As you have learned from your reading, knowing when a part or system will fail is important for a company. Mean time between failures

$($MTBF$)$ is the expected time between failures of a part, process, or system and is a common matrix for a firm to use to understand how

often a failure will occur.

Assume that you are the manager of a production line and are responsible for keeping the machines running $24$ hours per day, $365$ days per

year. When a machine breaks, it must be repaired and put back onto operation as soon as possible. The problem is that your machines are

always breaking down, and you really do not have a good understanding of how often a machine breaks down.

Hint: For this assignment, you will NOT be using the OM software but should use Excel to work the problem.

Step $1$: Calculate the MTBF

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 broke

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:

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

breakdowns at the current rate?