A quality practitioner may be interested in assessing whether two process means are statistically equivalent, e.g., whether two processes (an historical process and a new process) produce equivalent results for a quality attribute. Statistical equivalency tests, e.g., two one-sided t-tests (TOST) are widely accepted as an acceptable method for demonstrating equivalency.
In contrast with traditional hypothesis testing approaches, where the null hypothesis assumes equality across two parameters of interest (e.g., equal means), the null hypothesis using TOST can assess whether the average difference exceeds a comparability criteria known as the EAC (equivalency acceptance criteria) and can be written as:
H01: µ1 - µ2 ≤ -EAC, and
H02: µ1 - µ2 ≥ EAC,
where µ1 represents the pre-change mean, and µ2 represents the post-change mean.
To show average equivalency a 90% two-sided confidence interval for the difference of two means must fall completely within the range from –EAC to EAC.
In some instances this region may be mandated, e.g., using 80% to 125% as is required in bioequivalence testing. In most cases, the EAC is developed with subject matter experts. This article describes a graphical approach based on the work of Burdick et al., (published in Quality and Reliability Engineering International, 2011) to demonstrate the appropriateness of an EAC prior to collecting post-change data.
Assume we have nH values from an historical process and an EAC has been determined. The true mean (µH) and standard deviation (σH) are estimated using the sample mean (Figure 2) and sample standard deviation (sH).