Redundancy Allocation using Multiple Weighted Objectives

surplusage Allocation victimization septuple Weighted ObjectivesRedundancy Allocation using denary angleed neutrals heuristic programAbstractA new flair for optimisation of formation dependability was put send and tested. In this transcription, the main aim is to increase the individual dodging reliability. The point of intersection of individual system reliability octuples to the reliability of the entire system. Hence the quaternary weighted objective heuristic involves breaking down of the line into multiple objectives and in turn into contrasting single objective problem. Then this sequence is done by solving the one-dimensional programing formulation. The results obtained ar efficacious solutions which depends on the readily available tools. Thus, on the whole this new system is more efficient when compargond to the already available practices for both efficiency and carrying into action. basis of ArticlesThe main aim of this journal is to design an best solution to maximize the system reliability. It involves solving a challenging no.linear programming that is widely studied and applied.A new multiple weighted objective manner was introduced by converting the problem into diametric individual objective to maximize individually subsystem reliability for a series and parallel system. The problem is further reborn to a sequential standard linear programming algorithms in a updated process. It is easily adapted process as it easily accepts problems with a amalgamate of personas with a high-performance level. Various mathematical programming and other optimization methods where solved using periphrasis parcelling. The redundancy allocation was solved by constraining the problem to only one type of component of the subsystem using dynamic programming. Surrogate approach is a efficient way to go multiple constraints with dynamic programming. Mathematical programming approaches restricts by allowing one component choice fo r separately subsystem.In the example shown in the figure on a lower floor shows a series parallel system. For each subsystem, there argon multiple, available equivalent weight components available for used. The design involves single component selection for each subsystem or multiple components selected in parallel. The decision variables for redundancy allocation argon choice of components and level of redundancy. The MWO involves converting single objective into multiple sub objectives. The following step is to combine multiple objectives into single objective into single objectives using objective weights. Different optimization was implemented with integer programming and using max-min concept to obtain an optimal pareto solution.NomenclatureXij number of components of type j used in subsystem iR(x)- System reliabilityRi(xi)- reliability of subsystem iWi objective weight assigned to the ith subsystemRimin- minimum subsystem reliability for subsystem i definition of the work presented in journal articlesThe objective of the problem is to maximize the system reliability R(x), given the constraints of the system which is mainly a series-parallel system. There are mi pieceally equivalent components available with different reliability, be and weight for each subsystem. There are cardinal general solution strategies for multiple objective problem. The first strategy is to obtain a composite tend by combining the multiple objective functions. The stand by strategy is by obtaining a pareto-optimal set which is not a genuinely effective method for the series-parallel configuration system, as there would be only possible optimal solution for one subsystem with very high reliability and other with very low reliability. The solution whitethorn have a feasible optimal outcome technically tho practically it is a very forgetful solution for the series-parallel configuration.The formulation consists of some(prenominal) plainive features that is presented. First is by translation method to obtain an equivalent linear formulation for the redundancy allocation problem by using standard integer formulation tools and features. The second is that this formulation allows mixing the part components as a linearized formulation and therefrom not limiting the solution space.A sequence of Algebraic operations is used to convert multiple objective problem into equivalent subsystem problem. numeral weights are combined to result in multiple objectives. All objectives are equally important and are assigned with equal weights as nonstarter is grammatical cased due to hardship of some(prenominal) independent system. A initial system design solution is derived by obtaining the solution for the problem. There are several possible possibilities to create a new problem. There are two alternatives, one is to increase iteratively and systematically the objective weights. And the other is to iteratively add constraints and lop the minimum subsyste m reliability. The original problem formulation, and the surrogate multiple objective formulation, are presented below as enigmas P1 P2.Problem 1Problem 2 Problem P3 is a nonlinear integer programming that is difficult to solve. An equivalent linear programming is formulated through a series of objective rendering. An equivalent objective function has the same optimal solution. preaching of ContributionsThe MWO heuristic depends on an other or surrogate detailing. For the surrogate issue, the goal is to maximize the reliability of every subsystem exclusively to form a multiple objective optimization. It is reproducible that, if the dependability of every subsystem is increased, then the entire system reliability allow likewise be high. By taking different problem and different general solution to combine various individual solution into a combined single objective solution for the system. The author considers different distinct characteristics and cases for formulating a linear programming for redundancy allocation. He undertakes two different strategies, first being transforming the standard integer programming tools and software. The second he combines parts for linear formulation and not restricting the solution space. He formulated an equivalent linear program that is obtained series of objective transformation for a non-linear integer programming which is usually difficult to solve. An similar unbroken value is subtracted