Probability of detection



Dear all,

I am doing a research and a part of this research is a little bit of statistics. Can anyone check if my calculation is correct? Thanks in advance!

The inspector needs to fill in the object number five times in the current report.
Let’s assume that the probability that the inspector fills in the object number each time correctly is 95%.
This means that after five times the probability to fill all of the object numbers correctly decreases to 77 % (Equation 1).

0,95 x 0,95 x 0,95 x 0,95 x 0,95 x 100% = 77% Equation 1

The second report requires from the inspector that the object number gets filled in once, because the information shall be
repeated automatically throughout the report. This means that the probability of accuracy stays at 95 %.

Based on these numbers, the current report has 92 errors after 400 reports and the automatic report 20 errors.
As previously mentioned in phase three of the primary process (Figure ***), there is a quality check after the
inspector completed the report. Let’s assume that this person detects 95 % of all errors. The probability of
detection decreases to 77 % for the current report (Equation 1) and for the automatic report it stays at 95 %.

The amount of errors that will go undetected to the customer is:

Current report: 20 wrong object numbers based on 400 reports are sent to the client.
Automatic report: one wrong object number based on 400 reports is sent to the client.