August_EDFA_Digital

edfas.org ELECTRONIC DEV ICE FA I LURE ANALYSIS | VOLUME 24 NO . 3 8 cess conditions. In a simple experiment, wemight wish to evaluatewhether a proposedprocess changewill improve our performance by conducting a two-sample t-test for difference in means. [2] Power calculations are used to determine an appropriate sample size per group [3] based on desired risk values, α and β (where α represents the probability of rejecting the null hypothesis of equivalence when the populations means are equal and power = 1−β represents the probability of rejecting the null hypoth- esis of equivalence when the population means differ by some specified effect size). At levels of α = 0.05 with power = 0.80 at a relative effect size of δ/σ = 0.5, n evalu- ates to ~63 (meaning 63 from each population group for 126 total samples). We can validate that result using our MC populations by runningmultiple trials of drawing two independent samples of 63 Y values from our MC popula- tion, conducting t-tests for differences in means between two independent samples and then tabulating the frac- tion of those trials where p-value of the computed t-test statisticwas below0.05 (i.e., the number of trials for which wewouldhave rejected thenull hypothesis of equivalency at our specified α = 0.05 divided by the total number of trials run). We then repeat this exper- iment adding various offsets of δ/σ to one of the samples. Our effective α value is determined by tabulating the fraction of trials where we reject the null hypothesis when there was no actual difference applied to the comparison sample, while our effective power is deter- mined by the fraction of trials for which we would reject the null hypothesis when a shift of δ/σ=0.5hasbeenappliedtothe comparison sample. Sampling randomly over their entire populations, all three of our MC populations exhibited a similar operating characteristic (OC) curve with α = 0.05 and power (1−β) = 0.80 (Fig. 8). Randomly samplingacross theentire population is not feasible in practice, however. A more realistic simulation would be to randomly select a starting point and then take the next 63 sites in sequence from that point within the process stream. Sampling in that manner produces markedly different responses for W2W and L2L (Fig. 9), with effective α rising dramatically such that now about half/three quarters of the time, un-shifted samples are being flagged for differences. At the same time their effectivepower for detecting a rela- tive 0.5σ shift is reduced. Fig. 7 L2L disposition rates match W2W; no L2L adjustments required. Fig. 8 The t-test OC curves under random sampling match expectations.