A manager wants to determine an appropriate learning percentage for processing insurance claims for storm damage. Toward that end, times have been recorded for completion of each of the first six repetitions. Repetition 1 2 3 4 5 6 Time (minutes) 50 46 43 38 37 34 Use the following table for calculation. Learning curve coefficients 70% 75% 80% 85% 90% Unit Number Unit Time Total Time Unit Time Total Time Unit Time Total Time Unit Time Total Time Unit Time Total Time 1 1.000 1.000 1.000 1.000 0.000 1.000 1.000 1.000 1.000 1.000 2 0.700 1.700 0.750 1.750 0.800 1.800 0.850 1.850 0.900 1.900 3 0.568 2.268 0.634 2.384 0.702 2.502 0.773 2.623 0.846 2.746 4 0.490 2.758 0.562 2.946 0.640 3.142 0.723 3.345 0.810 3.556 5 0.437 3.195 0.513 3.459 0.596 3.738 0.686 4.031 0.783 4.339 6 0.398 3.593 0.475 3.934 0.562 4.299 0.657 4.688 0.762 5.101 7 0.367 3.960 0.446 4.380 0.534 4.834 0.634 5.322 0.744 5.845 8 0.343 4.303 0.422 4.802 0.512 5.346 0.614 5.936 0.729 6.574 9 0.323 4.626 0.402 5.204 0.493 5.839 0.597 6.533 0.716 7.290 10 0.306 4.932 0.385 5.589 0.477 6.315 0.583 7.116 0.705 7.994 11 0.291 5.223 0.370 5.958 0.462 6.777 0.570 7.686 0.695 8.689 12 0.278 5.501 0.357 6.315 0.449 7.227 0.558 8.244 0.685 9.374 13 0.267 5.769 0.345 6.660 0.438 7.665 0.548 8.792 0.677 10.052 14 0.257 6.026 0.334 6.994 0.428 8.092 0.539 9.331 0.670 10.721 15 0.248 6.274 0.325 7.319 0.418 8.511 0.530 9.861 0.663 11.384 16 0.240 6.514 0.316 7.635 0.410 8.920 0.522 10.383 0.656 12.040 17 0.233 6.747 0.309 7.944 0.402 9.322 0.515 10.898 0.650 12.690 18 0.226 6.973 0.301 8.245 0.394 9.716 0.508 11.405 0.644 13.334 19 0.220 7.192 0.295 8.540 0.388 10.104 0.501 11.907 0.639 13.974 20 0.214 7.407 0.288 8.828 0.381 10.485 0.495 12.402 0.634 14.608 21 0.209 7.615 0.283 9.111 0.375 10.860 0.490 12.892 0.630 15.237 22 0.204 7.819 0.277 9.388 0.370 11.230 0.484 13.376 0.625 15.862 23 0.199 8.018 0.272 9.660 0.364 11.594 0.479 13.856 0.621 16.483 24 0.195 8.213 0.267 9.928 0.359 11.954 0.475 14.331 0.617 17.100 25 0.191 8.404 0.263 10.191 0.355 12.309 0.470 14.801 0.613 17.713 26 0.187 8.591 0.259 10.449 0.350 12.659 0.466 15.267 0.609 18.323 27 0.183 8.774 0.255 10.704 0.346 13.005 0.462 15.728 0.606 18.929 28 0.180 8.954 0.251 10.955 0.342 13.347 0.458 16.186 0.603 19.531 29 0.177 9.131 0.247 11.202 0.338 13.685 0.454 16.640 0.599 20.131 30 0.174 9.305 0.244 11.446 0.335 14.020 0.450 17.091 0.596 20.727 a. Determine the approximate learning percentage. Hint: Compute this by averaging the various learning rate estimates available using the 'doubling' concept for all possible unit time ratios (e.g., T2/T1, T4/T2, etc.) (Do not round intermediate calculations. Round your answer to the nearest 5 percent.) b. Using your rounded answer from part a, estimate the average completion time per repetition, assuming a total of 30 repetitions are planned. (Round your answer to 3 decimal places.)
A manager wants to determine an appropriate learning percentage for processing insurance claims for storm damage. Toward that end, times have been recorded for completion of each of the first six repetitions.
Repetition | 1 | 2 | 3 | 4 | 5 | 6 |
Time (minutes) | 50 | 46 | 43 | 38 | 37 | 34 |
Use the following table for calculation.
