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Standard Handbook of Machine Design P3

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CHAPTER 2 STATISTICAL CONSIDERATIONS Charles R. Mischke, Ph.D., RE. Professor Emeritus of Mechanical Engineering Iowa State University Ames, Iowa 2.1 INTRODUCTION / 2.2 2.2 HISTOGRAPHIC EVIDENCE / 2.3 2.3 USEFUL DISTRIBUTIONS / 2.9 2.4 RANDOM-VARIABLE ALGEBRA / 2.13 2.5 STOCHASTIC ENDURANCE LIMIT BY CORRELATION AND BY TEST / 2.16 2.6 INTERFERENCE / 2.19 2.7 NUMBERS / 2.25 REFERENCES / 2.27 NOMENCLATURE A Area, constant a Constant B Constant b Constant C Coefficient of variation d Diameter Fi /th failure, cumulative distribution function F(JC) Cumulative distribution function corresponding to x ft Class frequency f(x) Probability density function corresponding to x h Simpson's rule interval i. | CHAPTER 2 STATISTICAL CONSIDERATIONS Charles R. Mischke Ph.D. P.E. Professor Emeritus of Mechanical Engineering Iowa State University Ames Iowa 2.1 INTRODUCTION 2.2 2.2 HISTOGRAPHIC EVIDENCE 2.3 2.3 USEFUL DISTRIBUTIONS 2.9 2.4 RANDOM-VARIABLE ALGEBRA 2.13 2.5 STOCHASTIC ENDURANCE LIMIT BY CORRELATION AND BY TEST 12.16 2.6 INTERFERENCE I 2.19 2.7 NUMBERS 2.25 REFERENCES 2.27 NOMENCLATURE A Area constant a Constant B Constant b Constant C Coefficient of variation d Diameter F th failure cumulative distribution function F x Cumulative distribution function corresponding to x f Class frequency f x Probability density function corresponding to x h Simpson s rule interval i failure number index LN Lognormal N Normal n design factor sample size population n mean of design factor distribution P Probability probability of failure R Reliability probability of success or survival 2.1 2.2 STANDARD HANDBOOK OF MACHINE DESIGN r Correlation coefficient S ax Axial loading endurance limit S e Rotary bending endurance limit Sy Tensile yield strength S e Torsional endurance limit SIU Tensile ultimate strength x Variate coordinate Xi ith ordered observation x0 Weibull lower bound y Companion normal distribution variable z z variable of unit normal N 0 1 a Constant T Gamma function Ax Histogram class interval 0 Weibull characteristic parameter p Population mean 1 Unbiased estimator of population mean G stress o Standard deviation 3 Unbiased estimator of standard deviation C z Cumulative distribution function of normal distribution body of Table 2.1 Function j Fatigue ratio mean Axial fatigue ratio variate Rotary bending fatigue ratio variate 4 Torsional fatigue ratio variate 2.1 INTRODUCTION In considering machinery uncertainties abound. There are uncertainties as to the Composition of material and the effect of variations on properties Variation in properties from place to place within a bar of stock Effect of processing locally or nearby on properties Effect of thermomechanical .