Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability describes the ability of a system or component to function under stated conditions for a specified period of time. Reliability is closely related to availability, which is typically described as the ability of a component or system to function at a specified moment or interval of time. The reliability function is theoretically defined as the probability of success at time t, which is denoted R(t). This probability is estimated from detailed (physics of failure) analysis, previous data sets or through reliability testing and reliability modelling. Availability, testability, maintainability and maintenance are often defined as a part of "reliability engineering" in reliability programs. Reliability often plays the key role in the cost-effectiveness of systems. Reliability engineering deals with the prediction, prevention and management of high levels of "lifetime" engineering uncertainty and risks of failure. Although stochastic parameters define and affect reliability, reliability is not only achieved by mathematics and statistics. "Nearly all teaching and literature on the subject emphasize these aspects, and ignore the reality that the ranges of uncertainty involved largely invalidate quantitative methods for prediction and measurement." For example, it is easy to represent "probability of failure" as a symbol or value in an equation, but it is almost impossible to predict its true magnitude in practice, which is massively multivariate, so having the equation for reliability does not begin to equal having an accurate predictive measurement of reliability. Reliability engineering relates closely to Quality Engineering, safety engineering and system safety, in that they use common methods for their analysis and may require input from each other. It can be said that a system must be reliably safe. Reliability engineering focuses on costs of failure caused by system downtime, cost of spares, repair equipment, personnel, and cost of warranty claims. History The word reliability can be traced back to 1816, and is first attested to the poet Samuel Taylor Coleridge. Before World War II the term was linked mostly to repeatability; a test (in any type of science) was considered "reliable" if the same results would be obtained repeatedly. In the 1920s, product improvement through the use of statistical process control was promoted by Dr. Walter A. Shewhart at Bell Labs, around the time that Waloddi Weibull was working on statistical models for fatigue. The development of reliability engineering was