Risk and Uncertainty Reduction by Using Algebraic Inequalities /

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Record ID	marc_columbia/Columbia-extract-20221130-030.mrc:194384411:9713
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008 200512t20202020flua ob 001 0 eng
010 $a 2020005696
035 $a(OCoLC)on1155485691
035 $a(NNC)14926146
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024 7 $a10.1201/9781003032502$2doi
035 $a(OCoLC)1155485691$z(OCoLC)1203911354
037 $a9781003032502$bTaylor & Francis
042 $apcc
050 04 $aTA169.55.R57$bT63 2020
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072 7 $aMAT$x029000$2bisacsh
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082 00 $a620/.004520151297$223
049 $aZCUA
100 1 $aTodinov, M. T.,$eauthor.
245 10 $aRisk and uncertainty reduction by using algebraic inequalities /$cMichael T. Todinov.
250 $aFirst edition.
264 1 $aBoca Raton, FL :$bCRC Press, Taylor & Francis Group,$c2020.
264 4 $c©2020
300 $a1 online resource (xvii, 189 pages) :$billustrations
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
504 $aIncludes bibliographical references and index.
505 0 $a1. FUNDAMENTAL CONCEPTS RELATED TO RISK AND UNCERTAINTY REDUCTION BY USING ALGEBRAIC INEQUALITIES1.1 Domain-independent approach to risk reduction 1.2 A powerful domain-independent method for risk and uncertainty reduction based on algebraic inequalities 1.3 Risk and uncertainty2. PROPERTIES OF ALGEBRAIC INEQUALITIES AND STANDARD ALGEBRAIC INEQUALITIES 2.1 Basic rules related to algebraic inequalities 2.2 Basic properties of inequalities 2.3 One-dimensional triangle inequality 2.4 The quadratic inequality 2.5 Jensen's inequality 2.6 Root-mean square -- Arithmetic mean -- Geometric mean -- Harmonic mean (RMS-AM-GM-HM) inequality 2.7 Weighted Arithmetic mean-Geometric (AM-GM) mean inequality 2.8 Hölder's inequality 2.9 Cauchy-Schwarz inequality 2.10 Rearrangement inequality 2.11 Chebyshev's sum inequality 2.12 Muirhead's inequality 2.13 Markov's inequality 2.14 Chebyshev's inequality 2.15 Minkowski inequality3. BASIC TECHNIQUES FOR PROVING ALGEBRAIC INEQUALITIES 3.1 The need for proving algebraic inequalities 3.2 Proving inequalities by a direct algebraic manipulation and analysis 3.3 Proving inequalities by presenting them as a sum of non-negative terms 3.4 Proving inequalities by proving simpler intermediate inequalities 3.5 Proving inequalities by a substitution 3.6 Proving inequalities by exploiting the symmetry 3.7 Proving inequalities by exploiting homogeneity 3.8 Proving inequalities by a mathematical induction 3.9 Proving inequalities by using the properties of convex/concave functions 3.10 Proving inequalities by using the properties of sub-additive and super-additive functions 3.11 Proving inequalities by transforming them to known inequalities 3.12 Proving inequalities by a segmentation 3.13 Proving algebraic inequalities by combining several techniques 3.14 Using derivatives to prove inequalities4. USING OPTIMISATION METHODS FOR DETERMINING TIGHT UPPER AND LOWER BOUNDS. TESTING A CONJECTURED INEQUALITY BY A SIMULATION. EXERCISES 4.1 Using constrained optimisation for determining tight upper bounds 4.2 Tight bounds for multivariable functions whose partial derivatives do not change sign in a specified domain 4.3 Conventions adopted in presenting the simulation algorithms 4.4 Testing a conjectured algebraic inequality by a Monte-Carlo simulation 4.5 Exercises 4.6 Solutions to the exercises5. RANKING THE RELIABILITIES OF SYSTEMS AND PROCESSES BY USING INEQUALITIES 5.1 Improving reliability and reducing risk by proving an abstract inequality derived from the real physical system or process 5.2 Using inequalities for ranking systems whose component reliabilities are unknown 5.3 Using inequalities for ranking systems with the same topology and different components arrangements 5.4 Using inequalities to rank systems with different topologies built with the same type of components 6. USING INEQUALITIES FOR REDUCING EPISTEMIC UNCERTAINTY AND RANKING DECISION ALTERNATIVES6.1 Selection from sources with unknown proportions of high-reliability components 6.2 Monte Carlo simulations 6.3 Extending the results by using the Muirhead's inequality7. CREATING A