ADS-79D-HDBK Downloaded from https://www.everyspec.com required for the non normal distribution. Using the statistical properties of the CI data before replacement, when the gear was damaged, and after replacement, a t test can be used for determining the minimum sample size to reproduce the results of the hypothesis test. The t statistic is calculated as:
y y t (Equation 3) 2 1 Where ȳ 1 = sample mean of undamaged gear teeth n 1 = sample size of undamaged gears ȳ 2 = sample mean of gear teeth with pitting damage on two or more pinion teeth n 2 = sample size of damaged gears Sp = pooled or average standard deviation Using the pooled standard deviation estimated within the population, sample size is determined by setting the t statistic equal to the critical t values. Solving for n requires iterating through several n values to determine the sample size that solves the equation:
; 2 1( [ t n 1 + n 2 –2) + t(1- ; n 1 + n 2 –2)] = y y 2 1 (Equation 4) A minimum sample size for n using the data from ten helicopters was calculated to be 7.75 from these iterations. Due to the non-normality of data distribution, the minimum sample size must be 14% larger than the minimum sample size defined by the t test (as previously discussed above with the maximum loss of efficiency at 0.864). Therefore, 7.75/.864 = approximately 9 samples for minimum sample size when using the non normal distributed data from the NGB CIs. Per Table I-I, is equal to the type I error rate, reject null hypothesis when null hypothesis is true.
For this hypothesis it means to claim a significant difference in means when there is not. It should be noted that /2 is used for this hypothesis because µ 1 ≠ µ 2 could result in µ 1 > µ 2 or µ 1 2 . Also per Table I-I, is equal to type II error rate, fail to reject null hypothesis when null hypothesis is false (missed hit). For this hypothesis it means to claim no discernable difference in means when differences exist. Per the CI data from both distributions, with α = 0.05 and β = 0.05, a sample size of 9 undamaged gears ( n 1 ) and 9 damaged gears ( n 2 ) are required.
However, if the data from the helicopter shown in Figure I-7, with the CI that responded poorly to the damage, was removed from the dataset, bringing our dataset down to 9, only 7 damaged and undamaged gears would be required. This means that a minimum of CI data from 7 faulted components and 7 unfaulted components are required to confirm the CI can differentiate between faulted and unfaulted gears. This exercise indicates the importance of assessing the overall performance of the CI across the fleet, including false negatives and false positive indications, when determining sample sizes for 164 S p 1 1 n n 1 2 S p 1 1 n n 1 2