### Introduction

Much of the theory of reliability was developed initially for use in the electronics industry where components often fail with little if any prior warning. In such cases the hazard function or conditional failure rate function is constant and any functioning component or system is taken to be ‘as new’. There are other cases where the conditional failure rate function is time dependent, often proportional to the time that the system or component has been in use. The function may be an increasing function of time (as with random vibrations for example) or decreasing with time (as with concrete whose strength, up to a point, increases with time). If we can develop a lifetime model, we can use it to plan such things as maintenance and part replacement schedules, whole system replacements and reliability testing schedules.

#### Prerequisites

- be familiar with the results and concepts met in the study of probability
- understand and be able to use continuous probability distributions

#### Learning Outcomes

- appreciate the importance of lifetime distributions
- complete reliability calculations for simple systems
- state the relationship between the Weibull distribution and the exponential distribution

#### Contents

1 Reliability1.1 Lifetime distributions

1.2 The exponential distribution

2 System reliability

3 The Weibull distribution

3.1 Mean and variance of the Weibull distribution