That day, after half a day of machine parameter adjustments, the yield showed no improvement, and the boss's brows were tightly furrowed.
Oh my goodness, do you remember the yield of that last batch of new products? I remember at that time, our CPK value was around 1.08, a significant gap from the customer's requirement of 1.33. Every day, we chased after the machines, adjusting parameters repeatedly, from etch time to plasma power, trying each one in turn, but the yield remained stuck around 95%, with a DPMO of 6210. During that period, the boss would come every morning to ask about progress, and seeing my weary face, he could only sigh, his brows furrowed into the character "川" (river/three lines). Later, we discovered that the fundamental problem might not be those parameters, but rather our method of assessing problems.
Where was the problem? In reality, it was that we "felt" there was a problem, but lacked evidence.
Frankly, many times we engineers, relying on experience and intuition, "feel" that "this parameter has an issue" or "that process needs changing." But have you ever considered if your "feeling" is truly supported by data? Or is it just a coincidence? Hypothesis Testing, in the "Analyze" phase of the DMAIC process, is precisely for helping you clarify whether your "intuitions" truly hold water. It's not about forcing you to memorize formulas, but rather providing a rigorous logical framework to judge whether your improvement measures are truly effective, instead of just busywork.
How is it actually done? Persuading with data.
Frankly speaking, hypothesis testing is much like being in court, where you need to present evidence to prove whether your "hypothesis" is true or false.
- First, define the "Null Hypothesis (H0)" and the "Alternative Hypothesis (Ha)": This is the first step. The null hypothesis usually states "no change" or "no difference." For example, we suspect that a new cleaning process will reduce the number of particles on the wafer surface.
* Ha: The new cleaning process leads to a "significant reduction" in the number of wafer particles.
* So the key is to first assume "no difference," and then use data to disprove it.
- Collect Data: The next step is to run experiments and collect the number of wafer particles under both the old and new processes. Assume the average number of particles for the old process is 50, and for the new process is 45.
- Calculate the Test Statistic and P-value: This part is usually performed using software (Minitab or R). The P-value is key. It represents "how high the probability is of observing your current data if H0 were true."
- Draw Conclusions:
* If the P-value is greater than the significance level, then "fail to reject H0." This does not mean H0 is true, but rather that you do not have sufficient evidence to prove a significant difference. In other words, your efforts might have been in vain, or you might need more data.
* Therefore, the key point is that the P-value is like the strength of your evidence; the smaller the P-value, the stronger your evidence.
The Most Common Pitfall: Misinterpreting the P-value and Drawing Hasty Conclusions
I remember one time, we introduced a new coating parameter, and the P-value came out to be 0.06. At that time, a rookie engineer excitedly exclaimed, "Wow! It's 0.06, very close to 0.05, meaning our parameter is useful!" What happened then? Later, when actually implemented, the yield showed barely any improvement. Why? Because our initially set significance level was 0.05. A value of 0.06 is greater than 0.05, which means "fail to reject H0." You cannot claim effectiveness just because it's "very close"; that's no different from fortune-telling. Frankly, in the world of statistics, there's no such thing as "almost"; it's either pass or fail.
Another pitfall is that hypothesis testing can only tell you "whether there is a significant difference," not "how big the difference is" or "why there is a difference." Therefore, even if hypothesis testing tells you that an improvement is effective, you still need to understand the underlying physical or chemical mechanisms so that you can apply the knowledge to similar problems next time.
One Thing You Can Do Today
Next time you encounter a yield problem, don't rush to randomly adjust parameters; first, use hypothesis testing to validate your "intuition."