ABSTRACT
Consider a deck of cards numbered consecutively from 1 to 100. Random selection of a card-or the use of a computer-based random number generator in this range-gives an equal probability that any number be selected, whether it be 100 or 1 or any other number, and this probability is 1 in 100 or 1%. Suppose instead that the range, 1 to 100, has units of MPa, and represents the possible 28day compression strengths of concrete samples made to the same specification, with a required characteristic compressive strength of 50 MPa. Then these strengths will vary with a mean that will be, typically, somewhat larger than 50 MPa, possibly, say, 60 MPa; it is not difficult to see why the mean is somewhat higher, for the manufacturer will aim at a higher strength in an attempt to ensure that a sufficient number of the test results (possibly all) lie above the specified value. The distribution is said to be biased, where in this case this bias may be measured by the ratio of mean to characteristic strength. In limit states design, it is necessary to know the probabilistic distribution of these strengths, and of other resistance and load parameters.
