The present paper discuss the reliability characteristics of computer network system consisting of the devices load balancer, distributed database servers and a centralized server configured as series parallel system containing three subsystems. Subsystem 1: load balancer (LB) a device that act as a medium of channeling request to servers and receiving request or response from servers. Subsystem 2: identical distributed database servers (DDS) I, II and III connected in parallel, working under 2-out-of-3: G: policy, which manages and store some part of application data and Subsystem 3: centralized distributed database server (CDDS), which takes care of all the application data in DDS. Through the transition diagram, system of firstorder partial differential equations are derived and solved using supplementary variable techniques, Laplace transforms and copula method. All failures are assumed to be exponentially distributed, whereas repairs follow two types of distributions; general distribution and Gumbel-Hougaard family copula, partial failures are repaired by general distribution while complete failures are repaired by copula distribution. The objective is to obtain the expressions for availability, reliability, mean time to failure (MTTF) and cost function. Computations for reliability measures are taken as particular case by evaluating: reliability, availability, MTTF and cost analysis, so as to capture the effect of both failure and repair rates to reliability measures. The results of the computations are presented in tables and graphs. The analysis of the results obtained with respect to the availability and expected profit indicates that copula repair policy is reliable than general repair policy.

PurposeThis study deals with the reliability analysis of a hybrid series–parallel system consisting of two subsystems A and B with two human operators. Subsystem A has two units in active parallel while subsystem B consists of two-out-of-four units. Both units have exponential failure and repair time. The system under consideration has two states: partial failure state and complete failure state. The mathematical equations associated with the transition diagram have been formulated using regenerative point techniques. The system is analysed using Laplace transforms to solve the mathematical equations. Some important measures of reliability such as availability of system, reliability of the system, mean time to failure (MTTF), sensitivity for MTTF and cost analysis have been discussed. Some particular cases have also been derived and examined to see the practical effect of the model. The computed results are demonstrated by tables and graphs. Furthermore, the results of the designed model are beneficial for system engineers and designers, reliability and maintenance managers.Design/methodology/approachThis paper considered a hybrid series–parallel system consisting of two subsystems A and B with two human operators. The performance of the system is studied using the supplementary variable technique and Laplace transforms. The various measures of reliability such as availability, reliability, mean time to system failure (MTSF), sensitivity for MTTF and cost analysis have been computed for various values of failure and repair rates. Maple 13 software has been used for computations.FindingsIn this research paper, the authors have computed various measures of reliability such as availability, reliability, MTSF, sensitivity for MTTF and cost analysis for various values of failure and repair rates and find that failure due to human operators are more responsible for successful operation of the system and also regular repair should be invoked to improve system performance.Originality/valueThis research paper is the original work of authors. The references are well cited based on the importance of study. Nothing has been detached from any research paper or books.

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This paper is the stochastic analysis of a complex repairable system comprising of subsystems in a series arrangement under the [Formula: see text]-out-of-[Formula: see text]: [Formula: see text] type configuration. Both of the subsystems are in series arrangement and having auto transfer switches when some unit fails. Subsystem 1 is supposed to work under the [Formula: see text]-out-of-[Formula: see text]: [Formula: see text], scheme, and subsystem 2 which has four indistinguishable units in parallel arrangement with an auto switch functioning under the 1-out-of-4: [Formula: see text] scheme. A catastrophic failure is characterized as causing damage to the entire system. Units’ failure, switch failures, and catastrophic failure rates are constant, but repair rates are treated as variables with two types of distributions: general distribution and copula distribution. The model is analyzed using a supplementary variables approach, with probabilistic measures such as availability, reliability, MTSF, and profit functions derived.

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