Dependability analysis of semi-Markov systems

This paper presents a dependability analysis (Availability-Reliability-Maintainability, Mean times) for semi-Markov systems with finite state space, by a new method, based on algebraic calculus within a convolution algebra. This method permits us to obtain, by simple matrix calculus, closed form solutions of transition probabilities and dependability measures. It is a quite general method that does not need the semi-Markov kernel to be absolutely continuous. Thus we obtain, as an example, the classical availability formulae modelled by an alternating renewal process, by a simple algebraic calculus without probabilistic argument. A detailed application of the method is given.     

System Effectiveness Simulation Model with Nonparametric Dependability

The simulation model presented here is a useful extension of WSEIAC's system's effectiveness methodology. This model accepts information regarding uncertainty with the parametric estimates of the system's attributes. One of the system's attributes, defined as “dependability,” requires Markovian State Transition Process. Time-dependent queueing process and renewal theory application for this dependability matrix are avoided by resorting to a simulation technique. This dependability matrix requires reliability and repairability estimates, which are obtained based on a non-parametric approach. This approach is based on a test program with a very realistic environment where n identical units are placed on test for a mission duration T. At the end, the number of failed units r is noted. Units failed are not replaced. Times of failed units before failure are unknown. Based on these, the dependability matrix is generated, which results ultimately in generating a sampling distribution of system effectiveness of each subsystem and the overall system. This process is coded in FORTRAN IV.     

Dependability analysis of a very large volume neutrino telescope

This work considers a first order approximation to the dependability analysis of complex large scale installations. The dependability criterion used here is quantitative unavailability, and an appropriate unavailability model is presented. The model assumes that the system is symmetrical, has various levels of hierarchy, and components found in the same level are similar and function independently.The application example comes from very large volume neutrino telescopes installed under water or ice, consisting of several thousands of optical modules. The readout architecture of the detector has several levels of multiplexing including optical detection towers, branches and tower sectors. The paper presents results for various alternative detector layouts and distances of the detector from the onshore facilities. It also develops dependability requirements for major components and/or subsystems consistent with an overall system performance target. The results depict the dependence of the system unavailability on the number of optical modules and the alternative deep sea infrastructure configurations for transferring the measured signals.     

Dependability analysis of systems modeled by non-homogeneous Markov chains

The case of time non-homogeneous Markov systems in discrete time is studied in this article. In order to have measures adapted to this kind of systems, some reliability and performability measures are formulated, such as reliability, availability, maintainability and different time variables including new indicators more dedicated to electrical systems like instantaneous expected load curtailed and the expected energy not supplied on a time interval. The previous indicators are also formulated in the case of cyclic chains where asymptotic results can be obtained. The interest of taking into account hazard rate time variation, is to get more accurate and more instructive indicators but also be able to access new performability indicators that cannot be obtained by classical methods. To illustrate this, an example from an Electricité De France electrical substation is solved.     

Non‐Markovian State‐Space Models in Dependability Evaluation

The purpose of this paper is to provide an up‐to‐date treatment of advanced analytic, state‐space based techniques to study dependability models with non‐exponential distributions. We first provide an overview of different techniques for the solution of non‐Markovian state‐space based models, including phase‐type expansion and a general framework which allows us to deal with renewal, semi‐Markov, and Markov‐regenerative processes, trying to characterize them on dependability contexts. In the last part of the paper, we illustrate these techniques by means of some examples dealing with common non‐exponential reliability behaviors. Our aim is to provide a reference for practising engineers, researchers, and students in state‐space dependability modeling and evaluation. Copyright © 2012 John Wiley & Sons, Ltd.     

Dependability and performance stochastic modelling of a two-unit repairable production system with preventive maintenance

In this paper, a two-unit multistate repairable production system is considered in which preventive maintenance (PM) is implemented in order to improve its dependability and performance. A general model is provided for the production system using a semi-Markov process, for examining system’s limiting behaviour. Apart from combining redundancy with PM, we introduce scenarios like imperfect and failed maintenance which are usually met in real life production systems. For the proposed model, we calculate the availability, the mean time to failure and the total operational cost and we formulate optimisation problems settled with respect to the system’s inspection times. The main aim of our work is to determine the optimal inspection times and consequently the optimal PM policies to be adopted in order to optimise system’s dependability and performance.     

