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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 purpose of this paper is to propose a state dependent stochastic Markov model for availability analysis of process plant instead of traditional time dependent model.

The traditional concepts of system performance measurement and reliability (namely, binary; two-state concepts) are observed to be inadequate to characterize performance of complex system components. Availability analysis considering an intermediate state, such as a degraded state, provides a better alternative mechanism for system performance mapping. The availability model provides a better assessment of failure and repair characteristics for equipment in the sub-system and its overall performance. In addition to availability analysis, this paper also discusses the preventive maintenance (PM) program to achieve target availability. In this model, the degraded state is considered as a PM state. Using Markov analysis the optimum maintenance interval is determined.

Markov process provides an easier way to measure the performance of the process facility. This study also revealed that the maintenance interval has a major influence in the availability of a process facility as well as in maintaining target availability. The developed model is also applicable to the varying target availability as well as having the capability to handle even the reconfigured process systems.

Considering the degraded state as an operative state, a higher availability of the plant is predicted. The consideration of the degraded state of the system makes the availability estimation more realistic and acceptable. Availability quantification, target availability allocation and a PM model are exemplified in a sub-system of an liquefied natural gas facility.

The unique features of the present study are; Markov modeling approach integrating availability and PM; optimum PM interval determination of stochastically degrading components based on target availability; consideration of three-state systems; and consideration of increasing failure rates.

The purpose of this paper is to carry out a reliability analysis of a mechanical system considering the degraded states to get a proper understanding of system behavior and its propagation towards complete failure.

The reliability analysis of computerized numerical control machine tools (CNCMTs) using a multi-state system (MSS) approach that considers various degraded states rather than a binary approach is carried out. The failures of the CNCMT are classified into five states: one fully operational state, three degraded states and one failed state.

The analysis of failure data collected from the field and tests conducted in the laboratory provided detailed understandings about the quality of the material and its failure behavior used in designing and the capability of the manufacturing system. The present work identified that Class II (major failure) is critical from a maintainability perspective whereas Class III (moderate failure) and Class IV (minor failure) are critical from a reliability perspective.

This research applies to reliability data analysis of systems that consider various degraded states.

MSS reliability analysis approach will help to identify various degraded states of the system that affect the performance and productivity and also to improve system reliability, availability and performance.

Industrial system designers recognized that reliability and maintainability is a critical design attribute. Reliability studies using the binary state approach are insufficient and incorrect for the systems with degraded failures states, and such analysis can give incorrect results, and increase the cost. The proposed MSS approach is more suitable for complex systems such as CNCMT rather than the binary-state system approach.

This paper presents a generalized framework MSS's failure and repair data analysis has been developed and applied to a CNCMT.

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.

Reconfiguration mechanisms lead to the design of robust manufacturing systems which have the capability to allow the service continuity, in the presence of a failure, on the basis of a minimal degradation of performances. In this paper, a stochastic model is proposed to assess and to analyze the availability of reconfigurable systems whose equipments are subject to random failures. To distinguish between the normal behavior and the degraded one, the production rate is used as a performance measure. An availability model that takes into account the performance degradation is developed. Close form solutions of the steady‐state availability and the production rate of a reconfigurable system are calculated. Two optimization problems dealing with reconfigurable systems are also addressed. The paper considers a series system consisting of N stochastically independent components. Different technologies are assumed to be available for each component. The following design problems are studied: find the configuration, which allows maximizing the production rate of the system under resource constraints; and find the configuration that allows to reach some predetermined level of production rate at minimal cost. The design model of the first problem leads to mixed linear programming, while the design model of the second problem leads to integer linear programming. A numerical procedure is developed to solve both problems.

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 analyzed a complex system consisting n-identical units under a k-out-of-n: G; configuration via a new method which has not been studied by previous researchers. The computed results are more supportable for repairable system performability analysis.

In this paper, the authors have analyzed a complex system consisting n-identical units under a k-out-of-n: G; configuration via a new method which has not been studied by previous researchers. The supplementary variable technique has employed for analyzing the performance of the system.

Reliability measures have been computed for different types of configuration. It generalized the results for purely series and purely parallel configurations.

