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A Mathematical Logic Approach To Risk Based VV&A Dr. Peter P. Pandolfini (443) September 22, 2010

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I. D EFINING THE GOALS OF R ISK B ASED VV&A (RBA) SITUATION: A MODEL/SIMULATION (M/S) HAS A STATED LIST OF CAPABILITIES TO BE USED FOR STATED INTENDED PURPOSE(S) DESIRED: A RECOMMENDATION FOR EACH STATED CAPABILITY ON WHETHER: THE M/S CAN BE USED FOR THE INTENDED PURPOSE OR THE M/S SHOULD NOT BE USED FOR THE INTENDED PURPOSE AND THE CONFIDENCE IN THAT RECOMMENDATION DESIRED: A V&V PLAN WITH A CONFIDENCE IN EACH STATED CAPABILITYS RECOMMENDATION, THEREBY UNDERSTANDING THE RISK OF BEING INCORRECT IN THE RECOMMENDATIONS & FACILITATING RESOURCE TRADE- OFFS

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ELEMENTS OF METHODOLOGY COVERAGE: R EQUIRED CAPABILITIES ASSEMBLED AND RATED BY IMPORTANCE TO INTENDED USE ACTIVITIES: D EPTH OF EVIDENCE DETERMINED AS A FUNCTION OF FOUR TYPES OF TASKS TECHNIQUE: E XAMINATION TECHNIQUES THAT ARE INFLUENCED BY A CAPABILITY S LEVEL - OF - IMPORTANCE RESULT: A SCORECARD CONTAINING, FOR EACH CAPABILITY, ITS IMPORTANCE, ITS RECOMMENDATION, AND THE LEVEL - OF - CONFIDENCE IN THE RECOMMENDATION

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R ISK B ASED VV&A S CORECARD CAPABILITY I MPORTANCE ACTIVITIES & EXAMINATION TECHNIQUE R ECOMMENDATION CONFIDENCE ( PERCENTILE ) C1C1 C2AC2A C2BC2B C3C3 … C N -1 CNCN

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II. F ORMING THE V&V P LAN ACTIVITIES BASED ON COMPOSITE MODEL A CTIVITY SETS ORDERED BY INCREASING CONFIDENCE A. CM V&V B. DP VERIFICATION C. HISTORICAL RECORD ANALYSIS OR (CM V&V + DP VERIFICATION ) D. HISTORICAL RECORD ANALYSIS + CM V&V E. HISTORICAL RECORD ANALYSIS + DP VERIFICATION F. HISTORICAL RECORD ANALYSIS + CM V&V + DP VERIFICATION G. RESULTS VALIDATION H. CM V&V + RESULTS VALIDATION I. ( HISTORICAL RECORD ANALYSIS + RESULTS VALIDATION ) OR (DP VERIFICATION + RESULTS VALIDATION ) J. HISTORICAL RECORD ANALYSIS + CM V&V + RESULTS VALIDATION K. HISTORICAL RECORD ANALYSIS + DP VERIFICATION + RESULTS VALIDATION L. CM V&V + DP VERIFICATION + RESULTS VALIDATION M. HISTORICAL RECORD ANALYSIS + CM V&V + DP VERIFICATION + RESULTS VALIDATION TASKS W = C ONCEPTUAL M ODEL V ERIFICATION & V ALIDATION (CM V&V) X = D EVELOPMENT P RODUCT V ERIFICATION (DP VERIFICATION ) Y = H ISTORICAL R ECORD A NALYSIS Z = R ESULTS V ALIDATION E ACH INDIVIDUAL T ASK PROVIDES EVIDENCE OF VALUE IN THE ORDER SHOWN ( I. E., CM V&V < DP VERIFICATION < HISTORICAL RECORD ANALYSIS < RESULTS VALIDATION )

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F ACTOR T ABLE FOR A CTIVITIES S ELECTION F ACTOR ( A ) (a) ACTIVITY Sentence 1Sentence 2WeightingADJ Weighting Aw^~x^~y^~z-1100 B~w^x^~y^~z-3300 C~w^~x^y^~zw^x^~y^~z6600 Dw^~x^y^~z-9900 E~w^x^y^~z Fw^x^y^~z G~w^~x^~y^z Hw^~x^~y^z I~w^~x^y^z~w^x^~y^z Jw^~x^y^z K~w^x^y^z Lw^x^~y^z Mw^x^y^zw^x^y^z F OR EACH CAPABILITY

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F ACTOR T ABLE FOR T ECHNIQUES S ELECTION F ACTOR ( B ) (b) EXAMINATION TECHNIQUE MATURITY LEVEL TECHNIQUEWeighting w ADJ Weighting x ADJ Weighting y ADJ Weighting z ADJ Weighting A Use a LEVEL "1" technique B Use a LEVEL "2" technique C Use a LEVEL "3" technique D Use a LEVEL "4" technique E Use a LEVEL "5" technique F OR EACH CAPABILITY

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III. E VALUATING CONFIDENCE IN A R ECOMMENDATION F ORMING A W EIGHTED R AW S CORE : WRS = function[(a), (b)] F OR EACH CAPABILITY, ACTIVITIES SET, & SELECTED EXAMINATION TECHNIQUE E QUATIONS FOR WEIGHTED RAW SCORE:

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W EIGHTED R AW S CORE I NTERPRETATION C ONFIDENCE, BY QUINTILES WRS P ERCENTILES ( BASED ON CUMULATIVE DISTRIBUTION ) A SSIGN TO A CAPABILITY S R ECOMMENDATION

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A N E XAMPLE P ORTFOLIO OF C APABILITIES & THEIR EXAMINATION TECHNIQUES CAPABILITY I MPORTANCE ACTIVITIES & EXAMINATION TECHNIQUE R ECOMMENDATION CONFIDENCE ( PERCENTILE ) C1C1 M EDIUM L:C,C,ATBD12% TILE ; VERY LOW C2AC2A H IGH L:C,C,CTBD46% TILE ; MEDIUM C2BC2B M EDIUM F:C,C,ETBD29% TILE ; LOW C3C3 L OW L:C,C,ETBD79% TILE ; HIGH … C N -1 CNCN

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S UMMARY A SSEMBLE THE RELEVANT CAPABILITIES D ETERMINE IMPORTANCE FOR EACH CAPABILITY C OMPUTE WRS BASED ON F ACTOR ( A ) STATE & F ACTOR ( B ) STATES C OMPUTE PERCENTILE FOR RECOMMENDATION CONFIDENCE A SSEMBLE RBA S CORECARD & PERFORM V&V PLANNING TRADEOFFS E XECUTE PLAN AND DEVELOP RECOMMENDATION FOR EACH CAPABILITY C OVERAGE, A CTIVITIES, T ECHNIQUES

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