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With the object of translating some concepts and results from classical Reliability Theory into particular types of multistate systems, this article starts by presenting some basic definitions of fuzzy systems. The concepts of fuzzy coherent and fuzzy crisp‐based systems are examined and some results on fuzzy coherent structures are presented. Both static and non‐static models are considered.

The purpose of this study is to find the reliability of the three-component three-phased mission system, which can be repaired by considering the exponential distribution for repair and failure rates in the transitions between the phases based on states with Markov approach. Also, multilevel-phased mission systems are calculated based on states for partially working states.

The reliabilities of the repairable two-level and three-level three-component three-phased mission systems based on states are calculated with the Markov approach. The structure functions are obtained for each phase of the systems, and differential equations are created by the failure and repair of each working state component. These equations are solved using Laplace method.

Reliability values of two-level and three-level three-component three-phased systems with different failure, repair, and time intervals are calculated and compared. The intermediate states that multilevel systems handle differently from two-level systems provide a better investigation of the systems. So, these repairable systems offer transparent information in complex systems like transportation and energy, ensuring appropriate timing and cost for repair operations.

This study is original in terms of calculating the reliability of the repairable phased mission system based on the states using Markov method. It is also important in calculating the reliability of the repairable multilevel phased mission system based on states and making reliability comparisons according to different repair and failure rates, equal and different time intervals.

In certain environments, the system may not fail completely, but undergoes degradation, and the system productivity might decrease. Meanwhile, at the same time, the system may be vulnerable to shocks. A single-unit system prone to degradation and shocks is proposed in this study, and emphasis is placed upon determining its availability and cost rate.

The considered single-unit system is expected to have three states, namely, normal, degraded and failed. As the system enters the degraded state, it is said to be partially failed. The degraded state incurs higher degradation than the normal state and is more prone to shocks. Inspections are used to determine the state and failure type of the system. Inspections are predetermined to be carried out sequentially at time I, I+aI, I+aI+a2I,… where 0 < a ≤ 1, until the detection of degradation/failure. Perfect repairs are conducted instantly on spotting the partial/complete failure. Two cases have been considered of repair taking constant times and random times.

Explicit results on the reliability, availability (both point and limiting availability) and long-run average cost rate (LRACR) of a sequentially inspected single-unit system prone to degradation and shocks under constant and random repair times are given. Numerical example of an oil pipeline system is taken to clarify the acquired results.

A sequentially inspected single-unit system prone to degradation and shock is studied unlike done previously.

To find the reliability characteristics of repairable weighted (u, v)- out-of-(x, y) system using the interval valued universal generating function (IUGF).

In this paper (u, v)-out-of-(x, y) system is an extension of the k-out-of-n system. Here, the interval valued universal generating function (UGF) is present and the corresponding operators are defined.

The present paper proposes a interval valued universal generating function (IUGF) to compute the reliability indices of the considered system. The current study investigates the reliability and sensitivity of the proposed system with respect to system parameters by applying Markov process with the help of the interval valued UGF approach.

In this work, the considered system, i.e. repairable weighted (u, v)-of-the- (x, y) is the extension of k-out-of-n system for the assessment of reliability characteristics using the interval valued UGF.

The paper presents reliability, maintainability and life cycle cost (LCC) analysis of a computerized numerical control (CNC) turning center which is manufactured and used in India. The purpose of this paper is to identify the critical components/subsystems from reliability and LCC perspective. The paper further aims at improving reliability and LCC by implementing reliability-improvement methods.

This paper uses a methodology for the reliability analysis based on the assessment of trends in maintenance data. The data required for reliability and LCC analysis are collected from the manufacturers and users of CNC turning center over a period of eight years. ReliaSoft’s Weibull++9 software has been used for verifying goodness of fit and estimating parameters of the distribution. The LCC of the system is estimated for five cost elements: acquisition cost, operation cost, failure cost, support cost and net salvage value.

The analysis shows that the spindle bearing, spindle belt, spindle drawbar, insert, tool holder, drive battery, hydraulic hose, lubricant hose, coolant hose and solenoid valve are the components with low reliability. With certain design changes and implementation of reliability-based maintenance policies, system reliability is improved, especially during warranty period. The reliability of the CNC turning center is improved by nearly 45 percent at the end of warranty period and system mean time between failure is increased from 15,000 to 17,000 hours. The LCC analysis reveals that the maintenance cost, operating cost and support costs dominate the LCC and contribute to the tune of 87 percent of the total LCC.

