Độ tin cậy của hệ thống máy tính và mạng P7

RELIABILITY OPTIMIZATIONThe preceding chapters of this book discussed a wide range of different techniques for enhancing system or device fault tolerance. In some applications, only one of these techniques is practical, and there is little choice among the methods. However, in a fair number of applications, two or more techniques are feasible, and the question arises regarding which technique is the most cost-effective. To address this problem, if one is given two alternatives, one can always use one technique for design A and use the other technique for design B....
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Độ tin cậy của hệ thống máy tính và mạng P7 Reliability of Computer Systems and Networks: Fault Tolerance, Analysis, and Design Martin L. Shooman Copyright  2002 John Wiley & Sons, Inc. ISBNs: 0-471-29342-3 (Hardback); 0-471-22460-X (Electronic)7RELIABILITY OPTIMIZATION7 .1 INTRODUCTIONThe preceding chapters of this book discussed a wide range of different tech-niques for enhancing system or device fault tolerance. In some applications,only one of these techniques is practical, and there is little choice among themethods. However, in a fair number of applications, two or more techniquesare feasible, and the question arises regarding which technique is the mostcost-effective. To address this problem, if one is given two alternatives, onecan always use one technique for design A and use the other technique fordesign B. One can then analyze both designs A and B to study the trade-offs.In the case of a standby or repairable system, if redundancy is employed at acomponent level, there are many choices based on the number of spares andwhich component will be spared. At the top level, many systems appear as aseries string of elements, and the question arises of how we are to distributethe redundancy in a cost-effective manner among the series string. Specifically,we assume that the number of redundant elements that can be added is limitedby cost, weight, volume, or some similar constraint. The object is to determinethe set of redundant components that still meets the constraint and raises thereliability by the largest amount. Some authors refer to this as redundancy opti-mization [Barlow, 1965]. Two practical works—Fragola [1973] and Mancino[1986]—are given in the references that illustrate the design of a system witha high degree of parallel components. The reader should consult these papersafter studying the material in this chapter. In some ways, this chapter can be considered an extension of the materialin Chapter 4. However, in this chapter we discuss the optimization approach, 331332 RELIABILITY OPTIMIZATIONwhere rather than having the redundancy apply to a single element, it is dis-tributed over the entire system in such a way that it optimizes reliability. Theoptimization approach has been studied in the past, but is infrequently used inpractice for many reasons, such as (a) the system designer does not understandthe older techniques and the resulting mathematical formulation; (b) the solu-tion takes too long; (c) the parameters are not well known; and (d) constraintschange rapidly and invalidate the previous solution. We propose a techniquethat is clear, simple to explain, and results in the rapid calculation of a familyof good suboptimal solutions along with the optimal solution. The designer isthen free to choose among this family of solutions, and if the design featuresor parameters change, the calculations can be repeated with modest effort. We now postulate that the design of fault-tolerant systems can be dividedinto three classes. In the first class, only one design approach (e.g., parallel,standby, voting) is possible, or intuition and experience points only to a sin-gle approach. Thus it is simple to decide on the level of redundancy requiredto meet the design goal or the level allowed by the constraint. To simplifyour discussion, we will refer to cost, but we must keep in mind that all thetechniques to be discussed can be adapted to any other single constraint or,in many cases, multiple constraints. Typical multiple constraints are cost, reli-ability, volume, and weight. Sometimes, the optimum solution will not satisfythe reliability goal; then, either the cost constraint must be increased or thereliability goal must be lowered. In the second class, if there are two or threealternative designs, we would merely repeat the optimization for each classas discussed previously and choose the best result. The second class is onein which there are many alternatives within the design approach because wecan apply redundancy at the subsystem level to many subsystems. The thirdclass, where a mixed strategy is being considered, also has many combinations.To deal with the complexity of the third-class designs, we will use computercomputations and an optimization approach to guide us in choosing the bestalternative or set of alternatives.7 .2 OPTIMUM VERSUS GOOD SOLUTIONSBecause of practical considerations, an approximate optimization yielding agood system is favored over an exact one yielding the best solution. The param-eters of the solution, as well as the failure rates, weight, volume, and cost, aregenerally only known approximately at the beginning of a design; moreover, insome cases, we only know the function that the component must perform, nothow that function will be implemented. Thus the range of possible parametersis often very broad, and to look for an exact optimization when the parametersare known only over a broad range may be an elegant mathematical formula-tion but is not a practical engineering solution. In fact, sometimes choosing theexact optimum can involve considerable risk if the solution is very sensitiveto small changes in parameters. OPTIMUM VERSUS GOOD SOLUTIONS 333 To illustrate, let us assume that there are two design parameters, x and y,and the resulting reliability is z. We can visualize the solution as a surface inx, y, z space, where the reliability is plotted along the vertical z-axis as the twodesign parameters vary in the horizontal xy plane. Thus our solution is a surfacelying above the xy plane and the heig ...