BS 6000-3:2005 pdf download.Guide to the selection and usage of acceptance samplingsystems for inspection of discrete items inlots —— Part 3:Guide to sampling by variables.
When data originate from a normal distribution, departures of the probability plot from linearity are duesolely to sampling fluctuations. Conversely, data from other types of distribution will tend to show
departures from linearity of a characteristic type, helping in the determination of the family ofdistributions to which the data belong.Knowledge of this family can indicate the appropriatetransformation to make to the data in order to bring these closer to normality.
Figure 4a) to Figure 8b) show the density functions and examples of normal probability plots based on asample of size 100 for, respectively, a lognormal "square-root-normal" , Cauehy, Laplace and exponentialdistribution. (For brevity, the distribution for which the square root of the variable has a normal
distribution is referred to as the “square-root-normal”distribution.)On some of the normal probabilityplots, a straight line has been drawn through the data points to aid the eye in identifying the characteristicdifferences.For the lognormal distribution, there is a pronounced downward concavity.The normal
probability plot of the square-root-normal distribution is similar to that of the lognormal distribution,except that the concavity is less pronounced. This is only to be expected, as both distributions can be
transformed to normality with the Box-Cox transformation (see 3.3.4), but the value of Box-Cox parameter入=0 for the lognormal distribution is twice as far away from the nullvalue 入= 1 as the value入= %/ requiredfor the square-root-normal distribution.
The Cauchy distribution is almost indistinguishable from the normal distribution towards its centre, butthe extra thickness of its tails results in the plot being relatively high for low values of x and relatively lowfor high values of x, the extremities of the plot being almost horizontal.The Laplace distribution is similar,except that there is a shorter region in the normal probability plot where the distribution is
indistinguishable from the normal distribution, and the extremities of the plot are far from horizontal.Theexponential distribution has a very characteristic shape, rising very steeply at the left and becoming almosthorizontal towards the right.
