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Reliability Improvement of Circular k-out-of-n: G Balanced Systems through Center of Gravity

Yongkyu Cho, Seung Min Baik, Young Myoung Ko

Abstract

This paper considers a circular k-out-of-n: G balance system equipped with homogeneous and stationary units. Building on previous research by Endharta et al. (Reliability Engineering & System Safety, 2018), we propose a new balance definition in circular k-out-of-n: G balance systems based on the concept of center of gravity. According to this condition, a circular k-out-of-n: G balance system is considered balanced if its center of gravity is located at the origin. This new balance condition is not only simple but also advantageous as it covers the previous two balance conditions of symmetry and proportionality. To evaluate the system's reliability, we consider the minimum tie-sets, and extensive numerical studies verify the enhancement of system reliability resulting from the proposed balance definition.

Reliability Improvement of Circular k-out-of-n: G Balanced Systems through Center of Gravity

Abstract

This paper considers a circular k-out-of-n: G balance system equipped with homogeneous and stationary units. Building on previous research by Endharta et al. (Reliability Engineering & System Safety, 2018), we propose a new balance definition in circular k-out-of-n: G balance systems based on the concept of center of gravity. According to this condition, a circular k-out-of-n: G balance system is considered balanced if its center of gravity is located at the origin. This new balance condition is not only simple but also advantageous as it covers the previous two balance conditions of symmetry and proportionality. To evaluate the system's reliability, we consider the minimum tie-sets, and extensive numerical studies verify the enhancement of system reliability resulting from the proposed balance definition.
Paper Structure (18 sections, 5 theorems, 15 equations, 10 figures, 1 table)

This paper contains 18 sections, 5 theorems, 15 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Literature Review
  3. System Description
  4. Balance Conditions
  5. BC1: System is symmetric
  6. BC2: System is spread proportionally
  7. BC3: System has a center of gravity at origin
  8. Relationship between the balance conditions
  9. Reliability Evaluation
  10. Minimum tie-sets
  11. System reliability
  12. A descriptive numerical example
  13. Numerical Analysis
  14. Reliability comparison for the systems with various parameters
  15. Summary with interpretation
  16. ...and 3 more sections

Key Result

Proposition 1.1

For a circular $k$-out-of-$n$: G balanced system with an index set of non-failed units $U$, the axis of symmetry is located between units $u_1$ and $u_{l+1}$ for $l$ such that $E^{(l)}=D_U$. Thus, $|\mathbf{E}_U^B|$ can represent the number of axes of symmetry in the system and the system balance is

Figures (10)

  • Figure 1: An illustrative example of a multi-rotor drone and its corresponding system model
  • Figure 2: Illustrative examples for BC1
  • Figure 3: Representative examples of the systems satisfying BC2
  • Figure 4: Illustrative examples for BC2
  • Figure 5: Illustrative examples for BC3 (the colored 'x'-markers represent the center of gravity for each subsystem)
  • ...and 5 more figures

Theorems & Definitions (15)

  • Definition 1: BC1
  • Proposition 1.1: Endharta et al. EYK2018
  • Remark 1.1
  • Definition 2: BC2
  • Remark 2.1
  • Remark 2.2: Endharta and Ko EK2020
  • Definition 3: BC3
  • Remark 3.1
  • Proposition 3.1
  • proof
  • ...and 5 more