MEANINGFUL INTERPRETATION OF EXISTING ABSTRACT INEQUALITIES AND LINKING IT TO REAL APPLICATIONS7.1 Meaningful interpretations of an abstract algebraic inequality with several applications to real physical systems 7.2 Avoiding underestimation of the risk and overestimation of average profit by a meaningful interpretation of the Chebyshev's sum inequality 7.3 A meaningful interpretation of an abstract algebraic inequality with an application to selecting components of the same variety 7.4 Maximising the chances of a beneficial random selection by a meaningful interpretation of a general inequality 7.5 The principle of non-contradiction8. INEQUALITIES MINIMISING THE RISK OF A FAULTY ASSEMBLY AND OPERATION8.1 Using inequalities for minimising the deviation of reliability-critical parameters 8.2 Minimising the deviation of the volume of manufactured cylindrical workpieces with cylindrical shape 8.3 Minimising the deviation of the volume of manufactured workpieces in the shape of a rectangular prism 8.4 Minimising the deviation of the resonant frequency from the required level, for parallel resonant LC-circuits 8.5 Maximising reliability by using the rearrangement inequality 8.6 Using the rearrangement inequality to minimise the risk of a faulty assembly 9. DETERMINING TIGHT BOUNDS FOR THE UNCERTAINTY IN RISK-CRITICAL PARAMETERS AND PROPERTIES BY USING INEQUALITIES9.1 Upper-bound variance inequality for properties from different sources 9.2 Identifying the source whose removal causes the largest reduction of the worst-case variation 9.3 Increasing the robustness of electronic devices by using the variance-upper-bound inequality 9.4 Determining tight bounds for the fraction of items with a particular property 9.5 Using the properties of convex functions for determining the upper bound of the equivalent resistance for resistors with uncertain values 9.6 Determining a tight upper bound for the risk of a faulty assembly by using the Chebyshev's inequality 9.7 Deriving a tight upper bound for the risk of a faulty assembly by using the Chebyshev's inequality and Jensen's inequality10. USING ALGEBRAIC INEQUALITIES TO SUPPORT RISK-CRITICAL REASONING 10.1 Using the inequality of the negatively correlated events to support risk-critical reasoning 10.2 Avoiding risk underestimation by using the Jensen's inequality 10.3 Reducing uncertainty and risk associated with the prediction of the magnitudes ranking related to random outcomes 11. REFERENCES
520 $a"This book provides the reader with a domain-independent method for reducing risk through maximizing reliability, reducing epistemic uncertainty, reducing aleatory uncertainty, ranking the reliabilities of systems and processes, minimizing the risk of faulty assemblies, and ranking decision-making alternatives in the presence of deep uncertainty"--$cProvided by publisher.
545 0 $aMichael T. Todinov, PhD, has a background in mechanical engineering, applied mathematics and computer science. Prof.Todinov pioneered reliability analysis based on the cost of failure, repairable flow networks andnetworks with disturbed flows, domain-independent methods for reliability improvement and risk reduction and reducing risk and uncertainty by using algebraic inequalities.
588 $aDescription based on online resource; title from digital title page (viewed on November 05, 2020).
650 0 $aRisk assessment$xMathematics.
650 0 $aSystem failures$xPrevention$xMathematics.
650 0 $aRisk management$xMathematics.
650 0 $aInequalities (Mathematics)
650 6 $aÉvaluation du risque$xMathématiques.
650 6 $aGestion du risque$xMathématiques.
650 6 $aInégalités (Mathématiques)
650 7 $aTECHNOLOGY / Manufacturing$2bisacsh
650 7 $aMATHEMATICS / Mathematical Analysis$2bisacsh
650 7 $aMATHEMATICS / Probability & Statistics / General$2bisacsh
650 7 $aInequalities (Mathematics)$2fast$0(OCoLC)fst00972020
650 7 $aRisk management$xMathematics$2fast$0(OCoLC)fst01098180
655 4 $aElectronic books.
776 08 $iPrint version:$aTodinov, M. T..$tRisk and uncertainty reduction by using algebraic inequalities$bFirst edition.$dBoca Raton, FL : CRC Press, [2020]$z9780367898007$w(DLC) 2020005695
856 40 $uhttp://www.columbia.edu/cgi-bin/cul/resolve?clio14926146$zTaylor & Francis eBooks
852 8 $blweb$hEBOOKS