Reliability and Cost Analysis of Series System Models Using Fuzzy Parametric Geometric Programming

Abstract

In this paper, we have discussed series system models with system reliability and cost. We have considered two types of the model; the former focuses on a problem of optimal reliability for series system with cost constraint and the latter is a center system cost model with reliability goal. It is necessary to improve the reliability of the system under limited available cost of system and also to minimize the systems cost subject to target goal of the reliability. Practically, cost of components has always been imprecise with vague in nature. So they are taken as fuzzy in nature and the reliability models are formulated as a fuzzy parametric geometric programming problem. Numerical examples are given to illustrate the model through fuzzy parametric geometric programming technique.

Posynomial Parametric Geometric Programming with Interval Valued Coefficient

“…In this paper, we have developed a method to find the optimal solution by the GP technique when some parameters are imprecise in nature. There are very few paper (Cao [33,34], Yang and Cao [35], Liu [17,37,40], Ojha and Das [38], Mahapatra and Mahapatra [5]) where the impreciseness of parameters is considered. The solution procedure of these papers by the GP technique states the interval value of the objective function and is also time consuming.…”

“…(Govil [2,3], Mahapatra and Roy [4], Mahapatra and Mahapatra [5]), engineering design (Choi and Bricker [6], Prasad et al [7]), integrated circuit design (Chu and Wong [8], Hershenson et al [9], Mandal and Visvanathan [10]), inventory management (Cheng [11], Kim and Lee [12], Lee [13], Jung and Klein [14], Abuo El Ata et al [15], Worrall and Hall [16], Liu [17]), project management (Scott and Jefferson [18]), etc. The most remarkable property of geometric programming is that a problem with highly nonlinear constraints can be transformed equivalently into a problem with only linear constraints.…”

Robust counterpart optimization for the redundancy allocation problem in series-parallel systems with component mixing under uncertainty

“…Mahapatra and Roy [40] used a fuzzy multi-objective optimization method for optimization of a series and complex system reliability. Mahapatra and Mahapatra [21] considered the problem of minimizing system cost of a series system with the target of system reliability in fuzzy environment and formulated the reliability model as a fuzzy parametric geometric programming problem. Recently, Soltani and Sadjadi [22] presented a robust possibilitic programming approach and developed robust models for RAP with active strategy.…”

Evaluation of Maximum Reliability Using Co-efficient of Variance for Parallel System Model

“…Yuan et al [20] and Epstein et al [2] have applied different technique and solution on series system in different environment. Mahapatra et al [13] used geometric programming on a reliability optimization problem for a series system to maximize the system subject to minimum cost under triangular fuzzy number. Abdul razak et al [1] presented a new method for finding fuzzy system reliability analysis based on uncertainties, in which fuzzy models are represented by trapezoidal fuzzy number.…”