ABSTRACT
It is common in applications to ignore the influence of sample size and population size when evaluating confidence lower limit of Mean Time to Failure (MTTF) for products with exponential failure distribution. The conventional method assumes that failure times or lives of different samples are independent identically distributed random variables. This assumption holds reasonably when the population size is much larger than the sample size. However, it will induce substantial inaccuracies when the sample size is not negligible to the population. To this problem, the influence from the sample size to the confidence limit of MTTF is analyzed when the population is determined. First, the conventional method is reviewed. Then, the formulae based on hypergeometric distribution are derived to reflect the relationships among sample size, population size, confidence level and confidence limit. Finally, an example is presented to illustrate the suitability of the proposed method and to show the computation errors from the conventional method.
