Practical Reliability Engineering, 5th Edition

2

Reliability Mathematics

2.1 Introduction

The methods used to quantify reliability are the mathematics of probability and statistics. In reliability work we are dealing with uncertainty. As an example, data may show that a certain type of power supply fails at a constant average rate of once per 10⁷ h. If we build 1000 such units, and we operate them for 100 h, we cannot say with certainty whether any will fail in that time. We can, however, make a statement about the probability of failure. We can go further and state that, within specified statistical confidence limits, the probability of failure lies between certain values above and below this probability. If a sample of such equipment is tested, we obtain data which are called statistics.

Reliability statistics can be broadly divided into the treatment of discrete functions, continuous functions and point processes. For example, a switch may either work or not work when selected or a pressure vessel may pass or fail a test—these situations are described by discrete functions. In reliability we are often concerned with two-state discrete systems, since equipment is in either an operational or a failed state. Continuous functions describe those situations which are governed by a continuous variable, such as time or distance travelled. The electronic equipment mentioned above would have a reliability function in this class. The distinction between discrete and continuous functions is one of how the problem is treated, and not ...