Bathtub curve

Bathtub curveReliability specialists often describe the lifetime of a population of products using a graphical representation called the bathtub curve

Bathtub curve

three partsThe first part is a decreasing failure rate, known as early failures. The second part is a constant failure rate, known as random failures. The third part is an increasing failure rate, known as wear-out failures. name is derived from the cross-sectional shape

three parts (cont)bathtub curve is generated by mapping the rate of early "infant mortality" failures when first introduced, the rate of random failures with constant failure rate during its "useful life", and finally the rate of "wear out" failures as the product exceeds its design lifetime.

three parts (cont)bathtub curve does not depict the failure rate of a single item, but describes the relative failure rate of an entire population of products over time. Some individual units will fail relatively early (infant mortality failures), others (we hope most) will last until wear-out, and some will fail during the relatively long period typically called normal life. Failures during infant mortality are highly undesirable and are always caused by defects and blunders: material defects, design blunders, errors in assembly, etc.

three parts (cont)Normal life failures are normally considered to be random cases of "stress exceeding strength." However, as we'll see, many failures often considered normal life failures are actually infant mortality failures. Wear-out is a fact of life due to fatigue or depletion of materials (such as lubrication depletion in bearings). A product's useful life is limited by its shortest-lived component. A product manufacturer must assure that all specified materials are adequate to function through the intended product life

Reliability

Reliability requirements Reliability requirements address the system itself, test and assessment requirements, associated tasks and documentation. Reliability requirements are included in the appropriate system/subsystem requirements specifications, test plans, and contract statements.

System reliability parameters Requirements are specified using reliability parameters. The most common reliability parameter is the mean-time-between-failure (MTBF), which can also be specified as the failure rate or the number of failures during a given period. These parameters are very useful for systems that are operated on a regular basis, such as most vehicles, machinery, and electronic equipment. Reliability increases as the MTBF increases. The MTBF is usually specified in hours, but can also be used with other units of measurement such as miles or cycles.

reliability parameters (cont)In other cases, reliability is specified as the probability of mission success. For example, reliability of a scheduled aircraft flight can be specified as a dimensionless probability or a percentage.A special case of mission success is the single-shot device or system. These are devices or systems that remain relatively dormant and only operate once. Examples include automobile airbags, missiles. For such systems, the probability of failure on demand (PFD) is the reliability measure.

reliability parameters (cont)This PFD is derived from failure rate and mission time for non-repairable systems. For repairable systems, it is obtained from failure rate and MTTR and test interval.