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A concept which is closely related to MTBF, and is important in the computations involving MTBF, is the mean down time (MDT). MDT can be defined as mean time which the system is down after the failure. Usually, MDT is considered different from MTTR (Mean Time To Repair); in particular, MDT usually includes organizational and logistical factors ...
Now the formulae do need to know MDTs to calculate MTBFs in general case (and vice versa), but that's a fact of life (the faster you repair parallel components - the less chances are for the whole system to fail, and IMO all the math models which assume that the time is discreet and everything is fixed on the next time slot - are significantly ...
This is useful to estimate the failure rate of a system when individual components or subsystems have already been tested. [18] [19] Adding "redundant" components to eliminate a single point of failure may thus actually increase the failure rate, however reduces the "mission failure" rate, or the "mean time between critical failures" (MTBCF). [20]
In survival analysis, the cumulative distribution function gives the probability that the survival time is less than or equal to a specific time, t. Let T be survival time, which is any positive number. A particular time is designated by the lower case letter t. The cumulative distribution function of T is the function
In a system the mean time between outages (MTBO) is the mean time between equipment failures that result in loss of system continuity or unacceptable degradation.
In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimated.This can be thought of as a generalisation of many classical methods—the method of moments, least squares, and maximum likelihood—as well as some recent methods like M-estimators.
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Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...