Reliability analysis of generalized multi-state k-out-of-n systems

Abstract

The recently proposed generalized multi-state k-out-of- n system model provides more flexibility in describing practical systems. In this model, there are n components in the system where each component and the system can be in one of M + 1 possible states: 0, 1, 2, …, M. The system is in below state j if there exists an integer value l, (1 ≤ i ≤ j) such that at least kl components are in states below l. Although the model has several practical applications, existing methods for computing either the exact or approximate reliability of these systems are computationally inefficient and limited to very small systems. This paper proposes an efficient method and a detailed algorithm to compute the exact reliability of multi-state k-out-of- n systems with independent and identically distributed components. The method is based on conditional probabilities and is applicable for all cases of multi-state k-out-of- n systems with respect to the recent definitions of this system.

Approximate Analysis of Multi-State Weighted k-Out-of-n Systems Applied to Transmission Lines

“…A binary-stated k-out-of-n: G system is anticipated to be reliable unless the number of working components is no less than a pre-specified threshold k [2], and a binary-stated k-out-of-n: F system is inaccessible when the number of failed components is no less than k [3]. However, some engineering systems such as power/oil lines transmission systems perform the intended tasks at multiple performance levels, which indicates the system's capability (electric power, oil, etc.)…”

Mixture Representations for Three-State Systems With Three-State Components

“…Multi-state systems with multi-state components have a wide range of applications in diverse fields. Various multi-state extensions of well known -out-of-and consecutive--out-ofsystems have been defined and studied in the literature ( [3], [8], [9], [11], [15]- [20]). In these extensions, both the system and its components are multi-state.…”

“…Assume that the first and second level structures or equivalently the Rule I and Rule II are characterized respectively by the functions and . Then the lifetime of the three-state system can be expressed as (3) and the lifetime of the system in state 2 is defined by (4) Clearly, the abovementioned three-state -out-of-:G system is included in this general definition when , and , where is the th smallest in . There are some other systems which can be represented in this way.…”

Comparisons of standby and parallel systems in reliability, replacement, scheduling and application

“…Two typical redundancies are standby and parallel systems, which have been studied extensively in the literature. [3][4][5] However, there is no study to compare them from the viewpoints of reliability measures, maintenance policies, engineering applications, etc.…”