Product descriptions and specifications frequently require that a product have a minimum specified reliability. Reliability has both qualitative or descriptive aspects, the ability of the product to perform its intended function, and quantitative aspects, as a measure of the probability of success.
The probability of success is measured in one of two ways:
attributes, success or failure: the probability of a success on a single usage or trial; for example, the opening or closing of a switch.
time-to-failure analysis, the probability that the product will perform its intended function for a specified period of time such as, for example, a warranty period for an automobile.
If we assume that components succeed or fail independently, the reliability of a system is the product of the reliabilities of the components. If there is a standby component, the probability that the standby will be successfully employed is the product of the probability that the main component fails and the probability that the standby component works.
For time-to-failure components or systems, the failure rate tends to follow the bathtub curve: a high but declining failure rate when the product is new, constant failure rate during the normal service period, followed by increasing failure rate, or wear out. The following diagram is typical:
The central period of constant failure rate is characterized by the exponential distribution; it represents the majority of the service lifetime of the product. Manufacturers try to reduce or eliminate the defects that cause early failures through quality assurance activities and employee motivation, in order to increase customer satisfaction and reduce complaints or the possibility of lawsuits. The wear out period is the time that one might expect the customer to strongly consider purchasing a replacement, because of the difficulty in getting satisfactory service. Warranties usually cover early failures and the beginning of non-normal service life, but not wear out.
The interpretation of the reliability-MTBF relationship is that during the normal service-life period, if T is a specified lifetime, such as a warranty period, the reliability R is R = e(-T/MTBF) where e = 2.71828 is the base of natural (Naperian) logarithms, and T is frequently called the “mission time” of the system.
