Mechanical Engineer's Handbook [Vol 2 - Instrum., Sys, Ctls, by Myer Kutz PDF

By Myer Kutz

ISBN-10: 0471449903

ISBN-13: 9780471449904

ISBN-10: 0471719870

ISBN-13: 9780471719878

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Extra resources for Mechanical Engineer's Handbook [Vol 2 - Instrum., Sys, Ctls, MEMS]

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5. Define H0 and H1. Choose the confidence level ␥ of the test. Form an appropriate probabilistic statement. Using the appropriate statistical distribution, perform the indicated calculation. Make a decision concerning the hypothesis and / or determine confidence limits. Two types of error are possible in statistical testing. A Type I error is that of rejecting a true null hypothesis (rejecting truth). A Type II error is that of accepting a false null hypothesis (embracing fiction). The confidence levels and sample size are chosen to minimize the probability of making a Type I or Type II error.

From the propagation of variance, ␴ d2 becomes ␴ 2d ϭ ␴ 2x1 ϩ ␴ 2x2 ϭ ␴ 21 ␴ 22 ϩ n1 n2 (55) 28 Instrument Statics where ␴ 12 and ␴ 22 are each estimates of the population variance ␴ 2. A better estimate of ␴ 2 is the combined variance ␴ 2c , and it replaces both ␴ 21 and ␴ 22 in Eq. (55). The combined variance is determined by weighting the individual estimates of variance based on their degrees of freedom according to the relation ␴ c2 ϭ ␴ˆ 21v1 ϩ ␴ˆ 22v2 v1 ϩ v2 (56) Then ␴ d2 ϭ ͩ ␴ˆ 2c ␴ˆ 2 1 1 ϩ c ϭ ␴ c2 ϩ n1 n2 n 1 n2 ͪ (57) Under the hypothesis H0 that ␮1 ϭ ␮2 (no effect due to treatment), the resulting probabilistic statement is ͫ Ί P Ϫt␴c Ί ͬ 1 1 1 1 ϩ Ͻ x1 Ϫ x2 Ͻ t␴c ϩ ϭ␥ n1 n2 n1 n 2 (58) If the variances of the items being compared are not equal (homogeneous), a modified t- (or d-) statistic is used,9,15 where d depends on confidence level ␥, degrees of freedom v, and a parameter ␪ that depends on the ratio of standard deviations according to tan ␪ ϭ ␴ˆ 1 / ͙n1 (59) ␴ˆ 2 / ͙n2 The procedure for using the d-statistic is the same as described for the t-statistic.

2. 3. 4. 5. 6. 7. 8. Introduction 33 Dimming of the headlights while starting a car Slowdown of an electric mixer lowered into heavy batter Freezing a showerer by starting the dishwasher Speedup of a vacuum cleaner when the hose plugs Two-minute wait for a fever thermometer to rise Special connectors required for TV antennas Speedup of a fan in the window with the wind against it Shifting of an automatic transmission on a hill These effects happen because one part of a system loads another. Most mechanical engineers would guess that weighing an automobile by placing a bathroom-type scale under its wheels one at a time and summing the four measurements will yield a higher result than would be obtained if the scale was flush with the floor.

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Mechanical Engineer's Handbook [Vol 2 - Instrum., Sys, Ctls, MEMS] by Myer Kutz

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