Redundancy Allocation using Multiple Weighted Objectives

Redundancy Allocation using Multiple Weighted Objectives Redundancy Allocation using multiple weighted objectives heuristic Abstract A new method for optimization of system reliability was put forward and tested. In this method, the main aim is to maximize the individual system 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 problem into multiple objectives and in turn into different single objective problem. Then this sequence is done by solving the linear programing formulation. The results obtained are efficient solutions which depends on the readily available tools. Thus, on the whole this new method is more efficient when compared to the already available practices for both efficiency and performance. INTRODUCTION of Articles The main aim of this journal is to design an optimal solution to maximize the system 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 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 allocation. 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. Mathematical programming approaches restricts by allowing one component choice for each subsystem. In the example shown in the figure below shows a series parallel system. For each subsystem, there are multiple, functional equivalent 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 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. Nomenclature Xij number of components of type j used in subsystem i R(x)- System reliability Ri(xi)- reliability of subsystem i Wi objective weight assigned to the ith subsystem Rimin- minimum subsystem reliability for subsystem i Explanation of the work presented in journal articles The 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 strategy 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 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 may have 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 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 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 combined to result in multiple objectives. All objectives are equally important and are assigned with equal weights as failure is caused due to failure of any 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 formulation, are presented below as Problems P1 P2. Problem 1: Problem 2 : Problem P3 is a nonlinear integer programming that is difficult 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 Contributions The 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 dependability 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 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 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 also maximizes the subsystem reliability. Discussion of Dificiency and Potential Improvements The 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 taking in account the size of the problem obtained from the CPU is very promising. Summary The 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. References David 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: 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 Failure Probability of Failure Mode Possible Failure Rate Probability Ranking Very High : Failure is almost inevitable à ¢Ã¢â‚¬ °Ã‚ ¥ 1 in 2 .50 à ¢Ã¢â‚¬ °Ã‚ ¤ p à ¢Ã¢â‚¬ °Ã‚ ¤ 1.00 10 Very High à ¢Ã¢â‚¬ °Ã‚ ¥ 1 in 3 .33 à ¢Ã¢â‚¬ °Ã‚ ¤ p 9 High : repeated Failure à ¢Ã¢â‚¬ °Ã‚ ¥ 1 in 8 .125 à ¢Ã¢â‚¬ °Ã‚ ¤ p 8 High à ¢Ã¢â‚¬ °Ã‚ ¥ 1 in 20 .05 à ¢Ã¢â‚¬ °Ã‚ ¤ p 7 Moderate : Occasional Failures à ¢Ã¢â‚¬ °Ã‚ ¥ 1 in 80 .0125 à ¢Ã¢â‚¬ °Ã‚ ¤ p 6 Moderate à ¢Ã¢â‚¬ °Ã‚ ¥ 1 in 400 .0025 à ¢Ã¢â‚¬ °Ã‚ ¤ p 5 Moderate : Infrequent Failure à ¢Ã¢â‚¬ °Ã‚ ¥ 1 in 2000 .0005 à ¢Ã¢â‚¬ °Ã‚ ¤ p .0025 4 Low : Relatively Few Failure à ¢Ã¢â‚¬ °Ã‚ ¥ 1 in 15,000 .0000667 à ¢Ã¢â‚¬ °Ã‚ ¤ p 3 Low à ¢Ã¢â‚¬ °Ã‚ ¥ 1 in 150,000 6.7 x 10^-6 à ¢Ã¢â‚¬ °Ã‚ ¤ p 2 Remote : failure is Unlikely à ¢Ã¢â‚¬ °Ã‚ ¥ 1 in 1,500,000 6.7 x 10^-7 à ¢Ã¢â‚¬ °Ã‚ ¤ p 1 Likelihood of Detection Detection Criteria Ranking Almost Impossible No known way detect failure mode 10 Very Remote Very unlikely to detect failure mode 9 Remote Unlikely to detect failure mode 8 Very low Very low chance to detect failure mode 7 Low Low Chance to detect failure mode 6 Moderate Moderate chance to detect failure mode 5 Moderately High Moderately high chance to detect failure mode 4 High Likely to detect failure mode 3 Very High Very likely to detect failure mode 2 Almost Certain Will almost certainly detect failure mode 1 Severity Rating Severity Criteria Ranking Hazardous-without Warning May endanger operator; noncompliance with regulations; affects the safe use of the product; failure will occur without warning 10 Hazardous-with Warning May endanger operator, noncompliance with regulations; affects the safe use of the product; failure will occur with warning. 9 Very High Process or product inoperable with loss of primary function; major disruption to the production line; product may have to be scrapped; customer very dissatisfied 8 High Process 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 dissatisfied 7 Moderate Process or product operable but comfort or convenience items inoperable; minor disruption to production line; a portion (less than   100%) of the product may have to be scrapped (no sorting); customer experience discomfort 6 Low Process 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 dissatisfaction 5 Very Low Minor 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 customer 4 Minor Minor 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 customer 3 Very Minor Minor 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) noticed by discrimination customers 2 None No Effect 1 Failure Analysis The 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 lead to the development of RCM technique. Failure Identifying 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. Some of the Type of Failures are Function Failure When 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 study has to been carried out on the required function. Evident failure When 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 Failure A 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.

