Step 3: Computing the equivalence test and interpreting the results
The parameter of interest in the equivalence test is the average difference between a historical process slope and a new process
slope. For the example, the EAC is defined as 1% per month. A 90% two-sided confidence interval on the difference in average
slopes between the historical and new processes is now computed with samples of lots from the two processes. If this confidence
interval fits within the range from –1% per month to –1% per month, then equivalence is demonstrated. This is analogous to
Scenario C in Figure 1. The formula for the 90% two-sided interval depends on the underlying
Figure 4. Confidence interval on difference for equivalence test of slopes.
model. For this example, the model that best fits the data assumes that lots are random. In this case, the 90% two-sided interval
is where nH and nN are the number of historical and new lots, respectively, and T is the number of time points for each profile. The term "Est.
Slope Variance" in the formula is the estimated variance of a slope estimate based on a single lot. This variance is assumed
to be equal for the two processes. In this example, bH = -1.13, bN = -1.56, T =4, nH = nN = 4, Est. Slope Variance = 0.0967, and t22;0.05 =1.717.
Figure 5. Plots of historical and new process slopes and equivalence acceptance criteria (EAC). EAC is donated in red lines.
The lower bound of the 90% two-sided confidence interval shown in Equation 3 is 0.05 % per month, and the upper bound is 0.81
% per month. Because the interval 0.05% per month to 0.81% per month is entirely contained in the range from –1% per month
to 1% per month, equivalence has been demonstrated. Figure 4 shows the confidence interval for the difference in average slopes
relative to the EAC. The fact that the confidence interval does not include the value 0 implies there is a statistically significant
difference between the two slopes with a statistical test size of 0.10 (p-value = 0.0633).