A loader has the following breakdown data,

Breakdown # Breakdown time Repair Starts Repair Ends

$1359383406$

$2883913970$

$3176917971830$

$4260926332686$

$5293929503000$

$6331433283348$

Calculate the following:

a$.$ Mean time to repair

b$.$ Mean time to Failure Method $($assuming an unrepairable system$)$

c$.$ Uptime Method

d$.$ What is the failure rate of loader as defined by MTBF method?

e$.$ Based on the data only, what is the reliability, i$.$e$.$ the probability that the machine does not breakdown within $150$ hours

f$.$ Based on the data only, what number would you use if you are trying to determine how long the machine would work without breaking down with a probability of $90\%$

g$.$ Assuming an exponential distribution and that the MTBF calculated above is the correct number, what would be the result of part f above

h$.$ Assuming that the MTBF follows a standard normal distribution, and that the MTBF calculated from the data above is the correct number what would be the result of part f above

i$.$ If the machine annual cost to own, operate and maintain is $40,000$ USD per year and under full working time conditions the machine works $1800$ hr per year