Reliability of systems by mixture forms of uncertainty

Utkin, Lev V.; Gurov, Sergey V.; Shubinsky, Igor Borisovich

doi:10.1016/s0026-2714(96)00002-9

Cited by 5 publications

(5 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let us consider a case when time to repair Y is a fuzzy variable. According to Utkin et al [9], (1) can be rewritten as:…”

Section: Fuzzy Time To Repairmentioning

confidence: 99%

“…If the function ϕ is monotonous and continuous, then, according to Dubois and Prade [7], we can write: (7) This implies that (4) can be rewritten as follows: (8) The functions ϕ( j, z j ) are continuous and have the range from 0 to ∞. Then Lemmas 1 and 2 imply that: (9) where z 0 is a root of the following equation: From (5) we have: (10) Here the value j 0 is an integer determined from the following double condition: (11) In particular, if ϕ( j, z) = z, i.e. the human experience is not changed, then (10) can be rewritten as follows:…”

Section: Proofmentioning

confidence: 99%

“…An approach for combining the various measures, in which random variables are taken as fuzzy variables whose membership functions [7] are just random variables, has been proposed by Cai et al [8] for analysing hardware-software systems. Another approach has been proposed by Utkin et al [9]: fuzzy variables are taken as random variables whose distribution functions are just fuzzy variables. In this paper we analyse the system on the basis of the second approach.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Analysis of computer integrated manufacturing systems by fuzzy human operator behaviour

Utkin

Gurov²,

Shubinsky³

1997

Journal of Quality in Maintenance Engineering

Self Cite

View full text Add to dashboard Cite

IntroductionOnly by maintaining high reliability of the computer integrated manufacturing system (CIMS), can the production line be operated steadily for a long time. One of the problems in CIMS is real-time constraints which must be satisfied. The inability of the system to meet real-time constraints is caused by failures and repairs of the system during the production process. The important measure characterizing the quality of the system under real-time conditions is processing time, which consists of operating time (required processing time under ideal conditions without failures) and downtimes during repairs. Under repair we understand all fault-compensation actions after which the system is as good as new. We will consider a manufacturing system with the human operator [1]. The human operator monitors the system to check whether everything is going as planned [2]. If a failure of the system occurs, the human operator interrupts the manufacturing process and determines what should be done to deal with the situation. In order to repair the system, the human operator needs a certain amount of time to analyse system damage.The considered system is extremely simple and has been studied in the probability context under the condition that all system characteristics, such as time to failure and time for repair, are random. However, most of the models considered have been governed by exponential distributions. This restricts their actual application. Moreover, an analysis of the probability behaviour of a system makes sense in practice if three conditions have to be satisfied[3]: an event is defined precisely; a large number of statistical samples are available; and probabilistic repetitiveness is embedded in the collected samples. This implies that the probabilistic assumption may be unreasonable in a wide variety of cases (software reliability [4], and behaviour of the human-machine systems [5]). In these cases, use of the possibility measure has been proposed in place of the probability measure [3,5].

show abstract

“…Let us consider a case when time to repair Y is a fuzzy variable. According to Utkin et al [9], (1) can be rewritten as:…”

Section: Fuzzy Time To Repairmentioning

confidence: 99%

Section: Proofmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Analysis of computer integrated manufacturing systems by fuzzy human operator behaviour

Utkin

Gurov²,

Shubinsky³

1997

Journal of Quality in Maintenance Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Utkin and Coolen [34] gave an overview of a lot of methods and models for reliability problems mixed with randomness and fuzziness. Utkin et al [35] studied a simple one-unit system description in the probability and possibility contexts. According to the situation of randomness and fuzziness existing in the actual project, Li et al [36] proposed a reliability-credibility model based on fuzzy theory, possibility theory, and credibility theory.…”

Section: Introductionmentioning

confidence: 99%

Reliability Analysis of Random Fuzzy Unrepairable Systems

Liu

2014

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

The lifetimes of components in unrepairable systems are considered as random fuzzy variables since randomness and fuzziness are often merged with each other. Then we establish the fundamental mathematical models of random fuzzy unrepairable systems, including series systems, parallel systems, series-parallel systems, parallel-series systems, and cold standby systems with absolutely reliable conversion switches. Furthermore, the expressions of reliability and mean time to failure (MTTF) are given for the above five random fuzzy unrepairable systems, respectively. Finally, numerical examples are given to show the application in a lighting lamp system and a hi-fi system.

show abstract

“…1016/j.ijsolstr.2008.01.005 general estimates of the reliability of the entire system represents an actual problem." (Utkin et al, 1997). Such a combination of the probabilistic and non-probabilistic convex analysis was performed by Elishakoff and Li (1999) to calculate the interval information (continuation) of the reliability function.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic interval reliability of structural systems

Qiu

Yang

Elishakoff

2008

International Journal of Solids and Structures

135

View full text Add to dashboard Cite

The probabilistic reliability approach is the most widely used method for reliability analysis. The recent research shows that the reliabilities of structural systems strongly depend on the parameters of the probability model. It is possible that the little error in the estimation of the parameters may lead to the remarkable error of the resulting probability. In this study, we introduce the interval approach into the conventional reliability theory. We present a novel approach which allows us to obtain the system failure probability interval from the statistical parameter intervals of the basic variables. This approach is a combination of the two techniques, namely the classical reliability theory and the interval analysis. In the end of this paper, we show the feasibility of the proposed approach through two examples of the truss systems.

show abstract

Reliability of systems by mixture forms of uncertainty

Cited by 5 publications

References 13 publications

Analysis of computer integrated manufacturing systems by fuzzy human operator behaviour

Analysis of computer integrated manufacturing systems by fuzzy human operator behaviour

Reliability Analysis of Random Fuzzy Unrepairable Systems

Probabilistic interval reliability of structural systems

Contact Info

Product

Resources

About