Failure data has been collected from a number of identical components. Assume that five failures have been observed during an accumulated time in service of 978 850 hours. (a) Find an estimate of the failure rate of the components. (b) What does it mean that the estimator used is unbiased? Provide a careful explanation. (c) What is the difference between the upper and the lower percentile of the chi-square distribution? (d) Express the relationship between the upper and the lower percentile (as a formula). (e) Use a table or a computer program to find the relevant percentiles of the chi-square distribution and determine a 90% confidence interval for the failure rate (use Eq. (9.5)). (f ) Carefully explain what is meant by a confidence interval in this situation.
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