The median (50^th percentile) active time to restore/repair a system after failu

Question

The median (50^th percentile) active time to restore/repair a system after failure, using specified procedures and resources, is not be more than 4.5 h. The maximum 15 per cent active restore/repair time should not be more than 13.5h (i.e. mean repair time=5.7h). Criticize the statement given and deduce what would be a realistic set of consistent numbers. You should use the following equations related to the log-normal distribution: sigma = [2(ln(t_MART - ln(t_m)]^1/2 and sigma Z_alpha = ln(t_alpha), where t_MART is the mean time to repair, t_m the median time to repair, and t_infinity the 'maximum' time to repair, evaluated at the 1-alpha percentile point on the distribution. Z_alpha the standardized normal deviate found in Appendix 1, and sigma is the standard deviation of the distribution.

Explanation / Answer

since the log normal is positively skewed we can expected mean to be greater than median but in this example we are given an upper bound on mean and median which does not necessarily meanthat the suggested relation between mean and median hold true.

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