I posted this a while back. The solutions are in red.
Suppose you need to select a consultant or verify the qualifications of some of your staff to perform designed experiments (DOE), statistical process control (SPC) and statistical analysis. What are five questions you could ask to see if the folks you are interviewing have the right stuff to do the job? Try these?
1. What is the difference between common cause and special cause variation? This was answered in a post a while ago.
2. In designed experiments the f statistic is used to evaluate whether or not a factor is significant. How would you explain the f statistic to a layman? In a DOE, the f statistic is proportional to the difference between the average response values at the varying levels of the factor divided by the variation with response at the same level. An example may help. Suppose we want to see if temperature affects the volume of solder paste deposits. We measure 5 paste volumes at 20C and 5 at 30C. The 5 readings at 20C have an average of 1000 cubic mils with a standard deviation of 100 cubic mils. At 30C the deposits are 1400 cubic mils, also with a standard deviation 100 cubic mils. In this case the f statistic will be proportional to (1400-1000)/100 = 4, strongly suggesting that temperature affects solder paste deposit volume.
3. What do the Shewhart Rules tell us? The Shewhart Rules tell us if it is likely that special cause variation is affecting a manufacturing process. As an example, let's assume we are measuring the average volume of 10 solder paste deposits on a PWB. The historic average for the deposits is 1200 cubic mils, and the 3 sigma control limits are +/- 300 cubic mils of this point. If the average of one of the set of 10 readings was 1650 cubic mils this would be about the control limit and would be a Shewhart Rule #1 violation. This violation would suggest that a special cause variation has entered the process. However, with 1000s of data points a Shewhart violation is possible even from common cause variation, since 3 sigma control limits will have 0.3% of their data outside of the control limits. However, if we got 4 Shewhart #1 violations in a row, we would surely have a special cause problem.
All in all there are a total of 8 Shewhart Rules.
4. I would like to sample a large population and test whether or not I can claim that the population has zero defects with a 95% confidence. How can I do this?
I showed in a post recently, that an infinite number of samples would be required.
5. What is Cpk? How does it differ from Cp?
Cp measure precision, Cpk measures precision and accuracy.
An extra: "Six Sigma" is widely claimed to be 3.4 ppm defects. Is this correct, if not why not?
3.4 ppm is wrong on two levels:
1. 3.4 ppm is 4.5 sigma for a one sided test. For a two sided test the defect rate would be 6.8 ppm.
2. True 6 sigma is about 2 ppb!
I'll share the answers in a few days.
Click on this link to find the Shewhart Chart above