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MIL-HDBK-189 Appendix C 20.2.2.4: failure-terminated tank test, 26 failures in miles

ToolReliability Growth
SourceU.S. Department of Defense (1981). Reliability Growth Management. MIL-HDBK-189, 13 February 1981. Appendix C, Section 20.2.2.4, and Tables C-II and C-III.
LevelProfessional

Problem

A tank failed at the cumulative mileages 1, 57, 187, 252, 310, 485, 693, 720, 727, 779, 1,028, 1,561, 1,766, 1,793, 1,938, 2,030, 2,065, 2,289, 2,423, 2,560, 2,879, 3,086, 3,456, 3,626, 4,252 and 4,582, the test ending at the last failure. Fit the Crow-AMSAA model for a failure-terminated test, check the fit at the 10 % level and give the mean miles between failures with a 95 % interval.

Inputs to Enter

  • Cumulative failure times as above; termination failure terminated (T* = 4,582); unit miles
  • Confidence 95 %, goodness-of-fit significance 0.10
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Answers

  • β̂ = 0.626, λ̂ = 0.132; intensity at the end 0.00355 per mile, mean miles between failures 281
  • Cramér–von Mises 0.058 as printed (biased β̂ in the statistic); 0.0545 with β̄ as the text prescribes; both far below the critical 0.172 (M = N − 1 = 25, α = 0.10)
  • 95 % interval from Table C-III (L 0.6333, U 1.919): 178 to 541 miles

Notes

Paste the 26 mileages, set the termination select to failure terminated and the unit to miles.

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