Deception Point Page 31

More laughter this time. â€Å"And,† she said, glancing down at the bottom of the screen, â€Å"I had certainly not imagined I would be sitting at the President's desk†¦ much less on it!† This brought a hearty laugh and some broad smiles. Rachel felt her muscles starting to relax. Just give it to them straight. â€Å"Here's the situation.† Rachel's voice now sounded like her own. Easy and clear. â€Å"President Herney has been absent from the media spotlight this past week not because of his lack of interest in his campaign, but rather because he has been engrossed in another matter. One he felt was far more important.† Rachel paused, her eyes making contact now with her audience. â€Å"There has been a scientific discovery made in a location called the Milne Ice Shelf in the high Arctic. The President will be informing the world about it in a press conference tonight at eight o'clock. The find was made by a group of hardworking Americans who have endured a string of tough luck lately and deserve a break. I'm talking about NASA. You can be proud to know that your President, with apparent clairvoyant confidence, has made a point of standing beside NASA lately through thick and thin. Now, it appears his loyalty is going to be rewarded.† It was not until that very instant that Rachel realized how historically momentous this was. A tightness rose in her throat, and she fought it off, plowing onward. â€Å"As an intelligence officer who specializes in the analysis and verification of data, I am one of several people the President has called upon to examine the NASA data. I have examined it personally as well as conferring with several specialists-both government and civilian-men and women whose credentials are beyond reproach and whose stature is beyond political influence. It is my professional opinion that the data I am about to present to you is factual in its origins and unbiased in its presentation. Moreover, it is my personal opinion that the President, in good faith to his office and the American people, has shown admirable care and restraint in delaying an announcement I know he would have loved to have made last week.† Rachel watched the crowd before her exchanging puzzled looks. They all returned their gaze to her, and she knew she had their undivided attention. â€Å"Ladies and gentlemen, you are about to hear what I'm sure you will agree is one of the most exciting pieces of information ever revealed in this office.† 35 The aerial view currently being transmitted to the Delta Force by the microbot circling inside the habisphere looked like something that would win an avant-garde film contest-the dim lighting, the glistening extraction hole, and the well-dressed Asian lying on the ice, his camel-hair coat splayed around him like enormous wings. He was obviously trying to extract a water sample. â€Å"We've got to stop him,† said Delta-Three. Delta-One agreed. The Milne Ice Shelf held secrets his team was authorized to protect with force. â€Å"How do we stop him?† Delta-Two challenged, still gripping the joystick. â€Å"These microbots are not equipped.† Delta-One scowled. The microbot currently hovering inside the habisphere was a recon model, stripped down for longer flight. It was about as lethal as a housefly. â€Å"We should call the controller,† Delta-Three stated. Delta-One stared intently at the image of the solitary Wailee Ming, perched precariously on the rim of the extraction pit. Nobody was anywhere near him-and ice cold water had a way of muffling one's ability to scream. â€Å"Give me the controls.† â€Å"What are you doing?† the soldier on the joystick demanded. â€Å"What we were trained to do,† Delta-One snapped, taking over. â€Å"Improvise.