Dependability modelling and evaluation by using stochastic Petri nets: application to two test cases

The systems modelling and the assessment of their performances are the two key phases of any reliability or risk analysis study. However, it is well known and admitted that most of the methods devoted to this goal are unsuitable if the physical behaviour of the systems cannot be made independent from the probabilistic behaviour, as is the case for dynamic process systems. To overcome this inefficiency, some alternative methods have recently appeared. But they are not very approachable and could be, for this reason, ignored by most of the practitioners. Among these methods, however, simulation methods should be confirmed. From this point of view, the authors propose a straightforward approach to this problem by using stochastic Petri nets on a simple and well-known dynamic system from the literature. In addition, for testing this approach, the authors have carried it out on a system with periodically tested components. The results obtained are compared to those already published, the limits of the method are underlined and its efficiency in solving this kind of problem is being examined.     

Dependability estimation for non-Markov consecutive-k-out-of-n: F repairable systems by fast simulation

A model of consecutive-k-out-of-n: F repairable system with non-exponential repair time distribution and (k-1)-step Markov dependence is introduced in this paper along with algorithms of three Monte Carlo methods, i.e. importance sampling, conditional expectation estimation and combination of the two methods, to estimate dependability of the non-Markov model including reliability, transient unavailability, MTTF, and MTBF. A numerical example is presented to demonstrate the efficiencies of above methods. The results show that combinational method has the highest efficiency for estimation of unreliability and unavailability, while conditional expectation estimation is the most efficient method for estimation of MTTF and MTBF. Conditional expectation estimation seems to have overall higher speedups in estimating dependability of such systems.     

Diagnosis Modelling for Dependability Assessment of Fault‐Tolerant Systems Based on Stochastic Activity Networks

The growing demand for safety, reliability, availability and maintainability in modern technological systems has led these systems to become more and more complex. To improve their dependability, many features and subsystems are employed like the diagnosis system, control system, backup systems, and so on. These subsystems have all their own dynamic, reliability and performances and interact with each other in order to provide a dependable and fault‐tolerant system. This makes the dependability analysis and assessment very difficult. This paper proposes a method to completely model the diagnosis procedure in fault‐tolerant systems using stochastic activity networks. Combined with Monte Carlo simulation, this will allow the dependability assessment by including the diagnosis parameters and performances explicitly. Copyright © 2014 John Wiley & Sons, Ltd.     

Study of Dependability Evaluation for Multi‐hierarchical Systems Based on Max–Min Composition

This article presents the model for calculating the performance of dependability for complex technical systems. According to ISO‐IEC 300, dependability is an overall indicator for the quality of service and considers simultaneously reliability, maintainability, and maintenance support. For a proper understanding of the quality of service for any technical system, it is important to define dependability performance at the level of single component as well as at the upper levels—levels of subsystems and entire system. As dependability indicators (reliability, maintainability, and maintenance support) have been defined as linguistic variables, the fuzzy max–min composition has been used for the dependability determination and integration of its indicators. A procedure for the synthesis of single components dependability performance to upper levels in complex technical system is proposed. Max–min composition is again used as a tool for fuzzy synthesis because it enables obtaining the comprehensive and synergetic effect in a process of dependability evaluation. A practical engineering example (mechanical systems at bucket wheel excavator) has been used to demonstrate the proposed dependability synthesis model. Copyright © 2012 John Wiley & Sons, Ltd.     

Prof. Dipl.-Ing. Dr. techn. Dr. h. c. Wilhelm Schneider

Summary In order to provide a firmer foundation on which some reciprocity theorems in Eshelbian mechanics where established earlier, a nonlinear and then linearized formulation of these theorems is presented. To carry out the required operations a simple two-degrees-of-freedom system was chosen. The analysis led to mostly algebraic expressions which are also illustrated graphically. Readers will be very sad to learn of the mournful death on January 7, 2007, of Prof. Dr. sc. techn. Dr. h. c. George Herrmann. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

学会园地

第八届中国辐射固化年会在上海召开；中国感光学会、中国科学院理化技术研究所共同举办公众科学日活动。