BS 6000-3:2005 pdf download

BS 6000-3:2005 pdf download.Guide to the selection and usage of acceptance sampling systems for inspection of discrete items in lots ——Part 3: Guide to sampling by variables.
When data originate from a normal distribution. departures of the probability plot from linearity are due solely 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 of distributions to which the data belong. Knowledge of this family can indicate the appropriate transformation to make to the data in order to bring these closer to normality.
Figure 4a) to Figure $b) show the density functions and examples of normal probability plots based on a sample of size 100 for. respectively. a lognormal, square-root.normar, Cauchy. Laplace and exponential distribution. (For brevity, the distribution for which the square root of the variable has a normal distribution is referred to as the “squure.root.normar distribution.) On some of the normal probability plots, a straight line has been drawn through the data points to aid the eye m identifying the characteristic differences, 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 Icas pronounced. This is only to be expected. as both distributions can be transformed to normality with the Bnx.Cox transformation (see 3.3.4k, but the value of Box-Cox parameter A = 0 for the lognormal distribution is twice as far away from the null value A = I as the value A = required for the square.root.norrnal distribution
The Cauchy distribution is almost indistinguishable from the normal distribution towards its centre, but the extra thickness of its tails results in the plot being relatively high for low values nix and relatively low for 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. The exponential distribution has a very characteristic shape, rising very steeply at the left and becoming almost horizontal towards the right.
These are a email selection frcim the many possible (listributiOns from which (tat-a might have arisen. In some cases. e.g. the lognormal and the equare.root-normal distributions, the distribution can be transformed to normality without knowing its parameters (see 3.3.2 and 3.3.3). In other cases. acceptance sampling by variables might not be possible without a method tailored to that family of distributions. If such a method does not exist, acceptance sampling by attributes might have to be used instead, the loss in efficiency being more than compensated for by the increase in integrity of the acceptance sampling results
Figure 4a) to Figure Sb) show normal probability plots for samples of size 100. Often there is not the luxury of such large samples. With small samples, it is less clear whether the departures from linearity of the normal probability plot are due to non.normality or merely to sampling fluctuations. In case of doubt. subjective assessment of departure from normality should be replaced by objective statistical tests, such as those given below.
Further information on tests for departure from normality is given in HS 2546.7 and uS 2546.4:1976, Section 2.
3.2.2 Statistical tests for departure from normality
3.2.2.1 Directional t’crsus omnibus tests
Statistical tests are used to determine the degree to which the available evidence supports a given null hypothesis, say H. The power of the test is the probability of rejecting the hypothesis 1111 in favour of the alternative hypothesis H1 when the alternative hypothesis is true.
When testing for departures from normality, the null hypothesis lI is that the distribution is normal while the alternative hypothesis H1 is that it is not normal, lithe alternative hypothesis is more specific, stating the alternative family of distributions to which the distribution belongs, then the test is said to be directional. Otherwise, it is said to be an omnibus test.