Probabilistic Design for Optimization and Robustness for Engineers

9 Tolerance analysis

9.1 Introduction

In the design of new products, processes, or services, one of the final steps is the establishment of tolerances and specifications. These values establish the criteria for system acceptance, quantify the amount of allowable variation to meet customer and functional requirements, and ensure interchangeability during the assembly of components and sub-assemblies.

This interchangeability may be viewed from two perspectives. First, we have the interchangeability of the final product. Here, one must be able to randomly select any final product and have it fit and function as intended. In addition, appropriate tolerances ensure interchangeability of components and sub-assemblies.

In discussing the development of tolerances and specifications, we first provide operational definitions. We use the term specification to denote the actual permitted values from a nominal or target condition and the term tolerance to denote the relative allowable deviation from nominal. So, for a hole specification of 10 ± 0.2 mm, the nominal (or target) would equal 10, the plus or minus tolerance would equal 0.2, the tolerance width would equal 0.4 mm, and the lower and upper specification limits would be 9.8 and 10.2, respectively. Table 9.1 further summarizes some common terms used in tolerance analysis.

Table 9.1 Tolerance analysis terminology.

Term	Code	Definition
Nominal (target)	N or T	Desired or specified value for a dimension
Lower specification ...