A k‐out‐of‐n reliability system with an unreliable server and phase type repairs and services: the (N, T) policy

Chakravarthy, Srinivas; Krishnamoorthy, A.; Ushakumari, P. V.

doi:10.1155/s1048953301000326

Cited by 31 publications

(15 citation statements)

References 24 publications

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“…If we consider as the cost of one inspection, then the total inspection cost would be (1) where is the number of periodic inspections. There is also an inspection when the system fails.…”

Section: Inspection Optimization Model and A Special Case Of A mentioning

confidence: 99%

“…For many systems, such as medical devices, unreliability could result in serious consequences; for example, disability or even death of patients. Redundancy is a cost-effective method of configuring a system at the design stage to achieve the desired level of reliability [1]. Computers with multiprocessors, multi-engine machines, aircraft engines, and electric generators are some examples of redundant systems.…”

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confidence: 99%

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Periodic Inspection Optimization of a k-Out-of-n Load-Sharing System

Taghipour

Kassaei

2015

IEEE Trans. Rel.

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In this paper, we consider a k-out-of-n load-sharing system with identical components sharing a certain amount of load. Each time a component fails, its load is distributed to the remaining components; we assume an increase in load increases the hazard rates of the remaining components. The system is periodically inspected to detect failed components. Two cases may occur in an inspection interval: if the number of failed components is less than , then the failed components are only rectified at periodic inspections; if the number of failures reaches , then the system fails, and at this time, all the failed components are inspected and rectified. A failed component is replaced or minimally repaired according to a probability which depends on its age at the failure time. The components' failures follow a Non-Homogenous Poisson Process (NHPP), and their intensity functions depend on their ages and the loads to which they are exposed at any moment. In this paper, we develop a model to find the optimal inspection interval for such a system, which minimizes the total expected cost incurred over the system lifecycle. We derive the analytical solution for the special case of a 1-out-of-2 system, and discuss its computational difficulties. We then present a simulation algorithm to find the required expected values in the objective function. Several numerical examples are presented to illustrate the proposed model.Index Terms-k-out-of-n system, load sharing system, periodic inspection, optimization, hidden failures, repairable systems, minimal repair, replacement.

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“…If we consider as the cost of one inspection, then the total inspection cost would be (1) where is the number of periodic inspections. There is also an inspection when the system fails.…”

Section: Inspection Optimization Model and A Special Case Of A mentioning

confidence: 99%

mentioning

confidence: 99%

Periodic Inspection Optimization of a k-Out-of-n Load-Sharing System

Taghipour

Kassaei

2015

IEEE Trans. Rel.

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“…where e (0) is a column vector whose last mm 1 entries are 0s and all other entries are 1s and e (1) is a column vector whose last m(m 1 + m 2 ) entries are 0s and all other entries are 1s. (2) Probability that system is down P down = 1 − θ 1 .…”

Section: System Performance Measuresmentioning

confidence: 99%

“…Godbole et al 3 improve upon the upper bounds for the reliability of a d-dimensional consecutive k-out-of-n; f -system. Chakravarthi et al 1 examine the reliability of a k-out-of-n system whose failed components are repaired by an unreliable server. The repair time of the server and that of failed components of the system are assumed to have the phase-type distributions.…”

Section: Introductionmentioning

confidence: 99%

RELIABILITY OF A k-OUT-OF-n SYSTEM WITH REPAIR BY A SERVICE STATION ATTENDING A QUEUE WITH POSTPONED WORK

Krishnamoorthy

Narayanan

Deepak³

2007

Int. J. Rel. Qual. Saf. Eng.

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In this paper the reliability of a repairable k-out-of-n system is studied. Repair times of components follow a phase type distribution. In addition, the service facility offers service to external customers which arrive according to a MAP. An external customer, who finds an idle server on its arrival, is immediately selected for service. Otherwise, the external customer joins the queue in a pool of postponed work of infinite capacity with probability 1 if the number of failed components in the system is < M (M ≤ n − k + 1) and if the number of failed components ≥ M it joins the pool with probability γ or leaves the system forever. Repair times of components of the system and that of the external customers have independent phase type distributions. At a service completion epoch if the buffer has less than L customers, a pooled customer is taken for service with probability p, 0 < p < 1 If at a service completion epoch no component of the system is waiting for repair, a pooled customer, if any waiting, is immediately taken for service. We obtain the system state distribution under the condition of stability. A number of performance characteristics are derived. A cost function involving L, M , γ and p is constructed and its behaviour investigated numerically.

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“…Many different techniques are used by engineers to design a system which can satisfy a minimum level of reliability. One of the most common and cost-effective design techniques is redundancy configuration [3]. Redundancy is the existence of alternative ways to perform a required function in a system.…”

Section: Introductionmentioning

confidence: 99%

Inspection optimization of load-sharing systems

Kassaei¹

2021

Preprint

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In this thesis, periodic inspection of a load-sharing k-out-of-n system has been studied to obtain the optimal inspection interval using the analytical and simulation approaches. The components of a load-sharing system are stochastically dependent, which makes the analysis of these systems more complex than those with independent components. In order to acquire the optimal inspection interval for the system, two models have been developed to study load-sharing systems with Tampered Failure Rate (TFR) and Cumulative Exposure (CE). The former considers only the current load of the components and the later accounts for the history of load. Various load intensities are examined to study the effects of this parameter on each model. It is observed that as the load intensity increases, the system needs more frequent inspections. The results also reveal that a system with the CE model requires a shorter inspection interval in comparison to that with the TFR model.

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A k‐out‐of‐n reliability system with an unreliable server and phase type repairs and services: the (N, T) policy

Cited by 31 publications

References 24 publications

Periodic Inspection Optimization of a k-Out-of-n Load-Sharing System

Periodic Inspection Optimization of a k-Out-of-n Load-Sharing System

RELIABILITY OF A k-OUT-OF-n SYSTEM WITH REPAIR BY A SERVICE STATION ATTENDING A QUEUE WITH POSTPONED WORK

Inspection optimization of load-sharing systems

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