 0.383 0.375 Therefore Equation 1.44 can be re-written as in Equation 1.46. (1.46) The shape of the Weibull curve varies depending on the value of its factors. B is the most important, as shown in Figure 1.10, and the As an example suppose that a sample of 100 items, selected at Weibull curve varies from an exponential (B = 1.0) to a normal random from a much larger population, gives their mean weight as distribution (B = 3.5). In practice 6 varies from about 1 11 3 to 5. Because 20kg with a standard deviation of 100g. The standard error of the mean is therefore 100/(100)1/2 = 10g and one can say with 99.73% the Weibull distribution can be made to fit a variety of different sets confidence that the mean value of the population lies between 20 of data, it is popularly used for probability distributions. I 3 X 0.01 or 20.03kg and 19.97kg. If in a sample of items the probability of occurrence of a particular attribute is Ps' then the standard error of probability Pc is defined as in Equation 1.47, where q=1-ps (1.47) The probability of occurrence of the attribute in the population is then given by Equation 1.48, where Y is again chosen to cover a certain confidence level. Event (1.48) Figure 1.10 Weibull curves (a=1) As an example suppose a sample of 500 items shows that 50 are defective. Then the probability of occurrence of the defect in the sample is 50/500=0.1.The standard error of probability is (0.1 x 0.9/500) 1/2 or 0.0134. Therefore one can state with 95.46% con- Analytical calculations using the Weibull distribution are cumber- fidence that the population from which the sample was drawn has a some. Usually predictions are made using Weibull probability defect probability of 0.1 + x 0.0134, i.e. 0.0732 to 0.1268; or one paper. The data are plotted on this paper and the probability predic- can state with 99.73% confidence that this value will lie between 0.1 tions read from the graph. +3 x 0.0134, i.e. 0.0598 to 0.1402. If two samples have been taken from the same population and 1.10 Sampling these and nsm gi