In today’s world of technology, it is impossible to see where computer system does not play an important role. The application of distributed systems is gradually becoming broad and diverse, and as a result of this, reliability prediction is a key concern. This paper, considered a distributed system with five standby subsystems A (the clients), B (two load balancers), C (two distributed database servers), D (two mirrored distributed database serves) and E (centralized database server) is considered arranged as series-parallel system. Exponential failure and repair are susceptible for all the components of this system. Each component’s failure rates are constant and considered to obey an exponential distribution, and they are repaired using general repair or copula repair. The system is evaluated using first-order partial differential equations and the supplementary variable technique, Gumbel-Hougaard family of Copula, to find expressions for reliability metrics of system strength such as availability, reliability, MTTF, sensitivity, and profit function. These reliability metrics have been validated for different parametric values and the results are presented in tables and figures. تفاصيل المقالة

The goal of this study is to provide an analytical framework for a standby serial sachet water plant. The plant is made up of five subsystems: a storage tank, filters, a tank, boosters, and a production machine, all of which are set up in a series-parallel configuration. The failure rates of both subsystems/units are continuous and supposed to tail exponential function, but repair is categories into the following; general repair for partially failed state while copula repair for complete failed state. A repair person is on-call 24 hours a day, seven days a week to repair failed units in the system. The transition diagram is used to obtain partial differential equations of degree one, which are resolved using supplementary variable procedure, Laplace conversion and MAPLE software, to derive expressions for numerous dependability agencies name; availability, reliability, MTTF, sensitivity MTTF, and cost of the sachet water plant. Arithmetical instances are delivered in order to demonstrate the achieved results and also to investigate the influence of parameters used. Tables and figures revealed that copula repair outperforms general repair in terms of returns. تفاصيل المقالة

Repair machines play a critical role in military, communication, industrial, and manufacturing settings. This study investigates the performance of a system that utilizes repair machines with human operators, employing Copula's attributes for estimation. The research focuses on a serial system composed of two subsystems, each consisting of two active components running in parallel. Both subsystems are manned by two human operators and assigned two repair machines for operation and maintenance, where the repair machines are considered failure-prone systems. The system experiences partial and complete malfunction during operation: Partial malfunction lead the system into reduced capacity mode, and a complete malfunction resulting in system failure. The research employs the technique of supplementary variable and transforms of Laplace to establish and solve the governing differential equations corresponding to schematic system's diagram. Performance models for the system such as profit, MTTF, availability, sensitivity of MTTF and reliability are numerically validated and presented through tables and graphs. These findings are highly valuable for evaluating performance, identifying ideal system designs, and developing workable maintenance plans. The research contributes to enhancing system performance, increasing production output, and improving revenue mobilization in various application domains. تفاصيل المقالة