keyword(s):  
Bayesian Estimation ◽  
Failure Rate ◽  
Estimation Method ◽  
New Method ◽  
Hierarchical Bayesian ◽  
Failure Data ◽  
Hierarchical Bayesian Estimation ◽  
Definition Of

This paper introduces a new method, named E-Bayesian estimation method, to estimate failure rate in zero-failure data. The definition of E-Bayesian estimation of the failure rate is given, based on the definition, the formulas of E-Bayesian estimation and hierarchical Bayesian estimation of the failure rate were provided, and properties of the E-Bayesian estimation, i. e. relations between E-Bayesian estimation and hierarchical Bayesian estimation, was discussed. Calculations were performed on practical problems, showing that the proposed new method is feasible and easy to operate.

A Bayesian approach to the optimization reliability costs

2013 ◽  
Vol 10 (6) ◽  
pp. 577-584
Author(s):  
S. Beleulmi ◽  
A. Bellaouar ◽  
M. Lachi
Keyword(s):  
Bayesian Estimation ◽  
Failure Rate ◽  
Bayesian Approach ◽  
A Priori ◽  
Reliability Testing ◽  
Classical Approach ◽  
Electronic Components ◽  
Virtual Testing ◽  
Bayesian Techniques ◽  
The Cost

The lack of reliability testing in a project finds its reason in financial considerations and deadlines. In this context, Bayesian techniques find their applications as they contribute to a significant reduction in the amount of reliability testing based on the classical approach, with the knowledge of the reliability data on a priori relevant components. This paper is devoted to a Bayesian approach to the optimization reliability costs of tests conducted on the electronic components installed in a lift. The Bayesian estimation provides a failure rate of 1,795·10-6 failure/hr to 60% confidence instead of 2,771·10-6 failure / hr after testing. A gain of 64, 77% in terms of time and therefore the cost of testing will be reduced considerably. When the number of failures increases (K0 = 2; 3 and 5), the real tests are not added to virtual testing and a decrease in time to be won has been recorded.

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