This research may be beneficial for industrial system performances whereas a k-out-of-n-type configuration exists.

Not sure as it is a theoretical assessment.

This research may not have social implications.

This work is the sole work of authors that have not been communicated to any other journal before.

The purpose of this paper is to introduce a method for modelling the multi-state repairable systems subject to stochastic degradation processes by using the coloured stochastic Petri nets (CSPN). The method is a compact and flexible Petri nets model for multi-state repairable systems and offers an alternative to the combinatory of Markov graphs.

The method is grounded on specific theorems used to design an algorithm for systematic construction of multi-state repairable systems models, whatever is their size.

Stop and constraint functions were derived from these theorems and allow to considering k-out-of-n structure systems and to identifying the minimal cut sets, useful to monitoring the states evolution of the system.

The properties of this model will be studied, and new investigations will help to demonstrate the feasibility of the approach in real world, and more complex structure will be considered.

The simulation models based on CSPN can be used as a tool by maintenance decision makers, for prediction of the effectiveness of maintenance strategies.

The proposed approach and model provide an efficient tool for advanced investigations on the development and implementation of maintenance policies and strategies in real life.

The quality of production is an essential factor for the performance measure of a system; a casting process is the same section. It is a type of metal-forming practice in which the required shape of metal is acquired by pouring molten metal into the mold cavity and allowing it to solidify. Casting is done to provide strength and rigidity to the parts of a system for bearing mechanical impacts. The purpose of this paper is to investigate the various aspects which affect the casting process in the foundry industry, in order to optimize the quality of casting, with the assumption that sufficient repair facility is always available.

The considered casting system can have many defects such as the mold shift defect, blowhole defect, defect of shrinkage and porosity, defect of inclusion, defect of cold shut and much more. The studied system can be in three states during the process, namely, good state, failed state and degraded state. The system can repair after minor failures as well as a major failure. The average failure rates of various defects of the system considered as constant and repairs follow the general time distribution. The system is analyzed with the help of the supplementary variable technique and the Laplace transformation for evaluating its various performance measures in order to improve its performance/production.

This work provides a strong understanding of the casting industry, that which failure affects the production of casting and how much. For better understanding, the results have been demonstrated with the help of graphs.

In the present paper, a mathematical model based on the casting process in manufacturing industry has been developed.

The reliability and maintainability of tunnel infrastructure and systems is an important factor in assuring normal operation of a tunnel. Evaluating availability of a large‐scale tunnel that includes civil, electrical, mechanical and electronic systems is a difficult task. The purpose of this paper is to present a methodology for performing such assessments, featuring the use of the Markov model.

The methodology involves application of failure mode, effect and criticality analysis (FMECA), state space diagram construction, formulation of state space equations, and development of transitional matrices. It also involves transformation of multi‐state models into two‐state models (each comprises of an “up” state and a “down” state) through the use of the frequency and duration method for determining the failure and repair rates, as well as the mean‐time‐between‐failures (MTBF) of the entire tunnel. By using the proposed bottom‐up approach, a MTBF tree linking the availability measures of individual equipment with those of sub‐systems, and ultimately the whole tunnel can be developed.

The tunnel availability measures obtained by this analysis can be used in making comparisons between different tunnel designs so as to determine the value for money of various options. Furthermore, weaknesses in a tunnel design can be identified in the analysis. The information obtained from this method can also be used to evaluate adequacy, security and maintainability of a tunnel.

The reliability and maintainability of tunnel infrastructure and systems are crucial factors for ensuring safety of tunnel operation. Unsafe conditions will cause closure of a tunnel. Efforts to improve availability of a tunnel often increase the tunnel's construction cost. Due to the complexity of tunnel systems, it is difficult to compare different tunnel designs, and trade‐off analyses to strike a balance between target availability and construction cost of a tunnel design are seldom performed. This paper presents a systematic methodology to address these issues. This methodology allows tunnel management to evaluate the adequacy, security and maintainability of a tunnel so that design weaknesses can be identified and the value of design improvements can be determined. The methodology can also be used to evaluate designs of other complex systems such as power generation or petrochemical processing plants.

A worked example demonstrating the application of the proposed methodology is presented in this paper.