Annual Report for 2010/11 and Forward Programme - Sellafield Ltd

SSEM/2011/4730 June 2011Log Pu239 Activity Histogram12108Frequency6420Figure 3.18. 239 Pu Activity Histogram.3.00E+003.10E+003.20E+003.30E+003.40E+003.50E+003.60E+003.70E+003.80E+003.90E+004.00E+004.10E+004.20E+004.30E+004.40E+004.50E+004.60E+004.70E+004.80E+004.90E+005.00E+005.10E+005.20E+005.30E+005.40E+005.50E+005.60E+005.70E+005.80E+005.90E+006.00E+00Log to base 10 of Pu239 ActivityLog Pu238 Activity Histogram141210Frequency864203.00E+003.10E+003.20E+003.30E+003.40E+003.50E+003.60E+003.70E+003.80E+003.90E+004.00E+004.10E+004.20E+00Figure 3.19. 238 Pu Activity Histogram.4.30E+004.40E+004.50E+004.60E+004.70E+004.80E+004.90E+00Log to base 10 of Pu238 Activity5.00E+005.10E+005.20E+005.30E+005.40E+005.50E+005.60E+005.70E+005.80E+005.90E+006.00E+00To more accurately assess if 241 Am activity in alpha-rich particles is log normally distributed astatistical probability plot (Figure 3.20) can be used. This type of plot displays the log activityplotted against the cumulative find percentage and shows the fit across the whole of thedistribution with the median activity being at the 50% point. Finds that follow the fitteddistribution (i.e. the central blue line) would represent a perfect fit and finds within the outerblues lines are within the 95% confidence interval. A curve in the tail indicates a skeweddistribution and a point far away from the line an outlier. The probability plot also gives theAnderson-Darling statistic (AD), which is a powerful statistical measure of normality. For thelog normal hypothesis to be rejected the p value must be less than or equal to the chosenstatistical alpha-level (i.e. for hypothesis testing an alpha-level of 0.1 corresponding to a 10%chance of rejecting the log normal hypothesis when it is true). A probability value greaterthan 0.1 would support the hypothesis that the 241 Am activity in alpha-rich finds is log normaldistributed. Note that for comparison, fitting the same data to a normal distribution (plot notshown) gives p < 0.05. In this case, if the null hypothesis was that the 241 Am activity in alpharichfinds was normally distributed it would be rejected in favour of the alternative hypothesisthat it is not normally distributed.© Nuclear Decommissioning Authority 2011. 44