|Table of Contents|

Section Contents

• Section 1 Introduction
• Section 2 Stress Analysis
• Section 3 Deflection Analysis
• Section 4 Statistical Considerations in Design
  • Section 4-01 Permutations and Combinations
  • Section 4-02 Probability
  • Section 4-03 Probability Theorems
  • Section 4-04 Random Variables
  • Section 4-05 Sample and Population
  • Section 4-06 The Normal Distribution
  • Section 4-07 Sampling Distributions
  • Section 4-08 Population Combinations
  • Section 4-09 Dimensioning - Definitions and Standards
  • Section 4-10 Statistical Analysis of Tolerancing
• Section 5 The Strength of Mechanical Elements
• Appendix Tables
• Index

Introduction

"Almost any product that you can conceive of can be made with a high degree of perfection. It is not made in this state of perfection simply because of economic reasons. The more inspection you buy, the more design you buy, the greater your chances of putting out a zero-defect product. But there comes a point where, if you have gotten your product 98 percent defect free, then if you spend a hundred times this much in design and in inspection you may only get 99 percent zero-free, and you may spend a thousand times as much to make it really perfect. So it just isn't economically feasible to make every product perfect.

This is acceptable manufacturing philosophy to the manufacturer. It is totally unacceptable to the consumer who gets that one rare product that is defective and meets serious unjury or death as a result of it." [By Craig Spangenberg, "You, Your Product, and the Law," Mechanical Engineering, vol. 90, no. 6, p. 19 June, 1968, by permission of the American Society of Mechanical Engineers.]

As indicated by this quotation, an uncertainty exists as to whether a product will actually perform satisfactorily. It is the purpose of this chapter to provide the tools needed by the design engineer to determine the numerical probability of success or failure.