On the availability of a warm standby system: a numerical approach

Vanderperre, E. J.; Makhanov, Stanislav S.

doi:10.1007/s11750-013-0285-9

Cited by 5 publications

(6 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some important examples include: 1-out-of-2:G systems with common cause failures and human errors [7], with imperfect sensing and switching [8], 2-out-of-5:G systems with common cause failures and replacements [9], k-out-of-n:G warm standby system with r repair facilities [10], [11], with balking and reneging components [12], with components with multiple failure modes [13], with unreliable repair facilities [14], warm standby systems with two nonidentical components and failure of switching [15], warm standby subsystems with two nonidentical components and in series connection with another subsystem [16]. In cases of nonexponential distributions, supplementary variable techniques [17]- [22] and PH distribution techniques [23], [24] can be used. Moreover, warm standby systems with s-identical components can be solved by developing iterative equations for state probabilities by event decomposition [25], [26].…”

Section: A Related Workmentioning

confidence: 99%

Availability Modeling of Generalized $k$ -Out-of- $n$ :G Warm Standby Systems With PEPA

Xiao-yue

Hillston

Feng

2017

IEEE Trans. Syst. Man Cybern, Syst.

View full text Add to dashboard Cite

Developing analytical availability models for k-outof-n:G warm standby repairable systems with many nonidentical components is tedious and error-prone, requiring specification of the generator matrix of a high dimensional Markov chain. Using the performance evaluation process algebra (PEPA) as an intermediary, this paper gives a new modeling approach for availability evaluation of such systems with r repair facilities. The components of the system are classified into n different groups that consist of statistically identical components following exponential time-to-failure and repair time distributions. A library of PEPA components and their actions are defined for system component groups, repair facilities, repair queue, and system dynamics. To capture the dependency of system states on components, a signaling mechanism is realized by actions with suitably high rates. A compilation tool is provided to automatically generate the PEPA model from a brief specification of the system, using the library components. This provides input for the PEPA analysis tool and is amenable to availability analysis. Examples are used to illustrate the proposed modeling method. Modeling with PEPA provides an efficient way to deal with availability evaluation of systems considered with many groups of repairable components.

show abstract

Section: A Related Workmentioning

confidence: 99%

Availability Modeling of Generalized $k$ -Out-of- $n$ :G Warm Standby Systems With PEPA

Xiao-yue

Hillston

Feng

2017

IEEE Trans. Syst. Man Cybern, Syst.

View full text Add to dashboard Cite

show abstract

“…Applying a general birth and death technique, e.g. [22] and taking the absorbing state D into account, yields the balance equations Taking the definition of directional derivative into account, for instance, Note that the initial condition N 0 = A, X 0 = f with probability one, entails that p A (0, x) = dF/dx. Moreover, P r {θ 6 t} = p D (t).…”

Section: Differential Equationsmentioning

confidence: 99%

A functional equation related to a repairable system subjected to priority rules

Vanderperre¹,

Makhanov

2016

Eur. J. Appl. Math

View full text Add to dashboard Cite

We analyse the survival time of a general duplex system sustained by an auxiliary cold standby unit and subjected to priority rules. The duplex system is attended by two general repairmen Rp and Rh. Repairman Rp has priority in repairing failed units with regard to repairman Rh provided that both repairmen are jointly idle. Otherwise, the priority is overruled. The auxiliary unit has its own repair facility. The duplex system has overall, break-in priority (often called pre-emptive priority) in operation and in standby with regard to the auxiliary unit. The analysis of the survival time is based on advanced complex function theory (sectionally holomorphic functions). The main problem is to convert a functional equation into a (parameter dependent) Sokhotski–Plemelj problem.

show abstract

“…Applying a general birth and death technique, e.g. Vanderperre and Makhanov (2013c), and taking the absorbing state D into account yields the balance equations…”

Section: Differential Equationsmentioning

confidence: 99%

“…To achieve computational results, the proper methodology could then be a numerical solution procedure of the extended differential equations (cf. Vanderperre and Makhanov 2013c). Therefore, the transient and stationary behaviour of the Tsystem is an open problem and needs further research.…”

Section: Open Problemmentioning

confidence: 99%

See 1 more Smart Citation

Reliability of Birolini’s duplex system sustained by a cold standby unit and subjected to a priority rule

Vanderperre¹,

Makhanov

2014

TOP

View full text Add to dashboard Cite

We analyse the survival time of Birolini's duplex system sustained by a cold standby unit subjected to a priority rule. We employ a stochastic process endowed with time-dependent transition measures satisfying coupled partial differential equations leading to the Laplace transform of the survival function. As an example, we consider Coxian distributions for failure and repair. Some graphs are displayed together with a security interval corresponding to a security level of 90 %.

show abstract

On the availability of a warm standby system: a numerical approach

Cited by 5 publications

References 13 publications

Availability Modeling of Generalized $k$ -Out-of- $n$ :G Warm Standby Systems With PEPA

Availability Modeling of Generalized $k$ -Out-of- $n$ :G Warm Standby Systems With PEPA

A functional equation related to a repairable system subjected to priority rules

Reliability of Birolini’s duplex system sustained by a cold standby unit and subjected to a priority rule

Contact Info

Product

Resources

About