Fracture Mechanics 1

Analysis of Reliability and Quality Control

Ammar Grous

• Publisher: Wiley-ISTE
• Year: 2013
• Print ISBN: 9781848214408
• eBook ISBN: 9781118580127
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Materials Science
• Index: Technology & Engineering

This first book of a 3-volume set on Fracture Mechanics is mainly centered on the vast range of the laws of statistical distributions encountered in various scientific and technical fields. These laws are indispensable in understanding the probability behavior of components and mechanical structures that are exploited in the other volumes of this series, which are dedicated to reliability and quality control.
The author presents not only the laws of distribution of various models but also the tests of adequacy suited to confirm or counter the hypothesis of the law in question, namely the Pearson (x2) test, the Kolmogorov-Smirnov (KS) test, along with many other relevant tests.
This book distinguishes itself from other works in the field through its originality in presenting an educational approach which aims at helping practitioners both in academia and industry. It is intended for technicians, engineers, designers, students, and teachers working in the fields of engineering and vocational education. The main objective of the author is to provide an assessment of indicators of quality and reliability to aid in decision-making. To this end, an intuitive and practical approach, based on mathematical rigor, is recommended.

Chapter 1

Elements of Analysis of Reliability and Quality Control

1.1. Introduction

The past few decades have been marked by a particularly intense evolution of the models of probability theory and of the theory of applied statistics. In terms of the reliability of materials and structures, the fields of application studying the future or replacement of traditional coefficients of security are complicating the empirical and economic sides of the laws of calculation. Regarding the approach to fatigue by fracture mechanics, practice in the laboratory and in construction produces a broad range of problems for which the use of probabilistic and statistical methods proves to be fruitful and sometimes even indispensable. The development of probability theory and of applied statistics, the abundance of new results, and unforeseen catastrophes cause us to pay particular attention to security matters, but with an acute technical and economical sense of concern. From this, comes the abounding introduction of reliability analysis methods.

Numerous studies of research have turned toward probability mechanics, which aim to predict the behavior of components and to establish a decision-making support system (expert systems). This text commits itself to using the criteria of fracture mechanics to predict, decipher, analyze, and model the reliability of mechanical components. The reliability of structural components uses an ensemble of mathematical and numerical links, which serve to estimate the probability that a component (structure) will reach a certain state of conventional failure. This is achieved using the probabilistic property of resistant elements of a structure as well as the load that is applied to it.

Contrary to a prescriptive classical approach, risk is estimated while maintaining that however conservative a regulation may be, it cannot be guaranteed to ensure complete safety. On the other hand, it is necessary for the user of reliability techniques to define what they consider the failure of a structure or of a component to entail. If in certain cases that could effectively correspond to the formation of a mechanism of failure, we will define many components and structures as failure criterion, a certain degree of which we will call damage.

The important parameters, which include resistance (R) of structure or stresses (S) applied to it, cannot be defined uniquely in terms of nominal or weighted values, but in terms of random variables characterized by their means, their covariance–variances, and their laws of distribution. The estimation of the reliability of a real structure (components) can generally only be approached using an intermediary of a model that is more or less simplified. The analysis of the model will be carried out with the help of mathematical algorithms, which are often given as approximation techniques where rigorous calculation leads to detrimental calculation times.

To evaluate the weak probabilities of component failure, it is normal to begin with the arbitrary integration of probability densities in the domain of failure, i.e. using simulation techniques. The advantage of this way of going about things resides in the necessity of knowing a form explicit to the domain of failure. The disadvantage is the weakness of the speed of convergence. Added to this is the high cost in calculation time. Numerous distribution laws have been used to model the reliability of components and structures. These distributions have not appeared with reliability but with fundamental research relative to diverse fields of application. We will present a few of these. The principal laws of distribution to model the reliability of the components are:

Table 1.1. Main distributions of probability used in reliability and in quality control

Title	Ordinary by distribution of
Discrete distributions with finite support	Bernoulli, discrete uniform, binomial, hypergeometric (Pascal distribution)
Discrete distributions with countable support	Geometric, Poisson negative binomial, logarithmic
Continuous distributions with compact support	Continuous uniform, triangular, beta
Continuous distributions with semi-infinite support	Exponential, gamma (or Erlang), inverse gamma, Chi square (Pearson, χ^2), Weibull (2 and 3 parameters), Rayleigh, log-normal (Galton), ...

Table of contents

• Cover page
• Contents
• Title page
• Copyright page
• Preface
• Chapter 1: Elements of Analysis of Reliability and Quality Control
• Chapter 2: Estimates, Testing Adjustments, and Testing the Adequacy of Statistical Distributions
• Chapter 3: Modeling Uncertainty
• Glossary
• Index