Redundancy Allocation using Multiple Weighted Objectives

Redundancy Allocation using Multiple Weighted ObjectivesRedundancy Allocation using quintuple weighted purposes heuristic programAbstractA rude(a) method for optimization of outline reliableness was put forward and tested. In this method, the main aim is to maximize the individual organisation reliability. The product of individual system reliability multiples to the reliability of the entire system. Hence the multiple weighted objective heuristic involves breaking down of the hassle into multiple objectives and in turn into variant mavin objective problem. Then this sequence is done by solving the linear programing formulation. The results obtained are efficient closures which depends on the readily available tools. Thus, on the whole this saucily method is to a greater extent efficient when compared to the already available practices for both efficiency and performance.INTRODUCTION of ArticlesThe main aim of this journal is to design an optimum solution to maximize the s ystem reliability. It involves solving a challenging nonlinear programming that is widely studied and applied.A new multiple weighted objective method was introduced by converting the problem into different individual objective to maximize each(prenominal) subsystem reliability for a series and parallel system. The problem is further converted to a sequential standard linear programming algorithms in a updated process. It is easily adapted process as it easily accepts problems with a mix of components with a high-performance level. Various mathematical programming and other optimization methods where solved using redundancy ap component partment. 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 accommodate multiple constraints with dynamic programming. numeral programming approaches restricts by allowing one component choice for each subsystem.In t he example shown in the figure below shows a series parallel system. For each subsystem, there are multiple, functional combining 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 are choice of components and level of redundancy. The MWO involves converting single objective into multiple sub objectives. The next metre 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 iExplanation of the decease 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 functionally equivalent components available with different reliability, cost and weight for each subsystem. There are two general solution strategies for multiple objective problem. The first dodge is to obtain a composite function by combining the multiple objective functions. The second strategy is by obtaining a pareto-optimal set which is not a very(prenominal) powerful 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 may expect a feasible optimal outcome technically but practically it is a very poor solution for the series-parallel configuration.The formulation consists of several distinctive features that is presented. First is by transformation method to obtain an equivalent li near 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 hence not limiting the solution space.A sequence of Algebraic operations is used to convert multiple objective problem into equivalent subsystem problem. Numerical weights are combine to result in multiple objectives. All objectives are equally important and are assigned with equal weights as failure is caused due to failure of whatever 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 reduce the minimum subsystem reliability. The original problem formulation, and the surrogate multiple objective f ormulation, are presented below as Problems P1 P2.Problem 1Problem 2 Problem P3 is a nonlinear integer programming that is catchy to solve. An equivalent linear programming is formulated through a series of objective transformation. An equivalent objective function has the same optimal solution.Discussion 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 coherent that, if the reliableness of every subsystem is increased, then the entire system reliability will 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 t ransforming 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 constant 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 withal maximizes the subsystem reliability.Discussion of Dificiency and Potential ImprovementsThe parameter that limits the process in this method is the solution time. Small problems that are less than five subsystems can be solved by integer programming formulation for many combinational problem, but for large problems that are greater than ten subsystems it is theoretically impossible to solve. In this process, most instances were solved in under 15 seconds. If by ta king 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 restraint 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. Tillman, and C. L. Hwang, Optimal Reliability Design basics and Applications. Cambridge, UK Cambridge Universi ty 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 also-ranProbability of Failure ModePossible Failure RateProbabilityRankingVery elevated Failure is almost inevitable 1 in 2.50 p 1.0010Very superior 1 in 3.33 p 9High repeated Failure 1 in 8.125 p 8High 1 in 20.05 p 7Moderate Occasional Failures 1 in 80.0125 p 6Moderate 1 in four hundred.0025 p 5Moderate Infrequent Failure 1 in 2000.0005 p .00254Low Relatively Few Failure 1 in 15,000.0000667 p 3Low 1 in 150,0006.7 x 10-6 p 2Remote failure is Unlikely 1 in 1,500,0006.7 x 10-7 p 1Likelihood of DetectionDetectionCriteriaRankingAlmost ImpossibleNo known way detect failure trend10Very RemoteVery unlikely to detect failure humor9RemoteUnlikely to detect failure agency8Very lowVery low chance to detect failure mode7LowLow Chance to detect failure mode6Moderate Moderate chance to detect failure mode5Moderately HighModerately high chance to detect failure mode4HighLikely to detect failure mode3Very HighVery likely to detect failure mode2Almost CertainWill almost certainly detect failure mode1Severity RatingSeverityCriteriaRankingHazardous-without exemplificationMay bring out operator noncompliance with regulations affects the safe use of the product failure will occur without warning10Hazardous-with WarningMay endanger operator, noncompliance with regulations affects the safe use of the product failure will occur with warning.9Very HighProcess or product in feasible with freeing of primary function major disruption to the production line product may have to be scrapped customer very dissatisfied8HighProcess or product operable but at reduced level of performance minor disruption to production line the product may have to be sorted and a proportion ( less that 100%) scrapped customer dissatisfied7ModerateProcess or product operable but co mfort or convenience pointednesss inoperable minor disruption to production line a portion (less than 100%) of the product may have to be scrapped (no sorting) customer learn discomfort6LowProcess 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 LowMinor disruption to production line product may have to be sorted and a portion ( less that 100% ) reworked cosmetic (fit and finish) defect (nonconformance ) noticed 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 disruption 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) notic ed by discrimination customers2NoneNo Effect1Failure analytic thinkingThe 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. concisely 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 lead 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. any(prenominal) of the Type of Failures areFunction FailureWhen the system fails to perform to do its intended function then its referred as Functional Failure. The mission and motive of the system w ill be directly be affected when the function fails. To understand about the functional failure a deep study has to been carried out on the required function.Evident failureWhen the failure is evident or is been made to evident to the operator, the failure is said to be an evident failure. Later, Display, dial or gauges, audible or alarms or other forms of 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.