Learning curve coefficients
70% | 75% | 80% | 85% | 90% | ||||||||||||||||
Unit Number |
Unit Time |
Total Time |
Unit Time |
Total Time |
Unit Time |
Total Time |
Unit Time |
Total Time |
Unit Time |
Total Time |
||||||||||
1 | 1.000 | 1.000 | 1.000 | 1.000 | 0.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | ||||||||||
2 | 0.700 | 1.700 | 0.750 | 1.750 | 0.800 | 1.800 | 0.850 | 1.850 | 0.900 | 1.900 | ||||||||||
3 | 0.568 | 2.268 | 0.634 | 2.384 | 0.702 | 2.502 | 0.773 | 2.623 | 0.846 | 2.746 | ||||||||||
4 | 0.490 | 2.758 | 0.562 | 2.946 | 0.640 | 3.142 | 0.723 | 3.345 | 0.810 | 3.556 | ||||||||||
5 | 0.437 | 3.195 | 0.513 | 3.459 | 0.596 | 3.738 | 0.686 | 4.031 | 0.783 | 4.339 | ||||||||||
6 | 0.398 | 3.593 | 0.475 | 3.934 | 0.562 | 4.299 | 0.657 | 4.688 | 0.762 | 5.101 | ||||||||||
7 | 0.367 | 3.960 | 0.446 | 4.380 | 0.534 | 4.834 | 0.634 | 5.322 | 0.744 | 5.845 | ||||||||||
8 | 0.343 | 4.303 | 0.422 | 4.802 | 0.512 | 5.346 | 0.614 | 5.936 | 0.729 | 6.574 | ||||||||||
9 | 0.323 | 4.626 | 0.402 | 5.204 | 0.493 | 5.839 | 0.597 | 6.533 | 0.716 | 7.290 | ||||||||||
10 | 0.306 | 4.932 | 0.385 | 5.589 | 0.477 | 6.315 | 0.583 | 7.116 | 0.705 | 7.994 | ||||||||||
11 | 0.291 | 5.223 | 0.370 | 5.958 | 0.462 | 6.777 | 0.570 | 7.686 | 0.695 | 8.689 | ||||||||||
12 | 0.278 | 5.501 | 0.357 | 6.315 | 0.449 | 7.227 | 0.558 | 8.244 | 0.685 | 9.374 | ||||||||||
13 | 0.267 | 5.769 | 0.345 | 6.660 | 0.438 | 7.665 | 0.548 | 8.792 | 0.677 | 10.052 | ||||||||||
14 | 0.257 | 6.026 | 0.334 | 6.994 | 0.428 | 8.092 | 0.539 | 9.331 | 0.670 | 10.721 | ||||||||||
15 | 0.248 | 6.274 | 0.325 | 7.319 | 0.418 | 8.511 | 0.530 | 9.861 | 0.663 | 11.384 | ||||||||||
16 | 0.240 | 6.514 | 0.316 | 7.635 | 0.410 | 8.920 | 0.522 | 10.383 | 0.656 | 12.040 | ||||||||||
17 | 0.233 | 6.747 | 0.309 | 7.944 | 0.402 | 9.322 | 0.515 | 10.898 | 0.650 | 12.690 | ||||||||||
18 | 0.226 | 6.973 | 0.301 | 8.245 | 0.394 | 9.716 | 0.508 | 11.405 | 0.644 | 13.334 | ||||||||||
19 | 0.220 | 7.192 | 0.295 | 8.540 | 0.388 | 10.104 | 0.501 | 11.907 | 0.639 | 13.974 | ||||||||||
20 | 0.214 | 7.407 | 0.288 | 8.828 | 0.381 | 10.485 | 0.495 | 12.402 | 0.634 | 14.608 | ||||||||||
21 | 0.209 | 7.615 | 0.283 | 9.111 | 0.375 | 10.860 | 0.490 | 12.892 | 0.630 | 15.237 | ||||||||||
22 | 0.204 | 7.819 | 0.277 | 9.388 | 0.370 | 11.230 | 0.484 | 13.376 | 0.625 | 15.862 | ||||||||||
23 | 0.199 | 8.018 | 0.272 | 9.660 | 0.364 | 11.594 | 0.479 | 13.856 | 0.621 | 16.483 | ||||||||||
24 | 0.195 | 8.213 | 0.267 | 9.928 | 0.359 | 11.954 | 0.475 | 14.331 | 0.617 | 17.100 | ||||||||||
25 | 0.191 | 8.404 | 0.263 | 10.191 | 0.355 | 12.309 | 0.470 | 14.801 | 0.613 | 17.713 | ||||||||||
26 | 0.187 | 8.591 | 0.259 | 10.449 | 0.350 | 12.659 | 0.466 | 15.267 | 0.609 | 18.323 | ||||||||||
27 | 0.183 | 8.774 | 0.255 | 10.704 | 0.346 | 13.005 | 0.462 | 15.728 | 0.606 | 18.929 | ||||||||||
28 | 0.180 | 8.954 | 0.251 | 10.955 | 0.342 | 13.347 | 0.458 | 16.186 | 0.603 | 19.531 | ||||||||||
29 | 0.177 | 9.131 | 0.247 | 11.202 | 0.338 | 13.685 | 0.454 | 16.640 | 0.599 | 20.131 | ||||||||||
30 | 0.174 | 9.305 | 0.244 | 11.446 | 0.335 | 14.020 | 0.450 | 17.091 | 0.596 | 20.727 | ||||||||||
a. Determine the approximate learning percentage. Hint: Compute this by averaging the various learning rate estimates available using the 'doubling' concept for all possible unit time ratios (e.g., T2/T1, T4/T2, etc.) (Do not round intermediate calculations. Round your answer to the nearest 5 percent.)
b. Using your rounded answer from part a, estimate the average completion time per repetition, assuming a total of 30 repetitions are planned. (Round your answer to 3 decimal places.)
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