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MIL-HDBK-189 Appendix C / 189C Table VI: Crow-AMSAA fit to 27 failures of two prototypes, time terminated at 300 h

ToolReliability Growth
SourceU.S. Department of Defense (1981). Reliability Growth Management. MIL-HDBK-189, 13 February 1981. Appendix C, Sections 20.1.3 and 20.2.1.4; and (2011). MIL-HDBK-189C, 14 June 2011. Table VI.
LevelProfessional

Problem

Two prototypes tested concurrently with design changes accumulated 27 failures at the combined times 2.6, 16.5, 16.5, 17.0, 21.4, 29.1, 33.3, 56.5, 63.1, 70.6, 73.0, 77.7, 93.9, 95.5, 98.1, 101.1, 132.0, 142.2, 147.7, 149.0, 167.2, 190.7, 193.0, 198.7, 251.9, 282.5 and 286.1 hours before the test stopped at 300 hours. Fit the Crow-AMSAA (NHPP) model, test its fit by the Cramér–von Mises statistic, and give the current MTBF with a 90 % interval.

Inputs to Enter

  • Cumulative failure times (loaded by default), time terminated at T = 300 hours
  • Confidence 90 %, goodness-of-fit significance 0.05
Open the Reliability Growth tool (loaded with this example)

Answers

  • β̂ = 0.716, λ̂β̂ = 0.325 (intensity 0.325 t^−0.284); ρ(300) = 0.0645 failures per hour, MTBF 15.5 hours; cumulative MTBF 300/27 = 11.1 hours
  • Unbiased β̄ = (N − 1)β̂/N = 0.690; Cramér–von Mises C² = 0.091 against the critical 0.218 (Table C-II, M = 27, α = 0.05): model accepted
  • 90 % interval on the MTBF from Table C-I (L 0.636, U 1.682): 9.9 to 26.1 hours

Notes

The tool's default data and termination are this example; press Submit. MIL-HDBK-189C §6.2.2.9 quotes F = 45 and β̂ = 0.826 for Table VI, which prints these 27 times; the 1981 values above are the ones the data give.

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