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Joint reliability importance (JRI) of components is the effect of a change of their reliability on the system reliability. The authors consider two coherent multi-component systems – a series-in-parallel (series subsystems arranged in parallel) and a parallel-in-series (parallel subsystems arranged in series) system. It is assumed that all the components in the subsystems are independent but not identically distributed. The subsystems do not have any component in common. The paper aims to discuss these issues.

For both the systems, the expressions for the JRI of two or more components are derived. The results are extended to include subsystems where some of the components are replicated.

The findings are illustrated by considering bridge structure as a series-in-parallel system wherein some of the components are repeated in different subsystems. Numerical results have also been provided for a series-in-parallel system with unreplicated components. JRI for various combinations of components for both the illustrations are given through tables or figures.

Chang and Jan (2006) and Gao et al. (2007) found the JRI of two components of series-in-parallel system when the components are identical and independently distributed. The authors derive the JRI of m=2 components for series-in-parallel and parallel-in-series systems when components are independent but need not be identically distributed. Expressions are obtained for the above-mentioned systems with replicated and unreplicated components in different subsystems. These results will be useful in analyzing the joint effect of reliability of several components on the system reliability. This will be of value to design engineers for designing systems that function more effectively and for a longer duration.

This paper considers a series‐parallel and a parallel‐series system, and investigates theoretically their fundamental characteristics: it is shown that the reliability of the series‐parallel system with the same number of series and parallel tends to one as its number goes to infinity. It would be of great interest that the golden ratio plays a role in analyzing two systems. Further, an optimal number of units for a series‐parallel system with complexity is derived.

The purpose of this paper is to investigate the stochastic comparisons of the parallel system with independent heterogeneous Gumbel components and series and parallel systems with independent heterogeneous truncated Gumbel components in terms of various stochastic orderings.

The obtained results in this paper are obtained by using the vector majorization methods and results. First, the components of series and parallel systems are heterogeneous and having Gumbel or truncated Gumbel distributions. Second, multiple-outlier truncated Gumbel models are discussed for these systems. Then, the relationship between the systems having Gumbel components and Weibull components are considered. Finally, Monte Carlo simulations are performed to illustrate some obtained results.

The reversed hazard rate and likelihood ratio orderings are obtained for the parallel system of Gumbel components. Using these results, similar new results are derived for the series system of Weibull components. Stochastic comparisons for the series and parallel systems having truncated Gumbel components are established in terms of hazard rate, likelihood ratio and reversed hazard rate orderings. Some new results are also derived for the series and parallel systems of upper-truncated Weibull components.

To the best of our knowledge thus far, stochastic comparisons of series and parallel systems with Gumbel or truncated Gumble components have not been considered in the literature. Moreover, new results for Weibull and upper-truncated Weibull components are presented based on Gumbel case results.

The purpose of this paper is to research the impact of hybrid series‐parallel and parallel‐series system configurations on system performances based on system reliability and to develop a configuration model to meet the requirement of reconfigurable manufacturing system (RMS).

Based on the criterion of system reliability, a RMS configuration model is presented – the hybrid parallel‐series model with waiting system characteristics. The configuration model is evaluated from reliability, productivity, and cost by combining system engineering theory, Boolean algebra methodology with statistical analysis theory. The model reliability has been used to ameliorate by adopting the integrated algorithm based on Shrama and Misra optimization algorithm.

The need for application of this method and model – some constraints must be limited, the hybrid parallel‐series configuration is superior and the integrated algorithm is effective to RMS system configuration.

Cost constraints, equipment weight constraints, and function independency of equipment are main limitations.

The model and method have been used to ameliorate the reconfigurable automobile parts product line in SH automobile motor company of Shanghai. The operation result illustrates the validity of this configuration model and algorithm.

The new RMSs configuration model has been proposed. The new algorithm is proposed to ameliorate and optimize a reconfigurable product line with the integrated algorithm based on Shrama and Misra algorithm. The actual running effect is significant.

A range of small self‐contained hydraulic machine test sets are now available which permit small groups of students to obtain the usual performance characteristics of pumps and turbines with some ease‐though at the expense of efficiency due to scale effects. As most lecture courses include the application of pumps to systems as well as the basic considerations affecting pump performance, it was felt that a layout that allowed the student to combine two pumps in series and then in parallel would introduce him to the hydraulic considerations involved as well as give a more flexible piece of equipment that would permit these tests and a performance test to be conducted (for the basic performance curves would have to be produced first). The apparatus evolved is described, and skeleton laboratory instructions are attached as an appendix. When two similar pumps are connected in series, the fluid passes through each in turn, and the total head produced is approximately double that of one pump as illustrated in figure 1. When two similar pumps are connected in parallel, the total head produced is that of one pump, but the flow is approximately doubled, as shown in figure 2. Figure 3 is a diagrammatic layout of the hydraulic system. The apparatus consists basically of two similar pumps A and B which can be run as single units, connected and operated in series, or connected and run in parallel as will be seen from figure 3, the valves 2 and 4 are closed when series operation is desired, and flow controlled by valve 6; when operation in parallel is required valve 3 is closed, all others being open. A single sump tank is provided, flow measurement is achieved by simple volumetric means and pressure is measured by bourdon‐type gauges, a, b, c and d. The pumps are supplied by Stuart Turner with a duty of 50 feet at approximately 1300 gpm at 2900 rpm, they may operate at 1450 rpm or 2900 rpm, are provided with swinging stators for torque measurement and with a revolution counter for average speed determination. As will be seen from the appendix, the sequence of tests to be performed requires the student to obtain the basic performance characteristics of each pump at the two rotational speeds possible, and to compare them using the Similarity laws; then to test the pumps connected in series and parallel and to compare the performance obtained with that predicted. Figures 4 and 6 give some typical curves and show that the actual performances in series and parallel do not quite fulfil those predicted ignoring losses‐the student is required to consider the contributory factors in his discussion. The writer is grateful to Plint and Partners Limited for their co‐operation.

