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In order for the final HEP calculation to be valid, the following assumptions are required to be fulfilled: There exists a seismic event initiator that leads to the establishment of air-based ventilation on the ITP processing tanks 48 and 49, possibly 50 in some cases.
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 ...
It is remarkable that the sum of squares of the residuals and the sample mean can be shown to be independent of each other, using, e.g. Basu's theorem.That fact, and the normal and chi-squared distributions given above form the basis of calculations involving the t-statistic:
when the probability distribution is unknown, Chebyshev's or the Vysochanskiï–Petunin inequalities can be used to calculate a conservative confidence interval; and as the sample size tends to infinity the central limit theorem guarantees that the sampling distribution of the mean is asymptotically normal .
A reliability engineer has the task of assessing the probability of a plant operator failing to carry out the task of isolating a plant bypass route as required by procedure.