Appendix A Algorithms
274
In counting statistics, one commonly uses a k factor to describe the desired
confidence level (probability).
By substituting a given k factor value for
Equation 15 on page 273 for one-tailed
distribution and in Equation 12 on page page 272 for two-tailed distribution, one can
compute the onfidence levels. For example for a k-factor value of 1.96 the confidence
level is 95% for “two-tailed” distribution. A confidence level of 95% means that that
for every 100 trials, the ratio of successful trials with respect to the total number of
trials should be 95:100.
The values of k-factor for both “one-tailed” and “two-tailed” distribution functions
with the corresponding confidence levels in percent are shown in the Table 18.
Table 18 Comparison table indicating
1-tailed and 2-tailed k-factor values
for different confidence levels
Confidence Level
(%)
k-factor
1 Tailed 2 Tailed
50 0 0.675
60 0.254 0.842
70 0.525 1.037
75 0.675 1.151
85 1.037 1.440
90 1.282 1.645
95 1.645 1.960
96 1.751 2.054
97 1.881 2.170
99 2.325 2.575
Note that k-factor for 95% confidence level for one-tailed distribution and k-factor
for 90% confidence level for two-tailed distribution has the same value of 1.645.
The monitor software uses a two-tailed distribution function since this more
accurately reflects actual operating conditions.
The confidence level for radiation contamination is set in the Common Setup and/or
Individual Detectors screens and defines the release limit level. Any increase in
contamination above the release limit results in rapid improvement in the confidence
level and quickly approaches a probability of 1.
K Alpha - False Alarm Due to Background Rate
The k factors for both the background interval and the probability of not missing a
true alarm are calculated on an individual detector basis. The probability of not false
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