Components In Coherent Systems Research Articles

Optimal age replacement time for coherent systems under Geometric Point Process

In spatial context, the understanding of event dynamics and point distributions is a fundamental requirement. This study addresses a critical need by introducing the Geometric Point Process (GPP) and explaining its potential impact on optimizing the determination of optimal replacement ages for coherent systems. Our paper has three overarching aims: firstly, to bridge the gap by presenting the novel GPP model that effectively captures the geometric distribution of points, filling a void in point process theory. Secondly, we calculate the optimal replacement age for the coherent system based on the principles of GPP. This involves employing the Infinitesimal-Look Ahead stopping rule within the framework of Smooth Semi-Martingale (SSM) decomposition. A comprehensive comparative analysis is conducted to assess the distinct features and advantages of the GPP in relation to other point processes, offering valuable insights into its applicability and performance. Lastly, we extend the practical application of GPP by examining optimal replacement strategies for components in coherent systems, offering a bridge between theory and real-world practices, especially in the context of aircraft and wind turbine component deterioration. Additionally, we conduct reliability and sensitivity analyses, providing management suggestions, and present Monte Carlo simulations as an alternative method for validating optimal solutions. This research invites the industrial community to utilize the proposed replacement policy, paving the way for exploring geometric characteristics in stochastic processes. The timeliness and significance of this work are underscored by the relatively unexplored field of smooth semi-martingales, with the most recent publication dating back to 2015 by Bueno.

Criticality-based allocation of active redundancies for asymmetric components in coherent systems

The active redundancy technique is widely used in reliability engineering to enhance the performance of reliability systems. In this paper, we utilize the criticality ordering to study optimal allocations of active redundancies in coherent systems comprising independent components. Firstly, we establish optimal allocation strategies for two heterogeneous active redundancies for components ranked by the criticality ordering, which is characterized by the structure relationships induced from the associated minimal cut sets. Our findings demonstrate that, under certain conditions where the criticality ordering (and reliability performances) between any two original components is required, the stronger redundancy should be allocated to the more critical component. Secondly, we investigate the best allocation policies for a batch of homogeneous active spares for different components while preserving the criticality ordering. It is shown that allocating more active redundancies to the more critical component results in a more reliable coherent system. Additionally, we prove that under certain conditions, an imbalance in the numbers of allocated spares leads to even greater reliability in the system. Thirdly, we study optimal allocations for any two components in coherent systems when their locations are quantified by minimal path sets. The optimal allocation policies are further derived, most of which are similar to those obtained by applying minimal cut sets. Numerical examples are provided to illustrate the main findings, and we apply our findings to a real-world scenario in an airplane cockpit system to enhance its reliability.

On inactivity times of failed components of coherent system under double monitoring

AbstractThis article discusses the stochastic behavior and reliability properties for the inactivity times of failed components in coherent systems under double monitoring. A mixture representation of reliability function is obtained for the inactivity times of failed components, and some stochastic comparison results are also established. Furthermore, some sufficient conditions are developed in terms of the aging properties of the inactivity times of failed components. Finally, some numerical examples are presented to illustrate the theoretical results.

Number of Failed Components in Coherent Systems

Number of Failed Components in Coherent Systems

Statistical quantification of nonlinear interference noise components in coherent systems.

We present and validate a statistical method able to separate nonlinear interference noise (NLIN) into a residual Gaussian (ResN) and a phase noise (NLPN) component. We take into account the interaction of the NLIN with the receiver's DSP, mainly through carrier phase recovery (CPR), by considering the amount of correlation of the NLPN component. This allows obtaining in a straightforward way an accurate prediction of the achievable post-DSP transmission performance. We apply our method on simulated data in different scenarios. For this purpose: (i) several different quadrature amplitude modulation (QAM) and probabilistically shaped (PS) formats are investigated and (ii) simulations with standard single mode fiber (SSMF) and dispersion shifted fiber (DSF) are performed. In all these cases we validate the results provided by our method through comparison with ideal data-aided CPR and a more practical blind phase search (BPS) algorithm. The results obtained are finally compared with the predictions of existing theoretical models and the differences with our approach are pointed out.

