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
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 3rd 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 COST
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 breakdowns at the current rate?
Continue to Step 3: Recommend and Submit . . .
**STEP 3: RECOMMEND AND SUBMIT
Submit one spreadsheet containing a tab for each step. Be sure to include a detailed analysis of your results on each of the tabs. Save your assignment using a naming convention that includes your first and last name and the activity number (or description). Do not add punctuation or special characters.
Review the Problems Rubric for detailed grading information.
Calculation for Mean Time Between Failures (MTBF) Transcript
I'd like to take a few minutes and go through the calculations for mean time between failure and the PM versus breakdown. This information is also in your textbook if you need to look at that. But let's go through an example real quick of how to calculate mean time between failure.
In this case, you're going to have your data given. In this case, you're going to have the number of failures as two. Then you're going to have the number of units tested. It's going to be 20 in this example. You're going to run your test over a thousand hours. And at 200 hours, one system is going to fail. And another system is going to fail at 600 hours. So you've got two failures over your thousand hours. To calculate your percentage of failures, you want to take the number of failures and divide by the number of units tested. So it's pretty straightforward and that's going to give you 10% in this example.
Next step is you want to take a look at the number of failures per operating hours. So your total operating time is going to be the test time, times the number of units tested. And that's going to give you 20,000 hours, the non-operating time. It's going to be the test time minus the point that System 1 fails, plus the test time minus the point that System 2 fails. And then to get your number of failures you're in, you're going to take the number of failures, which is 2 divided by the total time minus the non-operating time. And that's going to give you your N.
Then to calculate your mean time between failures, you're just going to take your N. And you're going to divide that, you're going to divide 1 by the N itself. And that's going to give you a mean time between failures of 9,400 hours. So that's pretty straightforward. For the breakdown operation, breakdown versus preventive maintenance, let's take this example here where we have an observation time of 12 months. If you have a breakdown, it's going to cost the company about $400 in loss productivity. If you hire a preventive maintenance company, it's going to be, it's going to cost you $200 a month. But with that, the preventive maintenance company is saying you can still expect about one breakdown per month. And again, this data will all be given to you or you'll be able to collect this data in the situation.
And then you're going to look at the number of breakdowns per month. So zero breakdowns, you had two machines that did not. In Month 2, you had six. And number of breakdowns two, you had four breakdowns that occurred. So your first step then, you're taking the, again, this data is given. So the first step is to calculate your frequency. So your frequencies for zero breakdowns, you're taking the observation time or actually you're taking the number of months that break down occurred in this case. Two divided by the observation time, which is going to give you 0.167 and you'll do the same for the next. You'll take the, you take the, the six, which the number of breakdowns are the number of months in breakdown divided by the total month. And you do the same thing for the next field.
And then to get your overall calculation, you have to take the number of breakdowns and multiply those by the frequency and then add each of those together. So in this case, we're going to take the 0 times 0.167 and then we're going to add that to 1 times 0.5 and then add that to 2 times 0.333. And that's going to give you an average breakdown of 1.16 per month.
So from there, it's pretty straightforward. To get your expected breakdown cost, you take your total breakdown cost and you multiply that by the breakdowns, expected breakdowns per month. And to get the preventive maintenance costs, it's much easier. You just need to take the preventive maintenance costs, multiply by the number of breakdowns and then add your breakdown cost.
So I hope this will help you as you work through the problem, but make sure that you go through the book also and look at those examples.
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