Question

An entrepreneur plans to sell 10,000 anti-gravity shoes at a price of $s per pair. It costs $m to manufacture a pair. [$s and $m are specified for each team.]

She promises the customers that any failed pair will be replaced (only once) by a brand new pair within the warranty period. The entrepreneur needs to determine the warranty period that will ensure at least a 20% profit (calculate profit based on total expenses).

You are asked to determine the maximum warranty period, in whole months, that she could afford to offer. A series of tests of 19 pairs (sampling) to estimate the Time-Of-Failure (TOF, in months) yields the data given in the attached document: ‘shoesDATA’. The “red entries” in the data indicate aborted tests, meaning the tests were stopped before failure occurred.

a) Using mean-ranking method fit the data to (usage of 'canned' programs for fitting distribution will be penalized) i) normal pdf ii) log-normal pdf

b) Determine in each of the cases in (a) its mean, mode, and median.

c) For each pdf, i. determine the warranty period. ii. What is your 80% confidence interval for the mean values? iii. Compare your warranty period to the corresponding mean time to fail (MTTF), ie., by what fraction of the std is your warranty period higher or lower than the MTTF. iv. If she makes the warranty to be the MTTF, what would your percentage of profit/loss would be? What if she offers a warranty for { +   = 0.5, 1, 1.5}?

d) Discuss, if and why anyone particular pdf is more suitable in your case.

Answer 1