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The purpose of this paper is to present a hybridized technique for analyzing the behavior of an industrial system stochastically by utilizing vague, imprecise, and uncertain data. If the collected data are used as such in the analysis, then they high range of uncertainties occurred in the analysis and hence performance of the system cannot be done up to desired levels. For this, two important tools namely Lambda-Tau methodology and particle swarm optimization are used to formulate the hybridized technique PSOBLT (Particle swarm optimization based Lambda-Tau) to analyze the behavior of the complex industrial systems stochastically up to a desired degree of accuracy using available information. Six reliability indices namely failure rate, repair time, mean time between failures(MTBF), expected number of failures (ENOF), availability and reliability of the system are used for the analysis of system's behavior. Expressions of these reliability indices are obtained using Lambda-Tau methodology and particle swarm optimization (PSO) is used to construct their membership function utilizing the quantified information of the system in the form of triangular fuzzy number. The washing unit of a medium size paper plant situated in the northern part of India has been considered to demonstrate the approach. The behavior analysis results computed by PSOBLT technique have a reduced region of prediction in comparison of existing technique region, i.e. uncertainties involved in the analysis are reduced. Thus, it may be a more useful analysis tool to assess the current system conditions and involved uncertainties.

In this research, we focus on covariate modelling to explore the interactions between industrial system and its enviroment in terms of the modelling fundamental characteristic — random and fuzzy uncertaity with an intention to decrease the fatal weakness of the modern dissection methodology. We extend the additive and multiplicative covariate models from these considering randomness alone into these considering both randomness and fuzziness in the sense as a mathematical extension to the existing covariate modelling. In terms of the form of logical function an engineering oriented fuzzy reliability model which could potentially count all the aspects associated with an operating system and its environment is proposed. Statistical estimation on the parameters of system fuzzy reliability is considered based on the general theory of the point processes. The impacts on the optimal plant maintenance from the engineering oriented fuzzy reliability modelling is also discussed. Finally we use an industrial example to illustrate the main theoretical developments.

When fuzzy information is taken into consideration in design, it is difficult to analyze the reliability of machine parts because we usually must deal with random information and fuzzy information simultaneously. Therefore, in order to make it easy to analyze fuzzy reliability, this paper proposes the transformation between discrete fuzzy random variable and discrete random variable based on a fuzzy reliability analysis when one of the stress and strength is a discrete fuzzy variable and the other is a discrete random variable. The transformation idea put forwards in this paper can be extended to continuous case, and can also be used in the fuzzy reliability analysis of repairable system.

Here, we appraise the reliability for numerous complex structures (series structure, parallel structure and bridge structure) using accuracy and score function under fuzzy environment. The main focus of this effort is to address an advanced technique for fuzzy reliability evaluation of various complex systems having different arrangements by treating reliability of the unit/component as an interval valued intuitionistic hesitant fuzzy element. This technique helps to handle uncertainty and hesitancy in multi-attribute group decision-making related issues, specially when information occurs in interval form in fuzzy set. A numerical illustration is also included to demonstrate the proposed technique.

Preventive maintenance of any system should depend on its starting, ending and operating conditions. Systems working with a minimum permissible reliability should be maintained at predetermined points to ensure its reliability do not fall below the permissible level. For any period, the starting condition of a system and the operating condition can be specified using fuzzy sets. Since the condition of the system at the end of a period depends on its starting condition and the operating condition during the period, linguistic variables are also required to specify it. This paper describes how to select periods of maintenance and the types of maintenance for such a system. The model utilizes the fuzzy set theory to determine the period length and the type of maintenance.

Chaos is ergodic, random, and can repeat traversal of all state in a certain range according to the laws of its own. At the same time, taking advantage of the ability of large-scale collective parallel computing of the neural network, we studied the neural network model with chaos characteristics. We applied it in the fuzzy reliability optimization of automotive transmission shaft considering the fuzziness and randomness of the design parameters. An example was given for the optimization calculation.