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K߱ g OwG7fChQ ;!x{> =,B.T1XRu,ݥ/D$xK7<ՀF@m!mfL*9b"p5/k 5ZphIܾ.%Nm5γ8\CEzbɫ2NȃwM7$U2ɊJ%7q} }ʕr뮋c=zFRdq @[:GA|CrׇG暆,HbuQR-,Ӡa_q5x[k۱W1}ŔT4iǃyR6_ 74୴F6΁Mve@_X>ǧr]{%C?.6հ&ٴIJ|:%Υ6#ߘ<9e9br=Ű<>d=\,Z ؚWq~X*Npڞjz;ă<vaXgO}kpnN-Z>uF*Vy|dYhҊ֭|Cԙ^1 cm<9OD6(‹"loKx-ت?(Yx /0qgOս4~6ͫQ-jez15k_s!p^V5@^Zr,юT߰&fj4`%]״, wL͋W1%Ś/H(N#HyM>÷t5e Pa_op(Cnد(2'dxQk.IҿGPL5-wm7>Z(bfkkVM^#uIENDB`3 A@@  |CNHYpothesis Testing of EQuivalence Copyright ɫƵ 2007  !' Calculated CV Modified CVQual.Equiv.Mean Strength (ksi)Standard DeviationCoefficient of Variation (CV)MinimumMaximumNumber of SpecimensPooled CV (see Note 2)Wmean for a=0.05  Mean Result for a=0.05Wmin_indiv for a=0.05Min_indiv. Result for a=0.05Wmean for a=0.01  Mean Result for a=0.01Wmin_indiv for a=0.01Min_indiv. Result for a=0.01Explanation/CommentsNormalized DataCoefficient of VariationMean Modulus (Msi) Pooled CV No. Specimens see Note 2for pooled C.V.2Pooled Standard Deviation (Baseline & Equivalence)Test Statistic, t0 Passing Range for t0 at a=5%&Passing range for mean modulus at a=5%Passing range tolerance at a=5%Result at a=5%Passing Range for t0 at a=1%&Passing range for mean modulus at a=1%Passing range tolerance at a=1%Result at a=1%Pooled CVt (%), see Note 1p-value of t-statisticvNote 1: Pooled CVt is the ratio of Pooled Standard Deviation (Sp) to the mean of all specimens computed for the t-test,Note 2: Pooled CV is the coefficient of variation computed using the qualification sample test results pooled across the different environmental condition with the appropriate number of specimens. These numbers are obtained from the ASAP program. Input ONLY if data passes the Anderson-Darling test.ENV4kTHIS SHEET HAS BEEN PROTECTED TO PREVENT ACCIDENTAL CHANGES. 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The following paragraphs highlight the methodology and provide instructions for the use of the spreadsheet. The statistical procedure in HYTEQ compares the qualification and equivalence test results of composite materials using the t-test for modulus properties and the mean and minimum values for strength properties. These tests are performed in accordance with references [1] and [2]. Space is provided to run separate comparisons for both normalized and 'as measured' data values for fiber dominated properties. All tests are performed with both the calculated coefficient of variation (C.V.) and with a modified co-efficient of variation. The modified co-efficient of variation is computed as follows: If the calculated C.V. is less than 4%, it is set to 6%. Else if the calculated C.V. is between 4% and 8%, it is set to 4% + 0.5*C.V. Else if the calculated C.V. is over 8% , it remains the same After the C.V. is modified, a modified standard deviation is computed based on it and the equivalency tests are performed using the modified value. The following paragraphs list the features of this version of HYTEQ and briefly outlline the procedure for using this spreadsheet. HYTEQ 2011 features: 1. Computes Equivalence test results at  = 0.05. 2. Computes Acceptance test results at  = 0.01. 3. A summary of the results is provided to show at a glance the results of all tests. 4. All computed test statistics are provided. 5. Each test is given a 'pass' or 'fail' indication for both the equivalency and acceptance criteria. 5. Modulus values are tested with a two-sided t-test 6. Strength values are tested with a one-sided test for both mean and minimum values. 7. Fiber dominated properties can be tested for both normalized and 'as measured' values. 8. For modulus tests, the p-value of the t-test statistic is provided. HYTEQ user guide: 1. Create a copy of the 'blank' worksheet for each test property to be evaluated. 2. Input values only in the turquoise shaded cells. 3. Input the Environmental Conditions in the top row for each set of tests. 4. Input sample statistics for both the original qualification material and the acceptance or equivalence sample in the appropriately labeled rows. 5. If the ASAP program indicates the qualification data passes the Anderson-Darling test, you may input the pooled co-efficient of variation. This is computed in ASAP and is based on the data from the qualification samples across all environmental conditions. For strength values, only the pooled C.V. is needed. For modulus values, input both the co-efficient of variation and the number of specimens used to compute it in the appropriately labeled cells. _________________________________________________________________________________ NOTES: [1]. The user is warned against changing the features/formulas/formats etc. [2]. The authors would appreciate any suggestions/corrections that you might have. _________________________________________________________________________________ References: [1]. John S. Tomblin, Yeow C. Ng and K. Suresh Raju, "Material Qualification and Equivalency for Polymer Matrix Composite Material Systems," DOT/FAA/AR-03/19, September. 2003. [2]. 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