The estimate of the mean time between failures, 
, obtained from tests is the expected, or the average value, or the mean life for that sample. Two or more samples from the same designated production line, tested under identical conditions, will give data from which different estimates of m, the true mean life, will be obtained. If it is claimed that the first estimate is the m of this equipment and we are asked to conduct another such test, we would be much embarrassed if it yields an m which turns out to be lower than that of the first estimate. To minimize the probability of being so embarrassed we utilize the concept of confidence level, such that the probability of our being proven wrong, or the risk ?, that the second 
turns out to be lower than the first, in the long run, is kept at a prechosen low level. The confidence level is designated by CL = 1 - ?, and the risk level by ?.
Confidence level is equal to the proportion of the samples (from whose test results their individual 
are calculated) whose confidence limits contain the true m.
This is illustrated in Fig. 7.1, where the lower, two-sided confidence limit on m, m L 2, and the upper, two-sided confidence limit on m, m U 2, for each sample is plotted, as well as the true MTBF
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