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The main purpose of the expert system presented in the paper is to support proper decision-making to perform the operation of the complex and crucial technical system in a rational way.

The proposed system was developed using the universal concepts of a semi-Markov process, quality space and a multi-objective analysis. The maintenance and operation processes of a machine were modelled in the form of a semi-Markov process, the quality space was used to exclude the operation and maintenance process of critical quality and finally, thanks to implementation of a multi-objective analysis, the assessment system was build.

By generating each flow of the process, the expert system supports optimization of a technical system operation to choose the best maintenance strategy. Application of the expert system created based on a real industrial system is presented at the end of the paper.

The limitations of the proposed approach can be found in the parts of simulation and assessment. As the number of states to be taken into consideration increases, the time of calculation gets longer as well. As regards the assessment, ranges of the criteria argument have to be determined. Unfortunately, in some industrial systems, they are difficult to define or they are infinite and should be artificially limited.

The system provides three most important benefits as compared to other solutions. The first benefit is the system ability to make a choice of the best strategy from the perspective of the accepted criteria. The second advantage is the ability to choose the best operation and maintenance strategy from the point of view of a decision-maker. And the third is that the decision-maker can be completely sure that the chosen way of operation is not of critical quality.

The novelty of the proposed solution involves the system approach to the expert system design, thanks to the described procedure which is flexible and can be easily implemented in different technical systems which have a crucial impact on reliability and safety of their operation. It is the unique combination of probability-based simulation, multi-dimensional quality considerations and multi-objective analysis.

Credit ratings serve as an important input in several applications in risk management of the financial firms. The level of credit rating changes from time to time because of random credit risk and, thus, can be modeled by an appropriate stochastic process. Markov chain models have been widely used in the literature to generate credit migration matrices; however, emergent empirical evidences suggest that the Markov property is not appropriate for credit rating dynamics. The purpose of this article is to address the non-Markov behavior of the rating dynamics.

This paper proposes a model based on Markov regenerative process (MRGP) with subordinated semi-Markov process (SMP) to obtain the estimates of rating migration probability matrices and default probabilities. Numerical example is given to illustrate the applicability of the proposed model with the help of historical Standard & Poor’s (S&P) credit rating data.

The proposed model implies that rating of a firm in the future not only depends on its present rating, but also on its previous ratings. If a firm gets a rating lower than its previous ratings, there are higher chances of further downgrades, and the issue is called the rating momentum. The model also addresses the ageing problem of credit rating evolution.

The contribution of this paper is a more general approach to study the rating dynamics and overcome the issues of inappropriateness of Markov process applied in rating dynamics.

The aim of this study is to demonstrate that hybrid redundancy systems are superior to the conventional N‐modular redundancy (NMR) systems.

The hybrid redundancy system is a synthesis of the NMR system and the standby redundancy. Each module of the NMR has access to k cold spares (k<N) and a repair facility. A semi‐Markov model for the hybrid redundancy system is developed and transient analysis is performed.

Some dependability measures such as availability, reliability, mean time to failure and steady‐state availability are obtained.

This paper presents the transient analysis of the hybrid redundancy systems. The results obtained will be useful to reliability engineers and reliability practitioners.

High reliability, maintainability, safety and supportability are expected from today’s modern systems. In the recent years supportability has been widely accepted as a major factor in logistics discipline. The main purpose of this paper is to demonstrate how advanced mathematical models can be used to analyse the effect of supportability on systems availability. The paper discusses supportability aspects and its effect on operational availability of complex systems using advanced mathematical models like Markov, semi‐Markov and non‐Markov models. The powerful mathematical models discussed in the paper would help reliability engineers and practitioners to predict the logistic support requirements to achieve specified operational availability.

Considers a system (machine) that is subject to failure (breakdown). Two characterizations are presented. In the first characterization, the state of the system is described by the real age of the machine and the number of failures incurred to date. In the second characterization, the state of the system is described by the real age of the machine and the virtual age of the machine. In either characterization, upon failure, the unit may undergo a repair which can partially reset the failure intensity of the unit. The degree of reset assumed by the repair is a function of the characterization utilized. The other alternative, at a failure, is to conduct a major overhaul that serves to refresh the failure intensity of the unit. General cost structures, depending upon (real age, number of failures) in characterization one or (real age, virtual age) in characterization two are permitted. The decision, on failure to repair or renew is formulated as a discrete semi‐Markov Decision process. Optimal decisions are of the threshold type. The threshold rules depend upon the characterization.

