Product Maturity 1

Theoretical Principles and Industrial Applications

Franck Bayle

• Publisher: Wiley-ISTE
• Year: 2022
• Print ISBN:
  9781786307392
• Edition: 1
• eBook ISBN:
  9781119902225
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

Every parent is concerned when a child is slow to become a mature adult. This is also true for any product designer, regardless of their industry sector. For a product to be mature, it must have an expected level of reliability from the moment it is put into service, and must maintain this level throughout its industrial use.

While there have been theoretical and practical advances in reliability from the 1960s to the end of the 1990s, to take into account the effect of maintenance, the maturity of a product is often only partially addressed.

Product Maturity 1 fills this gap as much as possible; a difficult exercise given that maturity is a transverse activity in the engineering sciences; it must be present throughout the lifecycle of a product.

1
Reliability Review

In this book, maturity is defined as the ability of a product to achieve the expected level of reliability from the moment it becomes operational for the end user. A review of what reliability means and a definition of the parameters on which it is based is therefore needed.

1.1. Failure rate

Reliability studies the occurrence of failures in time. These instances of failure are random; hence, they cannot be known in advance. This presents a challenge. To model them, we use the concept of random variable, which will be denoted by T throughout this book.

First, it is important to determine the various types of failures. There are three main categories, namely:

• – “youth failures”, which generally occur very early on in the lifecycle of a product. Youth failures are generally the result of manufacturing defects. Therefore, they concern only a small part of the population. They can be partially eradicated by specific tests, such as burn-in;
• – “catastrophic failures”, which are unexpected, sudden and independent of the time previously elapsed. These types of failures can therefore be observed at any point in the lifecycle of a product. They are generally the result of accidental overloads (heat, mechanical, electrical). They typically do not concern the entire product population and can be reduced by robustness tests, derating rules, etc.;
• – “aging” failures, which are observed across all the products in operation. These failures are generally not observed during the lifecycle of a product, with the exception of specific components with a “limited service life” or premature aging, as a result of poor sizing, a batch of defective components, etc. They affect the entire population and therefore must be absolutely pushed beyond the duration of use of the product. Consequently, design rules (derating rules, worst-case analysis, thermal, mechanical, electrical simulation, etc.), and specific aging tests can be implemented.

We begin by addressing intrinsic reliability. Intrinsic reliability refers to the reliability of a component, a card or a product in the absence of any maintenance. In order to estimate this, and in particular to know the type of failure involved, the most widely used parameter is the (instantaneous) failure rate denoted by λ, which is defined by:

[1.1]

Let us briefly analyze this equation and the following conventions. The term P denotes the “probability” and the symbol “/” stands for “knowing that”. The limit “lim” represents the instantaneous character of the failure rate. Therefore, equation [1.1] can be interpreted as follows:

Probability that the product will fail between “t and t+dt” knowing that it was operational (non-defective) at instant “t”.

To facilitate understanding of the concept of failure rate, the analogy with a human being can be used (Gaudoin and Ledoux 2007). Let us try to estimate the probability that a human being dies between 100 and 101 years of age. This probability is low since the majority of human beings die before they reach 100 years old. Furthermore, let us estimate the probability that a human being dies between 100 and 101 years of age, knowing that they were alive at 100 years old. This probability is high, as human beings do not live long after reaching 100 years of age.

The three failure categories can thus be symbolically represented using the concept of failure rate using the famous bathtub curve, as illustrated in the following figure.

Figure 1.1. Bathtub curve example

The most commonly used mathematical object for modeling failure rate is the Weibull distribution. According to this hypothesis, the latter is defined by:

[1.2]

where η is a scale factor (generally time-dependent) and represents typical service life, characterized by the fact that the failure rate is ~ 63.2% (1 – exp(-1)), irrespective of the value taken by the parameter β and therefore of the type of failure.

This modeling is interesting for the following three reasons:

• – the mathematical formulation is simple, as it involves a versatile power function (differentiable, integrable, etc.);
• – depending on the parameter β, this function is decreasing (β < 1), constant (β = 1) or increasing (β > 1). In other terms, it can represent the three types of previously defined failures;
• – the parameter β has a physical significance as it represents the aging dynamics of the observed failure mechanism. Indeed, as already noted, failure instants are characterized by r...

Table of contents

• Cover
• Table of Contents
• Title Page
• Copyright
• Foreword by Laurent Denis
• Foreword by Serge Zaninotti
• Acknowledgements
• Introduction
• 1 Reliability Review
• 2 Maturity
• 3 Derating Analysis
• 4 Components with Limited Service Life
• 5 Analysis of Product Performances
• 6 Aggravated Tests
• 7 Burn-In Test
• 8 Run-In
• List of Notations
• List of Definitions
• List of Acronyms
• References
• Index
• End User License Agreement