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ReliaSoft reference: Crow-AMSAA on 22 failure times, failure terminated at 620 h, with Fisher and Crow bounds

ToolReliability Growth
SourceReliaSoft Corporation (2015). "Crow-AMSAA (NHPP)." Reliability Growth and Repairable System Analysis Reference, ReliaWiki. Failure-times example.
LevelProfessional

Problem

A system failed at 2.7, 10.3, 12.5, 30.6, 57.0, 61.3, 80.0, 109.5, 125.0, 128.6, 143.8, 167.9, 229.2, 296.7, 320.6, 328.2, 366.2, 396.7, 421.1, 438.2, 501.2 and 620.0 hours, the test ending at the last failure. Estimate the Crow-AMSAA parameters, the instantaneous failure intensity and MTBF at 620 hours, and their 90 % two-sided Fisher-matrix and Crow bounds.

Inputs to Enter

  • The 22 cumulative failure times; failure terminated; confidence 90 %
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Answers

  • Σ ln T_i = 105.6355; β̂ = 0.6142, λ̂ = 0.4239; growth rate 1 − β = 0.386
  • Instantaneous intensity 0.02179 per hour, MTBF about 46 hours (45.89); cumulative intensity 0.03548
  • Fisher bounds: β 0.4325–0.8722, λ 0.1016–1.7691, MTBF_i 27.94–75.34 hours, MTBF_c 19.85–40.02
  • Crow bounds: β 0.4527–0.9350, MTBF_i 30.74–84.80 hours (Table C-III L 0.6701, U 1.848), MTBF_c 20.50–41.63 (χ² 29.79 and 60.48 on 44 df)

Notes

Paste the 22 times and switch the termination select to failure terminated. The local-information matrix and variances (Var λ 0.1352, Var β 0.01711) match the page's rounded values.

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