GERT Analysis of m-consecutive-k-out-of-n:F Systems with Dependence
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Manju Agarwal
Abstract
In this paper the reliability analysis of two new models generalizing the m-consecutive-k-out-of-n:F system is carried out using GERT:
Model I: m-consecutive-k-out-of-n:F system with (k-1)-step Markov dependence, and
Model II: m-consecutive-k-out-of-n:F system with Block-k dependence.
For both the models, the system consists of n linearly ordered components. In Model I, the system fails, if and only if there are at least m non-overlapping runs of k consecutive failed components having (k-1)-step Markov dependence. We call such a system m-consecutive-k-out-of-n:F with (k-1)-step Markov dependence. Model II represents an m-consecutive-k-out-of-n:F system, in which each subsequent occurrence of a block of k-consecutive failures increases the failure probability of the remaining components. We define such a system as m-consecutive-k-out-of-n:F with Block-k dependence. GERT provides a visual picture of the system and helps to analyze the system in a less inductive manner. Mathematica Software is used for systematic computations. Illustrative numerical examples for reliability evaluation of these systems showing the time efficiency of GERT analysis are also provided.
© Heldermann Verlag
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Articles in the same Issue
- Bivariate Density Classification by the Geometry of the Marginals
- Improving the Variability Function in Case of a Uni-Modal Probability Distribution
- New Results in Economic Statistical Quality Control
- Reliability Analysis Based on Scalar Fuzzy Variables
- A Bayesian Approach to Parallel Stress-Strength Models
- Max-Chart for Autocorrelated Processes
- A Note on Classes of Lifetime Distributions
- Sampling Risks for Chain Sampling Plans with Non-Constant Defective Probability
- Effects of Measurement Error on Controlling Two Dependent Process Steps
- GERT Analysis of m-consecutive-k-out-of-n:F Systems with Dependence
