Reliability assessment of systems using universal generating function in different environments
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Date
2016-01
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G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand)
Abstract
Due to the complexity of the real life systems it becomes mandatory to evaluate their reliability. Keeping this fact in view, the focus of the present research is on the development of reliability models with the help of UGF and FUGF. This study proposes nine different reliability models. Model 1 deals with the reliability (unreliability) of circular weighted-(n, f,k): G (F) systems with the application of UGF. In this model some conditions on weight are imposed and reliability have been compared. The sensitivity of the considered systems with respect to different parameters has also been examined. Models 2 introduces and analyzes the fuzzy reliability of linear weighted-(n, f, k, m): G (F) systems with the help of UGF and fuzzy exponential distribution. Also after imposing different conditions on weight, the fuzzy reliability and FMTTF of the proposed systems have also been compared. Model 3 focuses on the reliability, MTTF and sensitivity analysis of a complex system which consists of two non repairable subsystems, namely A and B connected in series and parallel, having non identical and independent components, each having different probabilities of success by using UGF. Model 4 studies a non repairable complex system which consists of two subsystems say A and B, connected in series. The subsystems A and B are weighted k-out-of-n: G and weighted l-out-of-m: G configurations respectively. All the components of the subsystems A and B are arranged in parallel. Five prepositions are developed to express the UGF of the proposed system. This study is further extended to evaluate the reliability characteristics such as reliability, MTTF and sensitivity of the proposed system based on these prepositions. Model 5 studies the fuzzy reliability measures of a linear m-consecutive weighted-kout-of-r-from-n: F system. This model provides an algorithim for the evaluation of fuzzy reliability of the proposed system based on application of UGF and fuzzy exponential distribution. It is assumed in the study that failure rate follows GrSTrFN in fuzzy exponential distribution. Further, GrSTrFN and its arithmetic operations are obtained. Model 6 investigates the fuzzy reliability characteristics of fuzzy weighted- k~-outof-n: G (F) system by using fuzzy exponential distribution and UGF. Expressions for fuzzy reliability, FMTTF and their (α, β)-cut have been discussed when systems follow trapezoidal intuitionistic fuzzy exponential distribution. Model 7 introduces and studies the reliability measures of a weighted-((f / (r, s)), k)/(m, n): G system based on UGF and Rayleigh distribution. In this model some prepositions are formed to understand the behaviour of the proposed system with respect to different varying parameters. Model 8 deals with the reliability analysis of a k-out-of-n: G system with redundancy and load sharing components in which load sharing is dependent on failure rates of working components under certain law by using UGF. Further this study presents the new formulas for load sharing in different environments. Model 9 investigates the fuzzy reliability measures of a redundant consecutive fuzzy weighted- k~-out-of-n FMSSs by using the combination of fuzzified stochastic process and FUGF. These systems is made up of n independent, nonidentical and non-repairable MSEs and a cold standby MSE whose state transition rate (failure rate) are provided by the decision makers as TFN. Also the fuzzy weight and fuzzy performance rate of each MSE is taken as TrIFN and TFN respectively. In this study we have developed formulae for FUGF in two cases: with redundancy and without redundancy. By using these expressions, formulae for fuzzy reliability and FMTTF of the proposed systems have been evaluated. Finally two prepositions are developed to count the effect of fuzzy weight k~on the fuzzy reliability and FMTTF of the proposed FMSSs. At last all the developed models are illustrated through numerical examples.