Presents two models. Model I deals with some characteristics of a single unit system with a sensing device and two types of repairmen. The unit is attached to a sensing device which completely monitors the operating or non‐operating status of the unit. The regular repairman is always available with the system and inspects the operation of the sensing device. If the device is not working, then an expert repairman is called to the system and the operational status of the unit is now monitored by the expert repairman. It is assumed that the failure of the unit, repair of the regular, expert and the status of the sensing device are stochastically independent random variables each having an arbitrary distribution. Several important results have been derived including profit with some applications. In model II, a two‐unit cold standby system with pre‐inspection is considered. In this model, first the regular repairman inspects every unit that fails to ascertain whether he is able to repair it or not. If he can repair it, he proceeds; otherwise an expert repairman is called. An analytical approach to find the optimum interchanging time of units by giving rest to the operative unit is obtained.

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 present paper analyzed a model consisting of one unit with a warm standby unit where the main unit has three states: up, degraded and down.

The semi-Markov model under the regenerative method is used to construct the mathematical model for the system.

The effectiveness measures of the system are discussed such as availability, reliability, steady-state availability and mean time to system failure. The life and repair times of the system units are assumed to be discrete follow discrete Weibull distribution. Also, the parameters of the discrete Weibull distribution are assumed to be fuzzy with bell-shaped membership function. An application is introduced to show the results obtained for the system and the profit of the presented model.

Rarely papers in literature treated the topic of the discrete-time semi-Markov process using a regenerative point technique.

This article presents the multi-state stress-strength reliability computation of a component having three states namely, working, deteriorating and failed state.

The probabilistic approach is used to obtain the reliability expression by considering the difference between the values of stress and strength of a component, say, for example, the stress (load) and strength of a power generating unit is in terms of megawatt. The range of values taken by the difference variable determines the various states of the component. The method of maximum likelihood and Bayesian estimation is used to obtain the estimators of the parameters and system reliability.

The maximum likelihood and Bayesian estimates of the reliability approach the actual reliability for increasing sample size.

Obtained a new expression for the multi-state stress-strength reliability of a component and the findings are positively supported by presenting the general trend of estimated values of reliability approaching the actual value of reliability.

Degraded failures and sudden critical failures are quite prevalent in industries. Degradation processes commonly belong to Weibull family and critical failures are found to follow exponential distribution. Therefore, it becomes important to carry out reliability and availability analysis of such systems. From the reported literature, it is learnt that models are available for the situations where the degraded failures as well as critical failures follow exponential distribution. The purpose of this paper is to present models suitable for reliability and availability analysis of systems where the degradation process follows Weibull distribution and critical failures follow exponential distribution.

The research uses Semi-Markov modeling using the approach of method of stages which is suitable when the failure processes follow Weibull distribution. The paper considers various states of the system and uses state transition diagram to present the transition of the system among good state, degraded state and failed state. Method of stages is used to convert the semi-Markov model to Markov model. The number of stages calculated in Method of stages is usually not an integer value which needs to be round off. Method of stages thus suffers from the rounding off error. A unique approach is proposed to arrive at failure rates to reduce the error in method of stages. Periodic inspection and repairs of systems are commonly followed in industries to take care of system degradation. This paper presents models to carry out reliability and availability analysis of the systems including the case where degraded failures can be arrested by appropriate inspection and repair.

The proposed method for estimating the degraded failure rate can be used to reduce the error in method of stages. The models and the methodology are suitable for reliability and availability analysis of systems involving degradation which is very common in systems involving moving parts. These models are very suitable in accurately estimating the system reliability and availability which is very important in industry. The models conveniently cover the cases of degraded systems for which the model proposed by Hokstad and Frovig is not suitable.

The models developed consider the systems where the repair phenomenon follows exponential and the failure mechanism follows Weibull with shape parameter greater than 1.

These models can be suitably used to deal with reliability and availability analysis of systems where the degradation process is non-exponential. Thus, the models can be practically used to meet the industrial requirement of accurately estimating the reliability and availability of degradable systems.

A unique approach is presented in this paper for estimating degraded failure rate in the method of stages which reduces the rounding error. The models presented for reliability and availability analyses can deal with degradable systems where the degradation process follows Weibull distribution, which is not possible with the model presented by Hokstad and Frovig.