Search results

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.

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.

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.

To create a benchmark for design evaluation of commercial web sites, to model customers' site navigation behavior, and to develop and implement algorithms for link‐structure personalization.

The principal methodology used for design benchmarking is a survey of corporate web sites of some US Fortune 500 companies and top Indian companies and statistical analysis of the data so collected. The principal methodological approach for modeling user behavior, user's interest and algorithms for link‐structure personalization, is the development of a Markov decision process (MDP) in the overall framework of a semi‐Markov model and implementing the same in a link‐structure personalization system.

It is observed that the functional web site features significantly differ for the sites dealing with various product categories whereas the non‐functional features do not. The over‐stressed or under‐stressed features in the Indian web sites are found. The statistics generated from the user behavior model are validated against the real life user behavior and found satisfactory. The appropriateness of the link‐structure personalization algorithms is established by comparing the set of links generated by the algorithm with the links generated by the optimal policy of the underlying MDP.

The corporate that have been considered are conglomerates offering a number of products and services. But we categorize these sites based on their major product offering. Our approach of modeling the user behavior as a semi‐Markov process is possible because of our advanced implementation infrastructure. Undesirable network effects like delays, bandwidth, etc. may not make such a model that attractive in a very traditional type of environment. But the data collected in such environment can still be mined after adequate pre‐processing and appropriate normalization

Using the benchmark proposed in this model a webmaster can evaluate his web site. The sites with low site evaluation index can be improved by adding features with high weight depending on the product offering of the company. Webmaster can design the three level information architecture described in the paper and subsequently implement link‐structure personalization algorithm to improve site navigability. Besides improving site navigability the user behavior data collected thereon can be mined to generate other valuable information.

To assess and enhance the usability of an ecommerce site our work proposes: a benchmark to evaluate commercial web site design; a stochastic model to study and understand user behavior; an algorithm to personalize link‐structure of a commercial web site, and a general framework to implement a link‐structure personalization system.

The purpose of this paper is to highlight the need for degradation data in order to improve the reliability and the mean residual life estimation of a specific item of equipment and to adapt the preventive maintenance tasks accordingly.

An initial reliability model which uses a degradation-based reliability model that is built from the collection of hitting times of a failure threshold. The proposed maintenance model is based on the cost/availability criterion. The estimation of both reliability and optimum time for preventive maintenance are updated with all new degradation data that are collected during operating time.

An improvement for the occurrences of maintenance tasks which minimizes the mean cost per unit of time and increases the availability.

Inspection tasks to measure the degradation level should be realized at least one time for each item of equipment at a specific time determined by the proposed methodology.

The introduction of a criterion which helps the maintainer to decide to postpone or not the preventive replacement time depending on the measured degradation level of a specific item of equipment.

This paper aims to present a case study where computer simulation is used to evaluate maintenance strategies targeted to cope with a critical failure of a repairable system.

The problem is characterized, modeled and simulated under different conditions and for finite time periods. The different states of the system and the possible transitions among these states are characterized. Transitions are conditioned by the failure dynamics and by the maintenance decision maker. The model is then formalized and the data requirements fulfilled.

The performance of several maintenance policies based on educated estimations about the equipment behavior, manufacturer recommendations, well‐known previous maintenance practices, etc. benchmarked against the results of certain modeling and optimization tools.

Practical implications of this work have to do with following the entire modeling process and maintenance policy assessment with an engineering team, exploring options and opportunities to support the maintenance managers.

Maintenance policy design exploration using semi‐Markovian process simulation modeling.

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 paper studies the event-history approach to microeconometric program evaluation. We present a mixed semi-Markov event-history model, discuss its application to program evaluation, and analyze its empirical content. The results of this paper provide fundamental insights into what can be learned from longitudinal microdata about, for example, the effects of training programs for the unemployed on their unemployment durations and subsequent job stability. They can guide the choice of particular models and methods for the empirical analysis of such effects.