Minimal repair of failed components in coherent systems

The minimal repair replacement is a reasonable assumption in many practical systems. Under this assumption a failed component is replaced by another one whose reliability is the same as that of the component just before the failure, i.e., a used component with the same age. In this paper we study the minimal repair in coherent systems. We consider both the cases of independent and dependent components. Three replacement policies are studied. In the first one, the first failed component in the system is minimally repaired while, in the second one, we repair the component which causes the system failure. A new technique based on the relevation transform is used to compute the reliability of the systems obtained under these replacement policies. In the third case, we consider the replacement policy which assigns the minimal repair to a fixed component in the system. We compare these three options under different stochastic criteria and for different system structures. In particular, we provide the optimal strategies for all the coherent systems with 1–4 independent and identically distributed components.

Stochastic Properties of Components in a Used Coherent System

Some coherent systems are such that failure of the system does not mean that all components fail. This paper investigates the stochastic behavior and reliability properties of the residual lifetime of live components in coherent systems under the assumption that the system fails at time t. We also investigate the stochastic properties of inactivity time of failed components in coherent systems where failure of some components does not cause the failure of the complete system.

More on optimal allocation of components in coherent systems

More applications of the principle for interchanging components due to Boland et al. (1989) in reliability theory are presented. In the context of active redundancy improvement we show that if two nodes are permutation equivalent then allocating a redundancy component to the weaker position always results in a larger increase in system reliability, which generalizes a previous result due to Boland et al. (1992). In the case of standby redundancy enhancement, we prove that a series (parallel) system is the only system for which standby redundancy at the component level is always more (less) effective than at the system level. Finally, the principle for interchanging components is extended from binary systems to the more complicated multistate systems.

More on optimal allocation of components in coherent systems

More applications of the principle for interchanging components due to Boland et al. (1989) in reliability theory are presented. In the context of active redundancy improvement we show that if two nodes are permutation equivalent then allocating a redundancy component to the weaker position always results in a larger increase in system reliability, which generalizes a previous result due to Boland et al. (1992). In the case of standby redundancy enhancement, we prove that a series (parallel) system is the only system for which standby redundancy at the component level is always more (less) effective than at the system level. Finally, the principle for interchanging components is extended from binary systems to the more complicated multistate systems.

Comparing Criticality of Nodes via Minimal Cut (Path) Sets for Coherent Systems

In 1989, Boland, Proschan, and Tong [2] introduced the notion of criticality ranking among nodes and developed a procedure for obtaining an optimal assignment of components in coherent systems. In this article we obtain characterizations of the criticality ranking in terms of minimal cut (path) sets for coherent systems. Furthermore, utilizing the characterizations, it is shown that the criticality ranking defined by Boland et al. [2] is consistent with the cut-importance ranking introduced by Butler in 1979 [4]. A relationship between the criticality ranking and the well-known and widely used Birnbaum reliability importance measure is also derived.

On measures of importance for components in multistate coherent systems

Measures of importance are quantitative criteria for ordering different components in the coherent system based on their critical roles in the functioning performance or the failure of the system. Brief review of measures of importance for the case of binary systems is presented. Extensions of measures of importance are introduced for the multistate coherent system. The main relations between these measures are established and some of their properties are also considered.

Calculation of Critical Importance for Multi-State Components

The application of the critical importance introduced by Birnbaum is restricted to 2-state components. Other authors have proposed importance measures and importance rankings for multi-state components in coherent systems. This paper introduces a sensitivity formula for multi-state components that applies to non-coherent systems as well and which reduces to the Birnbaum importance when applied to 2-state components. The event importances required in this formula can be obtained by the algorithm given. Since this algorithm is based on the inclusion-exclusion principle it is possible to combine the calculations of event importances, top probability, and top frequency in one computer program. one computer program.

Holographic recording and reconstruction in spatially incoherent white light

The proposed holographic method points out the possibilities presented by a classical imaging system when a holographic component is used. A holographic transparency playing the role of beam-splitter and condenser is set in the input plane of an incoherent imaging system. The intensity distribution recorded in the output plane is usually an interference pattern. Under some geometrical conditions this interferogram behaves as the hologram of information located inside any pupil plane. The holographic component-incoherent system allows the carrying out of a coherent analysis in systems linear in intensity.