A & A Industrial Products budgets for both scheduled maintenance and unscheduled repair costs for its plants' equipment, mostly large industrial machines. Budgets for scheduled maintenance activities are easy to estimate and are based on the equipment manufacturer's recommendations. The unscheduled repair costs, however, are harder to determine. Historically, A & A has estimated unscheduled maintenance using a formula based on the average number of hours of operation between major equipment failures at a plant. Specifically, plants were given a budget of $65.00 per hour of operation between major failures. This amount came from dividing aggregate historical repair costs by the total number of hours between failures. Then plant averages were used to estimate unscheduled repair cost. For example, if a plant averaged 450 hours of run time before a major repair occurred, the plant was allocated a repair budget of 450 X $65 = $29,250 per repair. If the plant was expected to be in operation 3150 hours per year, the company would anticipate seven unscheduled repairs (3150/450) annually and budget = (7x$29250 or) $204,750 for annual unscheduled repair costs.

Management is becoming more and more convinced this approach is not working. Not only are they upset about the difference between predicted and actual costs of repair, but plant managers believe the model does not account for potential differences among the company's three plants when allocating dollars for unscheduled repairs. The data included in the starter (Excel) file is from 64 randomly selected unscheduled repairs. Use the instructions below to guide your analysis of the data.

repairs cost hours of plant

operation

$ 34,771.52 528 3 $ 20,930.79 419 2 $ 47,934.56 685 1 $ 45,513.51 661 3 $ 44,994.35 644 3 $ 46,024.74 646 3 $ 31,368.16 524 3 $ 35,137.30 534 3 $ 25,865.20 495 3 $ 35,316.75 554 3 $ 44,624.50 641 3 $ 17,676.72 367 2 $ 19,802.38 394 2 $ 5,526.64 190 2 $ 19,227.53 432 2 $ 39,433.56 606 3 $ 35,039.73 547 3 $ 24,962.49 478 2 $ 16,228.46 354 2 $ 35,800.40 568 3 $ 21,298.56 450 2 $ 60,686.70 760 1 $ 48,078.79 674 1 $ 23,190.44 465 2 $ 23,625.64 443 2 $ 36,181.38 548 3 $ 58,862.21 771 1 $ 23,329.88 464 2 $ 45,175.04 640 3 $ 21,941.18 467 2 $ 20,324.06 433 2 $ 40,832.13 607 3 $ 1,507.60 70 2 $ 61,650.91 783 1 $ 30,041.39 506 3 $ 36,458.70 579 3 $ 46,191.67 655 3 $ 47,420.04 662 3 $ 64,142.73 791 1 $ 32,662.09 536 3 $ 40,711.63 589 3 $ 31,347.16 525 3 $ 19,160.13 410 2 $ 14,591.34 325 2 $ 47,684.44 652 3 $ 18,962.25 405 2 $ 39,026.16 587 3 $ 51,414.33 699 1 $ 18,513.72 405 2 $ 16,155.88 360 2 $ 41,027.82 595 3 $ 35,593.64 558 3 $ 32,055.21 520 3 $ 11,697.91 309 2 $ 26,002.04 488 3 $ 11,823.13 291 2 $ 41,093.23 593 3 $ 15,119.35 312 2 $ 49,139.47 683 3 $ 31,062.16 522 3 $ 13,972.69 307 2 $ 43,652.54 644 3 $ 20,567.51 403 2 $ 41,423.70 591 3

Tables and Graphs. At a minimum do the following, embellish at will

1. make frequency distribution table for the repair costs. TIP: Use pivot tables to make the table
   • Start with $1500 and use $10,000 as the class width.
   • Write observation or two about what this summary tells you. What do you find interesting from the information in your table?
2. Make histogram from your frequency distribution. TIP: You can make this from the frequency distribution table in #1 above.
   • Give your histogram a title and label your axes.
   • Comment on the shape.
3. Create frequency distribution table of the hours of operation between failures.
   • Start with a lower class of 50 and a class width of 100.
   • Write observation or two about what this summary tells you. What do you find interesting from the information in your table?
4. Make box and whiskers graphic of the hours of operation.
   • Give your graphic a title
   • Comment on the shape.
   • Are there any outliers? If so, what do you think it/they mean in this scenario?
5. Create frequency distribution and a relative frequency distribution of the plants. TIP: if you use the pivot table feature in Excel, you can easily turn one into the other by using the "value field settings."
6. Create bar graph of the distribution of the plants and interpret what the tables and bar graph of the plants tell you.
7. Find the descriptive statistics (perhaps using the Excel Data Analysis Toolpak) for each of the variables in your data set.
8. • Include the statistics in your report
   • Write paragraph using the means, medians, and standard deviations.
   • Add to your report a consideration for things like
     • You could also report on the minimum and maximum values if you think they add anything to the conversation
     • Does reporting this information for the plant variable make any sense?
9. Report appropriate counts. TIP: Create pivot table with row heading as the plant, and col headings as repair costs grouped like the frequency distribution. (Start with $1500 and use $10,000 as the class width). Grand total counts for table should be your sample size n = 64.
   • Insert the pivot table or count data source(s) into your report
   • Write some of your own observations from this data comparing the plants.
10. Probabilities - answer the questions below, plus anything you think should be included.
    • Using earlier info, what is the probability that the next call for unscheduled repair will be for plant #1?
    • Using earlier info, what is the probability the repair costs will exceed $41,500?
    • Assume the hours between unscheduled repairs follows an exponential distribution. Use the mean value of the hours rounded to the nearest integer as the average number of hours between unscheduled repairs.
      • Using the assumption and earlier info, what is the probability of an unscheduled repair in the next 800 hours of operation.
      • Using the assumption and earlier info, what is the probability of not needing an unscheduled repair in the next 800 hours?