by which the optimal solution is not changed. Maximization problem is converted to minimization problem. The solution that maximizes the system reliability also maximizes the subsystem reliability.Discussion of Dificiency and Potential ImprovementsThe parameter that limits the process in this method is the solution time. miserable problems that are little than five subsystems can be solved by integer programming formulation for many combinational problem, but for monolithic problems that are greater than ten subsystems it is th eoretically impossible to solve. In this process, most instances were solved in under 15 seconds. If by taking in account the size of the problem obtained from the CPU is very promising.SummaryThe multiple heuristic depends on the original problem into a multiple objective problem. The solution for this optimization problem can be determined by this method in an effective way. Many examples were tested using this method and the results that were obtained was good. It can give a fast check of feasibility for nonlinear problem formulations and for more difficult problem. It has simplicity and ease of implementation the heuristic was proved to be a good process to solve the redundancy allocation problem. The concern about the applicability of the MWO2 heuristic was solution time.ReferencesDavid W. Coit and Abdullah Konak Multiple Weighted Objectives Heuristic for the Redundancy Allocation Problem ieee transactions on reliability, vol. 55, no. 3, september 2006.W. Kuo, V. Prasad, F. Til lman, and C. L. Hwang, Optimal dependability Design Fundamentals and Applications. Cambridge, UK Cambridge University Press, 2000.D. W. Coit and A. E. Smith, Reliability optimization for series-parallel systems using a genetic algorithm, IEEE Transactions on Reliability, vol. 45, no. 2, pp. 254-260, June 1996.Probability of disasterProbability of Failure ModePossible Failure RateProbabilityRanking very mellowed Failure is roughly inevitable 1 in 2.50 p 1.0010 real high up 1 in 3.33 p 9High repeated Failure 1 in 8.125 p 8High 1 in 20.05 p 7 relent Occasional Failures 1 in 80.0125 p 6 talk over 1 in 400.0025 p 5Moderate unusual Failure 1 in 2000.0005 p .00254 moo comparatively Few Failure 1 in 15,000.0000667 p 3Low 1 in 150,0006.7 x 10-6 p 2remote control tribulation is Un credibly 1 in 1,500,0006.7 x 10-7 p 1Likelihood of DetectionDetectionCriteriaRankingAlmost unacceptableNo known way mark mishap mode10Very RemoteVery unlikely to detect mishap mode9Remote Unlikely to detect misadventure mode8Very lowVery low pretend to detect chastening mode7LowLow Chance to detect failure mode6ModerateModerate chance to detect failure mode5Moderately HighModerately high chance to detect failure mode4HighLikely to detect failure mode3Very HighVery likely to detect failure mode2Almost Certain leave behind almost certainly detect failure mode1 rigour RatingSeverityCriteriaRankingHazardous-without WarningMay endanger promoter noncompliance with regulations affects the unattackable use of the result failure forget materialize without warning10Hazardous-with WarningMay endanger operator, noncompliance with regulations affects the safe use of the ingathering failure will occur with warning.9Very HighProcess or reaping inoperable with loss of primary quill function major disruption to the production line product may have to be scrapped node very dissatisfied8HighProcess or product operable but at reduce level of performance minor disruption to production line the product may have to be sorted and a proportion ( slight that hundred%) scrapped customer dissatisfied7ModerateProcess or product operable but comfort or convenience items inoperable minor disruption to production line a portion (less than c%) of the product may have to be scrapped (no sorting) customer experience tenderness6LowProcess or product operable but comfort or convenience at reduced level of performance minor disruption to production line a 100% of the product may have to be reworked customer experience some dissatisfaction5Very Low nestling disruption to production line product may have to be sorted and a portion ( less that 100% ) reworked cosmetic (fit and finish) stigma (nonconformance ) sight by most customer4MinorMinor disruption to production line a portion of the product may have to be ( less than 100%) reworked on-line but out of station cosmetic (fit and finish) defect (nonconformance) noticed by average customer3Very MinorMinor disrupti on to production line a portion of the product may have to be (less that 100%) reworked on-line but in-station cosmetic (fit and finish) defect (nonconformance) noticed by discrimination customers2NoneNo strength1Failure AnalysisThe motive of RCM is not to prevent the failure but to preserve the functions. Initially the focus was mainly on preventing failure of every maintenance schedule. But the products became more complex and maintenance cost increase in absolute terms as well as percentage of the products total life cycle cost. Soon it was clear the preventing the failure was technically and economically impractical. Instead, they came up with the solution of preserving the function of the system which withdraw to the development of RCM technique.FailureIdentifying the functions and their function failure is an important step in RCM. Study about the failure mode identification will also have a greater impact on the system reliability. close to of the Type of Failures areFunc tion FailureWhen the system fails to perform to do its intended function then its referred as Functional Failure. The mission and motive of the system will be directly be affected when the function fails. To understand about the functional failure a deep learning has to been carried out on the required function.Evident failureWhen the failure is sheer or is been made to ostensible to the operator, the failure is said to be an evident failure. Later, Display, dial or gauges, audible or alarms or other forms of legal instrument alert the operator to the failure.Hidden FailureA hidden failure is a functional failure of an item that has occurred, which has not made any impact to the system, and also not evident to the operator, but which can cause a function failure to the end system. Because of the redundancy nature of the system, the system will not fail for the single point of failure. The system will lose its function on a multiple failures.