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Question 1 (10 points). For a newly installed machine, a series of 184 density measurements were taken over 46 daily samples of size 4 (that is, we have 46 sub-samples or groups of 4). The process is assumed to be in a state of a statistical control when μ = 252 and σ = 1.2. The data are contained in the DENSITY file. (2 points) Showing setup/work, what are the lower and upper control limits when we have these known parameters? (Calculate LCL and UCL) (1 point) Using the density data given, construct the (X ) ̅/S-chart. For the following problems, I recommend adjusting your plot window in RStudio (stretching it so it is wider) to allow you to view the Sample/Group numbers. (1 point) For which daily samples does the process variability appear to be in control? (1 point) For which daily samples does the process variability appear to be out-of-control? (1 point) Based on the (X ) ̅chart, what sequences of daily samples does the process mean appear to be above aim? (1 point) Based on the (X ) ̅chart, what sequences of daily samples does the process mean appear to be below aim? (1 point) Based on the (X ) ̅chart, what sequences of daily samples does the process mean appear to be on aim? (2 points) Suppose the engineer wanted to update the existing control limits based on these data. Should you object to or support the engineer’s plan to establish new control limits based on this data? Explain. Question 2. (15 points) Interpreting Regression Model Outputs Using the regression model shown below, describe the types of information and uses for each of the shaded boxes. (Note: I hand-labelled the boxes with the corresponding parts because some colors were not very distinct and we are not testing ability to distinguish colors) a. Blue Box: How do you determine which variables are the explanatory and response variables? b. Red Box: Describe, in detail, the types of information shown in the box. a. What does each column represent? b. What does each row represent? c. What can you use the Estimate and Std. Error columns for and how do you interpret the values in the Estimate column? d. What do the p-values indicate? c. Purple Box: Describe, in detail, the information that is provided in the purple box. What does the information tell you about the model/data? d. Green Box: What does the information in the green box tell you and how would you interpret the output? e. Orange Box: How is the information in the orange box different than the green box and how is the interpretation different? f. Yellow Box: How do we use the information in the yellow box in a multiple linear regression analysis?

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##############################
## Intro to Quality Control ##
##############################

## Install the "qcc" package -- only run this ONE time! (or it will install every time)
#install.packages("qcc")

## Library or "require" the package in order to use it
library(qcc)

## Read in the "density" dataset
density.data = read.csv(file.choose(), header = TRUE)

## Look at first few rows
head(density.data)
## Note there two variables: "density" and
## "sample" (there are 46 daily sample groups)

attach(density.data)

density.data <- qcc.groups(density, sample) ## Format the dataset so we can use qcc() function

## Construct control chart --
## The code below provides how to make an x-bar/S-chart,
## an x-bar/R-chart, an S-chart, an R-chart,
## a p-chart, and a c-chart

# Question 1.

# a.
LCL <- 252 + 3 * 1.2
UCL <- 252 - 3 * 1.2...

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