You decide to run a test to determine the mean time between failures. During the test, you start with $75$ operational machines on your production line producing widgets. You record breakdowns during a $120-$hour observation period in which three of the machines breke down. One at $40$ hours into the test, one at $50$ hours into the test, and the $3$rd failure comes at $90$ hours.

Use Excel and the data you collected to calculate the MTBF of your machines. Analyze your results and place them on the spreadsheet.

Continue to Step $2$: Calculate the Expected Breakdown Maintenance Costs $...$

Step $2$: Calculate the Expected Breakdown Maintenance Costs

After collecting and analyzing the MTBF data, you were surprised at how often your machines really broke down. At your last company, you remember that they had a service firm that would come in and perform preventive maintenance $($PM$)$ on your machines and you wonder if this would be an option to reduce breakdowns. However, before you go to your boss to pitch the idea, you want to see if using an outside PM firm would reduce your cost.

So you do some research on the cost and run another study on the number of breakdowns of your machines.

Over the last $12$ months, the machines have broken down at the rate indicated in the following table:

Number of Breakdowns

$0$

$1$

$2$

$3$

Number of Months that Breakdowns Occurred

$1$

$7$

$4$

$1$

You also do some research on breakdown cost and find that the average cost of a breakdown to your firm is $$350.$ You find a service firm and request a price quote from them. The PM service firm costs $$200$ per month, but they tell you that you can still expect on average of $2$ breakdowns per month even with the PM service.

Use Excel and the data to calculate the expected breakdown maintenance cost versus hiring the PM firm to service your machines.

Analyze your results and indicate which of the options you will recommend to your boss $-$ hire the firm or continue dealing with the