† 36 Wailee Ming lay on his stomach beside the extraction hole, his right arm extended over the rim trying to extract a water sample. His eyes were definitely not playing tricks on him; his face, now only a yard or so from the water, could see everything perfectly. This is incredible! Straining harder, Ming maneuvered the beaker in his fingers, trying to reach down to the surface of the water. All he needed was another few inches. Unable to extend his arm any farther, Ming repositioned himself closer to the hole. He pressed the toes of his boots against the ice and firmly replanted his left hand on the rim. Again, he extended his right arm as far as he could. Almost. He shifted a little closer. Yes! The edge of the beaker broke the surface of the water. As the liquid flowed into the container, Ming stared in disbelief. Then, without warning, something utterly inexplicable occurred. Out of the darkness, like a bullet from a gun, flew a tiny speck of metal. Ming only saw it for a fraction of a second before it smashed into his right eye. The human instinct to protect one's eyes was so innately ingrained, that despite Ming's brain telling him that any sudden movements risked his balance, he recoiled. It was a jolting reaction more out of surprise than pain. Ming's left hand, closest to his face, shot up reflexively to protect the assaulted eyeball. Even as his hand was in motion, Ming knew he had made a mistake. With all of his weight leaning forward, and his only means of support suddenly gone, Wailee Ming teetered. He recovered too late. Dropping the beaker and trying to grab on to the slick ice to stop his fall, he slipped-plummeting forward into the darkened hole. The fall was only four feet, and yet as Ming hit the icy water head first he felt like his face had hit pavement at fifty miles an hour. The liquid that engulfed his face was so cold it felt like burning acid. It brought an instantaneous spike of panic. Upside down and in the darkness, Ming was momentarily disoriented, not knowing which way to turn toward the surface. His heavy camel-hair coat kept the icy blast from his body-but only for a second or two. Finally righting himself, Ming came sputtering up for air, just as the water found its way to his back and chest, engulfing his body in a lung-crushing vise of cold. â€Å"Hee†¦ lp,† he gasped, but Ming could barely pull in enough air to let out a whimper. He felt like the wind had been knocked out of him. â€Å"Heee†¦ lp!† His cries were inaudible even to himself. Ming clambered toward the side of the extraction pit and tried to pull himself out. The wall before him was vertical ice. Nothing to grab. Underwater, his boots kicked the side of the wall, searching for a foothold. Nothing. He strained upward, reaching for the rim. It was only a foot out of reach. Ming's muscles were already having trouble responding. He kicked his legs harder, trying to propel himself high enough up the wall to grab the rim. His body felt like lead, and his lungs seemed to have shrunk to nothing, as if they were being crushed by a python. His water-laden coat was getting heavier by the second, pulling him downward. Ming tried to pull it off his body, but the heavy fabric stuck. â€Å"Help†¦ me!† The fear came on in torrents now. Drowning, Ming had once read, was the most horrific death imaginable. He had never dreamed he would find himself on the verge of experiencing it. His muscles refused to cooperate with his mind, and already he was fighting just to keep his head above water. His soggy clothing pulled him downward as his numb fingers scratched the sides of the pit. His screams were only in his mind now. And then it happened. Ming went under. The sheer terror of being conscious of his own impending death was something he never imagined he would experience. And yet here he was†¦ sinking slowly down the sheer ice wall of a two-hundred-foot-deep hole in the ice. Multitudes of thoughts flashed before his eyes. Moments from his childhood. His career. He wondered if anyone would find him down here. Or would he simply sink to the bottom and freeze there†¦ entombed in the glacier for all time.

Transitional Housing Program For The United States Essay

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Descriptive Personal Experience Essay - 1444 Words

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