Hypothesis Testing is among the most powerful tools used in Business Excellence. It takes away the decisions based on gut feeling or experience or common sense e.g. Site A has better performance than Site B, we should hire more experienced employees as their accuracy is higher, it takes lesser time if we use System A vs System B, older customers are less likely to use self-help as compared to other age groups, are we meeting the cut-off defective %age or not, based on the proportion defectives we see. Hypothesis testing allows to collect valid sample sizes and make decisions for population - it keeps the gut feeling and statements such as "in our experience" out of the picture. You have statistical proof of whatever you "feel" or "think" is right.
What must be kept in mind is that it is an OFAT testing technique - only one factor under consideration can be varied while all other Xs must be maintained constant.
Hypothesis Testing can be used in any and every phase of the DMAIC cycle.
Define - Usually all "1" tests or tests where we compare a population to an external standard are used in this phase e.g. 1 proportion test (if I have x out of y defects, am I meeting the client quality target of 95%?), 1 Sample Z, 1 Sample T, 1 Sample Sign etc. (Has the cost of living gone up as compared to the mean or median cost 10 years ago?). It helps us decide "do we even have a problem".
Measure - One can look at data and the eye can catch a "trend". But can we really say that the performance has dipped, is the difference in performance statistically significant. Hypothesis testing can give you the answer.
Analyze - this hardly needs any explanation as everyone has using hypothesis testing extensively in this phase to compare two populations or multiple populations e.g. do the five swimming schools create the same proportion of champions out of all enrolled in them, is the lead time for a process on machine A better than machine B, does Raw Material X give better quality than Raw Material Y, does Training Methodology 1 give better results as compared to Methodology 2, 3 and 4, does Vendor A have fewer billing discrepancies than Vendor B etc.
Improve - tests involving two populations are generally used. E.g. comparing Y pre and post solution implementation (we implemented a solution to improve the yield of a machine). Is the post-solution yield higher than pre-solution yield, is the TAT post solution better than the TAT before implementing the solution, are more customers buying our product than before etc.
Control - We get different CTQ numbers every month post we made an initial improvement. Can we really say that we have improved as compared to before? For 5 months after improve, if we saw a lower number for the metric, was that really different than other months. Can we say that we are consistent? We can use Hypothesis testing again.
Business Excellence is nothing but an iterative process to drive excellence throughout the business. As Hypothesis Testing helps us validate or invalidate what we suspect every step of the way in the DMAIC cycle, it is a "must use" tool for the armor.