The proposed methodology provides an excellent tool that can be utilized in industries, where safety, reliability, maintainability and availability of the system play a vital role. The approach may be improved by collecting data from more number of users of the CNC turning centers.

The approach presented in this paper is generic and can be applied to analyze the repairable systems. A real case study is presented to show the applicability of the approach.

The proposed methodology provides a practical approach for the analysis of time-to-failure and time-to-repair data based on the assessment of trends in the maintenance data. The methodology helps in selecting a proper approach of the analysis such as Bayesian method, parametric methods and nonparametric methods.

The purpose of this paper is to develop a new mathematical method for the reliability analysis and evaluation of multi-state system (MSS) reliability that agrees with specifics of such system. It is possible based on the application of multiple-valued logic (MVL) that is a natural extension of Boolean algebra used in reliability analysis.

Similar to Boolean algebra, MVL is used for the constriction of the structure function of the investigated system. The interpretation of the structure function of the MSS in terms of MVL allows using mathematical methods and approaches of this logic for the analysis of the structure function.

The logical differential calculus is one of mathematical approaches in MVL. The authors develop new method for MSS reliability analysis based on logical differential calculus, in particular direct partial logical derivatives, for the investigation of critical system states (CSSs). The proposed method allows providing the qualitative and quantitative analyses of MSS: the CSS can be defined for all possible changes of any system component or group of components, and probabilities of this state can also be calculated.

The proposed method permits representing the MSS in the form of a structure function that is interpreted as MVL function and provides the system analyses without special transformation into Boolean interpretation and with acceptable computational complexity.

Purpose – Research on hospital system organization is dated and cross-sectional. We analyze trends in system structure during 2000–2010 to ascertain whether they have become more centralized or decentralized.

Design/Methodology/Approach – We test hypotheses drawn from organization theory and estimate empirical models to study the structural transitions that systems make between different “clusters” defined by the American Hospital Association.

Findings – There is a clear trend toward system fragmentation during most of this period, with a small recent shift to centralization in some systems. Systems decentralize as they increase their members and geographic dispersion. This is particularly true for systems that span multiple states; it is less true for smaller regional systems and local systems that adopt a hub-and-spoke configuration around a teaching hospital.

Research Limitations – Our time series ends in 2010 just as health care reform was implemented. We also rely on a single measure of system centralization.

Research Implications – Systems that appear to be able to centrally coordinate their services are those that operate in local or regional markets. Larger systems that span several states are likely to decentralize or fragment.

Practical Implications – System fragmentation may thwart policy aims pursued in health care reform. The potential of Accountable Care Organizations rests on their ability to coordinate multiple providers via centralized governance. Hospitals systems are likely to be central players in many ACOs, but may lack the necessary coherence to effectively play this governance role.

Originality/Value – Not all hospital systems act in a systemic manner. Those systems that are centralized (and presumably capable of acting in concerted fashion) are in the minority and have declined in prevalence over most of the past decade.

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.

The purpose of this paper is to evaluate various reliability measures like reliability, expected lifetime (mean time to failure), signature reliability and compare networks based on the different flows.

The reliability characteristics of complex bridge networks have been evaluated using different algorithms with the help of universal generating function (UGF). Further, the signature reliability of the considered networks has been determined using Owen’s method.

The present paper proposes an efficient algorithm to compute the reliability indices of complex bridge networks having i.i.d. lifetime components (nodes, edges) with the help of UGF and Owen’s method. This study reveals that a slight change in the complex bridge network affects the reliability significantly. Finally, by the reliability structure function, proposed algorithms are used to find the signature and MTTF. From signature, we have determined the different failure probabilities corresponding to edges of the network.

In this work, we have evaluated reliability characteristics and signature reliability of the complex bridge networks using UGF method and Owen’s method respectively unlike done in the past.

The purpose of this paper is to deal with a linear multi-state sliding window coherent system which generalizes the consecutive k-out-of-r-from-n:F system in the multi-state case. The system has n linearly ordered multi-state elements consisting of m parallel independent and identically distributed elements. Every element of the system can have two states: completely working or totally failed. The system fails if the sum of performance rate is lower than the given weight.

The authors proposed to compute the signature, MTTF and Barlow–Proschan index with the help of UGF technique of multi-state SWS which consists of m parallel i.i.d. components in each multi-state window.

In the present study, the authors have evaluated the signature reliability, expected lifetime, cost analysis and Barlow–Proschan index.

In this study, the authors have studied a linear multi-state sliding window system which consists of n ordered multi-state element, and each multi-state element also consists of m parallel windows. The focus of the present paper is to evaluate reliability metrices of the considered system with the help of signature from using the universal generating function.