scholarly journals On Reliability of a Double Redundant Renewable System with a Generally Distributed Life and Repair Times

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 278
Author(s):  
Vladimir Rykov ◽  
Dmitry Efrosinin ◽  
Natalia Stepanova ◽  
Janos Sztrik
Keyword(s):  
Closed Form ◽  
Reliability Analysis ◽  
Stationary State ◽  
Life Time ◽  
Time Dependent ◽  
Regenerative Processes ◽  
Stieltjes Transform ◽  
Reliability Measures ◽  
Time Between Failures ◽  
Probabilistic Measures

The paper provides reliability analysis of a cold double redundant renewable system assuming that both life-time and repair time distributions are arbitrary. The proposed approach is based on the theory of decomposable semi-regenerative processes. We derive the Laplace–Stieltjes transform of two main reliability measures like the distribution of the time between failures and the time to the first failure. The transforms are used to calculate corresponding mean times. It is further derived in closed form the time-dependent and time stationary state probabilities in terms of the Laplace transforms. Numerical results illustrate the effect of the type of distributions as well as their parameters on the derived reliability and probabilistic measures.

scholarly journals Application of Decomposable Semi-Regenerative Processes to the Study of k-out-of-n Systems

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1933
Author(s):  
Vladimir Rykov ◽  
Nika Ivanova ◽  
Dmitry Kozyrev
Keyword(s):  
Closed Form ◽  
Time Dependent ◽  
System State ◽  
Regenerative Processes ◽  
Full System ◽  
Special Cases ◽  
Form Representation ◽  
History Of ◽  
First Time ◽  
Stationary Probabilities

This paper aimed to demonstrate the capabilities of decomposable semi-regenerative processes for the investigation of the k-out-of-n system. Proposed in 1955 by W. Smith, the regeneration idea has come a long way in terms of development and has found widespread applications. First, we briefly recall the history of the development of the regeneration idea and the main results of the theory of regenerative, semi-regenerative, and decomposable semi-regenerative processes. Then, the methods of the theory of decomposable semi-regenerative processes are used for the study of a k-out-of-n renewable system with exponentially distributed life and generally distributed repair times of its components. This system is very important for practice and its special cases have previously been considered (including by the authors); however, only special cases and using other methods are considered herein. In the current paper, two scenarios of system repair after its failure are considered for the first time: the partial and the full system repair scenarios. For both scenarios, the time-dependent system state probabilities are calculated in terms of their Laplace transforms. The closed form representation of the stationary probabilities for both scenarios are also presented. These latest results represent a new contribution to the study of this system.

RELIABILITY ANALYSIS OF PHASED MISSIONS

1995 ◽  
Vol 02 (04) ◽  
pp. 405-417
Author(s):  
WINFRID G. SCHNEEWEISS
Keyword(s):  
Markov Model ◽  
Reliability Analysis ◽  
Time Distribution ◽  
Life Time ◽  
Reliability Measures ◽  
Model Case ◽  
Component Failure ◽  
Triple Modular Redundancy ◽  
Mission Success ◽  
Modular Redundancy

It is shown that in a number of cases mission success probabilities and related reliability measures can be determined, once appropriate mission phases are defined. The results are general, i.e., not limited to the Markov model case, but intentionally kept “simple” by considering only few components and few different phases. The problems specifically addressed (and solved) are: (1) Non-ideal switches for activating spares, (2) and (3) degraded operation, and change from TMR (Triple Modular Redundancy) to simplex structure on the first component failure, respectively, (4) preventive renewals after alternating periods, and (5) load-dependent two-phased life time distribution.

scholarly journals Time-Dependent Reliability Analysis of Reinforced Concrete Beams Subjected to Uniform and Pitting Corrosion and Brittle Fracture

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1820
Author(s):  
Mohamed El Amine Ben Seghier ◽  
Behrooz Keshtegar ◽  
Hussam Mahmoud
Keyword(s):  
Reinforced Concrete ◽  
Brittle Fracture ◽  
Reliability Analysis ◽  
Pitting Corrosion ◽  
Structural Reliability ◽  
Time Dependent ◽  
State Function ◽  
Rc Beams ◽  
Highly Nonlinear ◽  
Reliability Method

Reinforced concrete (RC) beams are basic elements used in the construction of various structures and infrastructural systems. When exposed to harsh environmental conditions, the integrity of RC beams could be compromised as a result of various deterioration mechanisms. One of the most common deterioration mechanisms is the formation of different types of corrosion in the steel reinforcements of the beams, which could impact the overall reliability of the beam. Existing classical reliability analysis methods have shown unstable results when used for the assessment of highly nonlinear problems, such as corroded RC beams. To that end, the main purpose of this paper is to explore the use of a structural reliability method for the multi-state assessment of corroded RC beams. To do so, an improved reliability method, namely the three-term conjugate map (TCM) based on the first order reliability method (FORM), is used. The application of the TCM method to identify the multi-state failure of RC beams is validated against various well-known structural reliability-based FORM formulations. The limit state function (LSF) for corroded RC beams is formulated in accordance with two corrosion types, namely uniform and pitting corrosion, and with consideration of brittle fracture due to the pit-to-crack transition probability. The time-dependent reliability analyses conducted in this study are also used to assess the influence of various parameters on the resulting failure probability of the corroded beams. The results show that the nominal bar diameter, corrosion initiation rate, and the external loads have an important influence on the safety of these structures. In addition, the proposed method is shown to outperform other reliability-based FORM formulations in predicting the level of reliability in RC beams.

Uncertain time-dependent reliability analysis of corroded RC structures applying three-term conjugate method

2020 ◽  
Vol 115 ◽  
pp. 104599 ◽  
Author(s):  
Mansour Bagheri ◽  
Seyed Abbas Hosseini ◽  
Behrooz Keshtegar ◽  
José A.F.O. Correia ◽  
Nguyen-Thoi Trung
Keyword(s):  
Reliability Analysis ◽  
Time Dependent ◽  
Rc Structures ◽  
Uncertain Time

Some analyses on the control of queues using level crossings of regenerative processes

1980 ◽  
Vol 17 (3) ◽  
pp. 814-821 ◽  
Author(s):  
J. G. Shanthikumar
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Queueing Systems ◽  
Density Functions ◽  
Waiting Time Distribution ◽  
Regenerative Processes ◽  
Stieltjes Transform ◽  
Expected Number ◽  
Control Of Queues ◽  
Special Case

Some properties of the number of up- and downcrossings over level u, in a special case of regenerative processes are discussed. Two basic relations between the density functions and the expected number of upcrossings of this process are derived. Using these reults, two examples of controlled M/G/1 queueing systems are solved. Simple relations are derived for the waiting time distribution conditioned on the phase of control encountered by an arriving customer. The Laplace-Stieltjes transform of the distribution function of the waiting time of an arbitrary customer is also derived for each of these two examples.

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