Tektronix 071-0590-00 user manual Inaccuracy 95% = 2 σ / n ≈ 2/ n

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That is, n is within n of the expected count most of the time (68% of the time). If we take the inaccuracy of the measurement to be σ as a fraction of n, then

Inaccuracy68% = σ / n ≈ 1/ n . (7a)

This relationship is plotted in Figure 3 (the curve for 68% confidence).

Inaccuracy
in %
30
		95% Confidence
20
		68% Confidence
10
0	100	1000	10000
10

Number of errors measured n

Figure 3. Inaccuracy error-rate measurement can be expressed as a function of the number of errors measured. A confidence of 68 percent means that if the test is repeated, the measured error rate will be closer to the actual error rate than inaccuracy indicated 68 percent of the time. For 95 percent confidence, the inaccuracy is twice as large.

As an example, suppose it is desired that the accuracy be 0.10, or 10%. Then from Eq. (7a) the test must continue until n = 100. If the time to collect 100 errors turned out to be T = 19 hr, then r' = 100 / 19 hr =

5.26/ hr, and this is within 10% of the actual error rate r. That is, r is inferred to lie between 5.26 – 0.526 = 4.734 / hr and 5.26 + 0.526 = 5.78 / hr (with a confidence of 68%). Because of the statistical nature of the measurement, n = 100 can be more than 10% away from the expected measurement, but 68% of the time it will be less than 10% away.

You can increase your confidence level by using 2σ. The measured n = 100 is within 2σ (or 20% here) of the expected count 95% of the time (see the other curve in Figure 3). In the example of r' = 5.26 / hr, r is inferred to lie between 5.26 – 1.052 = 4.208 / hr and 5.26 + 1.052 = 6.312 / hr with a confidence of 95%. You are more confident the inaccuracy won't be exceeded, but the inaccuracy is twice as large.

To maintain a confidence of 95% (the higher curve in Figure 3) and still have an inaccuracy of 10%, you need to count more errors. If 2σ is to be 10% of n, then σ is 5% of n, or σ / n = 0.05. From Eq.(6) this

gives 1 / n = 0.05, or n = 400. The general expression for the inaccuracy with 95% confidence is

Inaccuracy95% = 2σ / n ≈ 2/ n . (7b)

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