ADS-79D-HDBK Downloaded from https://www.everyspec.com A summary of the results of the Weibull analyses is provided in Table I-IV. Note that any p-value estimate greater than 0.10 indicates an acceptable fit for a Weibull distribution. An r 2 value close to 1.0 also indicates an acceptable fit. To illustrate how sample size is determined, suppose we wish to demonstrate 90% reliability with 90% confidence for our green threshold = 20.0. With the β values from each dataset, we can compute sample sizes using Equation 12 for various CI values ≥ 20.0. Minimum sample sizes without encountering a fault for each β at different ―test to‖ CI values are provided in Table I-V.
It should be noted that neither Table I-IV nor Table I-V are associated with the example and data from the Nose Gear Box described above. There is evidence to suggest that the CI value to test should be chosen so that it is greater than or equal to the lowest faulted CI value. However, more research would be required before this conclusion can be reached definitively. a. If CI data follows a Weibull distribution, then this method can be used to reduce the minimum sample size required to demonstrate CI reliability at a desired level of confidence. 173 TABLE I-IV. Weibull Results Summary Before Gear After Gear p-value Acceptable Fit?
Data Replaced Replaced Threshold β η Estimate r2 Threshold CI Data set1 last CI recorded first CI recorded green 1.43 68.38 0.51 0.95 yes 8.95 red 1.40 70.11 0.32 0.92 yes 8.71 Data set2 last day max CI first day max CI green 1.49 74.44 0.44 0.94 yes 10.62 red 1.44 77.51 0.35 0.92 yes 10.26 Data set3 overall max CI first day max CI green 1.65 96.63 0.71 0.97 yes 16.50 red 1.67 96.58 0.59 0.95 yes 16.65 TABLE I-V. Minimum sample sizes for CIs Reliability = 90% Confidence = 90% Green Threshold = 20.0 Minimum Sample Size CI To Test To Dataset 1, β = 1.43 Dataset 2, β = 1.49 Dataset 3, β = 1.65 20.0 22 22 22 25.0 16 16 16 30.0 13 12 12 35.0 10 10 9 40.0 9 8 7