Where does probability fails.
Answers
Answer:
The formula for failure rate is: failure rate= 1/MTBF = R/T where R is the number of failures and T is total time. This tells us that the probability that any one particular device will survive to its calculated MTBF is only 36.8%.
Answer:
Step-by-step explanation:
The role and tools of lifetime management of civil concrete structures
H.S. Müller, in Non-Destructive Evaluation of Reinforced Concrete Structures: Deterioration Processes and Standard Test Methods, 2010
6.3.5 Failure probability and limit state function
The failure probability pf is defined as the probability for exceeding a limit state within a defined reference time period. When this occurs an unintentional condition of a considered building component is reached.
The magnitude of the failure probability is closely connected with the interaction of the resistance and the action functions and varies with time, see Fig. 6.3b. This interaction may be described by means of the so-called limit state function Z which is defined according to equation [6.1]:
[6.1]Z=R−S
where the function Z represents the elementary form of a limit state function in which R and S are random variables. If the value of Z turns to zero, the limit state will be reached. The stochastical properties of the function Z can be expressed in the form of a distribution function, if this function is considered to be normally distributed and the resistance R as well as the action S are expressed using related mean values μ and standard deviations σ, see Chapter 4.
By means of the introduction of the so-called reliability index β, a direct correlation between the reliability index β and the failure probability pf is obtained. For a normally distributed limit state function Z, the failure probability pf can be determined directly by