Quality Assurance and Tolerance

Prof. Dr.-Ing. Günter Kirschling lehrt an der Universität Gesamthochschule Kassel.

It is in general not possible to produce technical products having precisely predefined measures. Systematic and random deviations from nominal size cannot be avoided, and it is therefore necessary to define measurement tolerances. This book offers a comprehensive presentation of tolerance problems and their solution by statistical methods. All calculated solutions are presented in clear figure or graphical form. It is particularly appropriate for those working in the field of development and construction or in production and quality control, especially in mechanical engineering and related fields.

This book offers a comprehensive presentation of tolerance problems and their solution by statistical methods. All calculated solutions are presented in clear figure or graphical form. It is appropriate for those working in development and construction or in production and quality control.

1 Introduction.- 2 Concepts.- 3 Probability Calculation.- 3.1 Definition of Probability.- 3.2 Addition Formula (OR Formula).- 3.3 Multiplication Formula (AND Formula).- 4 Probability Distributions of Quantitative Characteristics.- 4.1 General.- 4.2 Normal Distribution.- 4.3 Abnormal Probability Distributions.- 4.4 Random Spread for Mean Values.- 5 Mathematical and Graphical Evaluation of Dimensional Series.- 5.1 General.- 5.2 Mathematical Evaluation Without Classification.- 5.3 Graphical Evaluation Without Classification.- 5.4 Mathematical Evaluation of Classified Dimensional Series.- 5.5 Graphical Evaluation of Classified Dimensional Series.- 5.6 Other Statistical Characteristics.- 5.7 The Significance of Statistical Characteristics.- 6 Mixed Distributions.- 6.1 Types of Mixed Distribution.- 6.2 Mixed Distribution Type 1.- 6.3 Mixed Distribution Type 2.- 6.4 Tschebyscheff's Extreme Case.- 7 Distribution Folds.- 7.1 Description of Fold Methods.- 7.2 Examples of Folding Methods.- 8 Relationship Between Tolerances and Production Distributions.- 8.1 Direct and Indirect Function Characteristics.- 8.2 Establishment and Observance Tolerances.- 8.3 Tolerances and Costs.- 8.4 Errors and Waste.- 8.5 Arithmetical Tolerance Calculation.- 8.6 Examples for Arithmetically Calculated Linear Dimensional Chains.- 8.7 The Sorting of Non-Conforming Parts.- 9 Tolerance Calculation Using Square Law.- 10 Statistical Calculation of Tolerances of Individual Values with Rectangular Distributions.- 10.1 General.- 10.2 Derivation of Reduction and Expansion Factors with Equal Individual Tolerances.- 10.3 Calculation of Dimensional Chains with Unequal Individual Tolerances and Rectangular Individual Distributions.- 10.4 Advantages of the Assumption of the Presence of Rectangular Distributions.-11 Statistical Tolerance Calculation of Individual Values with Trapezoid Distribution or with Triangular Distribution.- 11.1 Method of Calculation.- 11.2 Simple Formula to Check Fixed Linear Dimensional Chains.- 12 The Tolerance Model.- 13 Assessment of Completed Batches and Production Batches.- 13.1 General.- 13.2 Random Sample Dimension Tests.- 13.3 Selection of AQL Values for Random Sample Tests of Dimensions (Variable Testing).- 13.4 Quality Control Charts for Dimensions.- 14 Process Analysis and Process Capability.- 14.1 Process Analysis.- 14.2 Process Capability.- 15 Process Control.- 15.1 General Aspects.- 15.2 Process Control by Mean Value Quality Control Charts.- 15.3 Process Control by Original Value QCC's.- 15.4 Process Correction.- 16 Bibliography.- 17 Appendix.- Tables.