1
Introduction

"When an engineer, following the safety regulations of the Coast Guard or the Federal Aviation Agency, translates the laws of physics into the specifications of a steamboat boiler or the design of a jet airliner, he is mixing science with a great many other considerations all relating to the purposes to be served. And it is always purposes in the plural - a series of compromises of various considerations, such as speed, safety economy and so on."

Source: D. K Price, The Scientific Estate, 1968

1.1 Reliability Defined

The world demands that the performance of products and systems be improved while at the same time reducing their cost. The requirement to minimize the probability of failures, whether those failures simply increase costs and irritation or gravely threaten the public safety, has placed increased emphasis on reliability and safety. The formal body of knowledge that has been developed for analyzing such failures and minimizing their occurrence cuts across virtually all engineering disciplines, providing the rich variety of contexts in which reliability considerations appear. Indeed, deeper insight into failures and their prevention is to be gained by comparing and contrasting the reliability characteristics of systems of differing characteristics: computers, electromechanical machinery, energy conversion systems, chemical and materials processing plants, and structures, to name a few.

In the broadest sense, reliability is associated with dependability, with successful operation, and with the absence of breakdowns or failures. It is necessary for engineering analysis, however, to define reliability quantitatively as a probability.

Thus, reliability is defined as the probability that a system will perform its intended function for a specified period of time under a given set of conditions. System is used here in a generic sense so that the definition of reliability is also applicable to all varieties of products, subsystems, equipment, components, and parts.

A product or system is said to fail when it ceases to perform its intended function. When there is a total cessation of function - an engine stops running, a structure collapses, a piece of communication equipment goes dead - the system has clearly failed. Often, however, it is necessary to define failure quantitatively in order to take into account the more subtle forms of failure, through deterioration or instability of function. Thus, a motor that is no longer capable of delivering a specified torque, a structure that exceeds a specified deflection, a part that is seriously corroded or eroded (yet still working), or an amplifier that falls below a stipulated gain has failed. Intermittent operation or excessive drift in electronic equipment and the machine tool production of out-of-tolerance parts may also be defined as failures.

The way in which time is specified in the definition of reliability may also vary considerably, depending on the nature of the system under consideration. For example, in an intermittently operated system one must specify whether calendar time or the number of hours of operation is to be used. If the operation is cyclic, such as that of a switch, time is likely to be cast in terms of the number of operations. Some subsystems of the same system (e.g. jet engine) may have different time criteria that drives their failure. If reliability is to be specified in terms of calendar time, it may also be necessary to specify the frequency of starts and stops and the ratio of operating to total time.

In addition to reliability itself, other quantities are used to characterize the reliability of a system. The mean time to failure and failure rate are examples, and in the case of repairable systems, so also are the availability and mean time to repair. The definition of these and other terms will be introduced as needed.

1.2 Performance, Cost, and Reliability

Much of engineering endeavor is concerned with designing and building products for improved performance. We strive for lighter and therefore faster aircraft, for thermodynamically more efficient energy conversion devices, for faster computers, and for larger, longer lasting structures. The pursuit of such objectives, however, often requires designs incorporating features that more often than not may tend to be less reliable than older, lower performance systems, at least initially when the customer receives them. The trade-offs between performance, reliability, and cost are often subtle, involving loading, system complexity, and the employment of new materials and concepts.

Load is most often used in the mechanical sense of the stress on a structure. But here we interpret it more generally so that it also may be the thermal load caused by high temperature, the electrical load on a generator, or even the information load on a telecommunications system. Whatever the nature of the load on a system or its components may be, performance is frequently improved through increased loading. Thus, by increasing the weight of an aircraft, we increase the stress levels in its structure; by going to higher - thermodynamically more efficient - temperatures we are forced to operate materials under conditions in which there are heat-induced losses of strength and more rapid corrosion/erosion. By allowing for ever-increasing flows of information in communications systems, we approach the frequency limits at which switching or other digital circuits may operate.

As the physical limits of systems or their components are approached in order to improve performance, the number of failures increase unless appropriate countermeasures are taken. Thus, specifications for a purer material, tighter dimensional tolerance, and a host of other measures are required to reduce uncertainty in the performance limits and thereby permit one to operate close to those limits without incurring an unacceptable probability of exceeding them (i.e. failure). But in the process of doing so, the cost of the system is likely to increase. Even then, adverse environmental conditions, product deterioration, and manufacturing flaws all lead to higher failure probabilities in systems operating near their limit loads.

System performance may often be increased at the expense of increased complexity, the complexity usually being measured by the number of required components or parts. Once again, reliability will be decreased unless compensating measures are taken, for it may be shown that if nothing else is changed, reliability decreases with each added component. In these situations, reliability can only be maintained if component reliability is increased or if component redundancy is built into the system. But each of these remedies, in turn, must be measured against the incurred costs.

Probably the greatest improvements in performance have come through the introduction of entirely new technologies. For, in contrast to the trade-offs faced with increased loading or complexity, more fundamental advances may have the potential for both improved performance and greater reliability. Certainly, the history of technology is a study of such advances; the replacement of wood by metals in machinery and structures, the replacement of piston with jet aircraft engines, and the replacement of vacuum tubes with solid-state electronics all led to fundamental advances in both performance and reliability while costs were reduced. Any product in which these trade-offs are overcome with increased performance and reliability, without a commensurate cost increase, constitutes a significant technological advance.

With any major advance, however, reliability may be diminished, particularly in the early stages of the introduction of new technology. The engineering community must proceed through a learning experience to reduce the uncertainties in the limits in loading on the new product, to understand its susceptibilities to adverse environments, to predict deterioration with age, and to perfect the procedures for fabrication, manufacture, and construction. Thus, in the transition from wood to iron, the problem of dry rot was eliminated, but failure modes associated with brittle fracture had to be understood. In replacing vacuum tubes with solid-state electronics the ramifications of reliability loss with increasing ambient temperature and vibration had to be appreciated.

Whether in the implementation of new concepts or in the application of existing technologies, the way trade-offs are made between reliability, performance and cost, and the criteria on which they are based is deeply imbedded in the essence of engineering practice, for the considerations and criteria are as varied as the uses to which technology is put. The following examples illustrate this point.

• Consider an air conditioner. What is the worst that can happen if it quits? The customer is warm. So, when developing air conditioners, safety is not paramount, reliability is considered, but cost is "king." Hence, copper tubing for A/C units has given way to aluminum. Plastics for metal wherever possible for weight saving, less testing, and lower confidence levels in the testing are used.
• At the opposite extreme is the design of a commercial airliner, where mechanical breakdown could well result in a catastrophic accident. In this case, reliability is the overriding design consideration; degraded speed, payload, and fuel economy are accepted in order to maintain a very small probability of catastrophic failure. An intermediate example might be in the design...