The purpose of this paper is to design a ring network topology system and alter it into a series–parallel type framework. Then, reliability of the framework is analysed and authors also discussed the signature to analyse the most sensitive component.

This study presents a ring-shaped network system where this type of topology forms a single continuous pathway for signals through every node. In this study, a system consists of ring network topology is generalized in the series–parallel mixed configuration and reliability characteristics are evaluated with the assistance of universal generating function (UGF) technique. The system consists of wires, repeaters, components or computers and power supply. The wires and repeaters are in series, so, if they fail the whole system will fail and the signals will not go further. The components or computers are connected to each other in parallel configuration. So, the whole system will not fail until the last computer is working. There is also a two-unit power supply system which has one unit in a standby mode. On the failure of first power supply, the second one will start functioning and the whole system fails on the failure of both power supply.

By the assistance of UGF technique, reliability function of the framework is evaluated. Also, Barlow–Proschan index and expected lifetime for the designed system is estimated by considering a numerical example for the general ring-shaped network system.

UGF technique is very effective for estimating the reliability of a system with complex structure and having two performance rates, i.e. completely failed and perfectly working, or more than two, i.e. multi-state performance. This technique enables to estimate every components contribution in the working and failure of the whole system. A general model of ring-shaped network system is taken and generalized algorithm is drawn for the system. Then a particular numerical example is solved for illustrating the use of this technique.

The purpose of this paper is to introduce a method for modelling the multi-state repairable systems subject to stochastic degradation processes by using the coloured stochastic Petri nets (CSPN). The method is a compact and flexible Petri nets model for multi-state repairable systems and offers an alternative to the combinatory of Markov graphs.

The method is grounded on specific theorems used to design an algorithm for systematic construction of multi-state repairable systems models, whatever is their size.

Stop and constraint functions were derived from these theorems and allow to considering k-out-of-n structure systems and to identifying the minimal cut sets, useful to monitoring the states evolution of the system.

The properties of this model will be studied, and new investigations will help to demonstrate the feasibility of the approach in real world, and more complex structure will be considered.

The simulation models based on CSPN can be used as a tool by maintenance decision makers, for prediction of the effectiveness of maintenance strategies.

The proposed approach and model provide an efficient tool for advanced investigations on the development and implementation of maintenance policies and strategies in real life.

The purpose of this paper is to analyze a parallel system consisting of n dependent components with lifetimes following Weibull distribution. FGM Copula in multivariate case is used to generate the reliability function of the original system. A reduction method is introduced to improve system reliability. Other methods of hot, cold and warm duplication are established to improve system reliability. An application is introduced to show the results and compare between different improvement methods.

In this paper, a study of a parallel system consisting of n dependent and non-identical components is introduced. Reliability function of the original system is derived by using the concepts of copula, subject to Weibull distribution. Reliability function of the original system is improved according to reduction, hot duplication, warm and cold duplication methods. Reliability equivalence factors are introduced to compare between different system designs. Numerical illustration and real-time data application are discussed to show the results obtained in this paper.

Copulas can be used to model the reliability of systems with dependent units.

This paper is original. Improvement of the reliability of dependent systems is not discussed in literature. Copula is a useful tool to analyze the reliability of dependent systems. The introduced model is considered as a generalization of the models discussed in literature.

Large‐scale systems have been developed with increasing requirements of high quality and performance. It would be indispensable to define the reliability of more complex systems, considering their complexity. This paper defines a complexity of redundant systems as a logarithmic function of paths, using the concept of an entropy. Further, a reliability function of complexity is given, and the reliabilities of series and parallel systems with complexity are computed. As one of typical redundant systems, a majority voting system is analyzed, and an optimal number of components is derived. Finally, a complexity of network systems is also proposed.

This paper employs new methods to evaluate the availability of multistate series–parallel systems, in which a number of similar components are available in each subsystem.

In this paper, polynomial distribution function (PDF) is combined with universal generating function (UGF) and recursive algorithm (RA) methods to evaluate the availability of multistate series–parallel systems. To achieve this goal, the PDF is initially used to determine the performance rates and the probabilities corresponding to the performance states of the similar components in a subsystem. The obtained results are used to evaluate the system availability via the UGF and RA methods.

It is shown that the combined UGF and PDF (UGF-PDF) and also the combined RA and PDF (RA-PDF) methods require less computational time than did the UGF and RA methods, respectively.

In the UGF and RA methods, there is no difference in system availability evaluation time when considering similar or different components in each subsystem. But the proposed methods in this article do not have this restrictions; therefore, these methods can be used to evaluate system availability in optimal redundancy allocation problems. As a result, using these methods reduces the optimization time of those problems.