Problem 07 – 30
National Partamiento Co.
Months
in
Service
Number
Installed
Number
Failed
Number Not
Failed
Cumulative
Failures
Month x
Failures
Months in
Service
Monthly Failure Rate
1 24440 1 24439 1 1 1 0.00004092 0.00004092 Regression on number of units failed by month
2 24439 3 24436 4 6 2 0.00012275 0.00016367
10 24331 30 24301 139 300 10 0.00123299 0.00570133 Standard Error 1.828835338
11 24301 31 24270 170 341 11 0.00127567 0.00697700 Observations 12
12 24270 29 24241 199 348 12 0.00119489 0.00817189
Totals 199 1708 Totals ANOVA
df SS MS F Significance F
Regression 1 1201.47028 1201.47028 359.2227411 3.62759E-09
Average failure rate (lambda) = 0.000680109 Residual 10 33.44638695 3.344638695
Total 11 1234.916667
Months
in
Service
Number
Installed
Number
Failed
Number Not
Failed
Cumulative
Failures
Monthly
Failure Rate
27 23482 76 23406 1034 0.00323652 6 15.13403263 -1.134032634
28 23406 79 23327 1113 0.00337520 7 18.03263403 1.967365967
29 23327 82 23245 1195 0.00351524 8 20.93123543 0.068764569
30 23245 85 23160 1280 0.00365670 9 23.82983683 -0.82983683
31 23160 88 23072 1368 0.00379965 10 26.72843823 3.271561772
32 23072 90 22982 1458 0.00390083 11 29.62703963 1.372960373
33 22982 93 22889 1551 0.00404665 12 32.52564103 -3.525641026
34 22889 96 22793 1647 0.00419415
35 22793 99 22694 1746 0.00434344
36 22694 102 22592 1848 0.00449458
Percent failure over 36 months =
7.56
Projected failures using lambda = (0.00068011*36)= 0.02448396
0
5
10
15
0 2 4 6 8 10 12 14
Number Failed
Months in Service
Number Failed
Predicted Number Failed
3 24436 6 24430 10 18 3 0.00024554 0.00040921
4 24430 10 24420 20 40 4 0.00040933 0.00081854 SUMMARY OUTPUT
5 24420 11 24409 31 55 5 0.00045045 0.00126899
6 24409 14 24395 45 84 6 0.00057356 0.00184255 Regression Statistics
7 24395 20 24375 65 140 7 0.00081984 0.00266239 Multiple R 0.986365083
8 24375 21 24354 86 168 8 0.00086154 0.00352393 R Square 0.972916078
9 24354 23 24331 109 207 9 0.00094440 0.00446833 Adjusted R Square 0.970207686