Supply Chain Question

• Please answer the following questions based on the data file provided. To improve the taste of coffee, Nina’s coffee shop has conducted experiment by manipulating the level of temperature and the coffee grind fineness (or coarseness). Each time, they used a specially designed test strip to measure the level of caffeine that is extracted.
• Please answer the series of questions related to the statistical distributions.
• Taguchi Loss Function:

Illustration: Coffee Data

• Please list all the treatment groups.
• Which group will you consider as the baseline group? (Note: this question is the key to the rest of the questions.)
• On the response variable, please find out all the means for each treatment group.
• In general, for the baseline group, how much increase in the extracted caffeine can be observed when the temperature is changed from low to high? (Note: Do not over think. Just look at the corresponding average. Nothing “statistically significant” stuff here.)
• In general, for the baseline group, how much increase in the extracted caffeine can be observed when the level of grind fineness increases from low to high? (Note: Do not over think. Just look at the corresponding average. Nothing “statistically significant” stuff here.)
• For the baseline group, how much increase in the extracted caffeine can be observed when the level of grind fineness increases from low to high and also the high temperature water is applied?
• Please draw an interaction plot based on the data. The Y-axis will be the extracted caffeine, and the X-axis will be the level of fineness. (Hint: it will be easier if you refer to the answers from question 3) above.
• If there is no interaction effect (or the interaction effect is not statistically significant), for the baseline group, how much increase in the extracted caffeine can be observed when the level of grind fineness increases from low to high and the high temperature water is applied?
• The provided dataset is not yet ready to run the regression analysis as/is. First, please modify the data appropriately. Then, run the regression analysis and paste the result below as a picture.

• Please draw the sampling distribution and the population distribution on the same x-axis in one space. The parameters: n = 16, µ = 25, s = 12, the population is assumed to be normal distribution. (Note: first, draw a horizontal line, to make it as the x-axis. We have done this before during a class in chapter 8.)
• What is the difference between LCL/UCL and LSL/USL? Please explain what each pair does. Then, elaborate the difference lends on the two distributions mentioned from question 1).
• When k = 3 is used in this case, what is the LCL/UCL respectively? (Note: Without generating R-bar and looking up control chart number table, we will simplify this by using the sampling distribution.) How often (in %) the line will be stopped for a special cause inspection when the process is not out-of-control?
• Based on the following operating characteristics curve, when the sample size is doubled from 4 to 8, what much does such increase improve the chance of detecting a 1 standard deviation mean shift? (note: this question is not connected to the question 3 and do not over think! A visual inspection on the graph is all you need. Pay attention to the meaning of the x-axis and the y-axis first.)

• When first source of variation introduces s₁² amount of variance and the second source introduce s₂² amount of variance. These two sources are known to be the only sources of variation. What is the total amount of variations measured by the variance? (Hint: think about the Taguchi loss function.)
• When a centered process has a C_pk = 1.2, what is the DPMO? (Hint: to make it easier, simply assume µ = 0, s = 1).
• The expected loss for the following process with a discrete quality dimension, k = 0.2, and process target = 13.5

Deming’s System of Profound Knowledge proposes four areas: appreciation of system (not silo mentality), knowledge in psychology, knowledge of variations, and theory of knowledge. Use some specific examples (e.g., topics, examples, lessons) from this class, explain how they improved your understanding in above areas. (Note: we did not quite explain the psychology aspect, so please leave the psyc