Category: Theory and definitions
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Random failure is exponential reliability decay
When something decays or grows “exponentially” it means that it changes regularly by a constant factor. An example of exponential growth is the principle in a compound interest bank account which increases at regular intervals by a constant factor. Assume that you drive your car normally. You replace tires whenever the tread depth falls below the manufacturer’s safety…
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Conditional failure probability, reliability, and failure rate
What is the relationship between the conditional failure probability H(t), the reliability R(t), the density function f(t), and the failure rate h(t)? In the article Conditional probability of failure we showed that the conditional failure probability H(t) is: X is the failure time. By definition the denominator is the survival or reliability function at time t, i.e. P(X>t)…
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Conditional probability of failure
The most powerful information sought by all maintenance engineers and managers boils down to the conditional failure probability. It is the probability of an item failing in an upcoming period of interest knowing that it is currently in an unfailed state. If you knew that the conditional probability of failure of a given part or component were unusually high…
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MTTF is the area under the reliability curve
The reliability curve, also known as the survival graph eventually approaches 0 as time goes to infinity. How do we show that the area below the reliability curve is equal to the mean time to failure (MTTF) or average life of the item? We would like to show that the expected or average life of an…
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Random failure and the MTTF
Nowlan and Heap said that the (conditional) probability of occurrence of most failure modes is constant throughout the life of a component. They described this behavior as being that of “random” failure. What is the Mean Time to Failure (MTTF) of a randomly failing part? In cases of random failure the formula for a component’s reliability (survival) over…