1. Which of the following situations suggest a process that appears to be operating in a state of statistical control?

a. A control chart with a series of consecutive points that are above the center line and a series of consecutive points that are below the center line.

b. A control chart in which no points fall outside either the upper control limit or the lower control limit and no patterns are present.

c. A control chart in which several points fall outside the upper control limit.

d. All of the above.

2. A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.

Referring to the table, suppose the analyst constructs an R chart to see if the variability in production times is a control. What is the lower control limit for this R chart?

a. 4.84
b. 3.37
c. 2.98
d. 1.34

3. A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favoring the incumbent candidate is too erratic.

A medical facility does MRI's for sports injuries. Occasionally a test yields inconclusive results and must be repeated. Using the following sample data and n = 200, determine the upperandlowercontrollimits for the fraction of retests using 2-sigma limits. Is the process in control?
Sample
1 2 3 4 5 6 7 8 9

Find the upperandlowercontrollimits for an X-bar chart and R-chart for the width of a chair seat when sample grand mean (based on 30 samples of 6 observations each) is 27 inches and the average range is 0.35 inches.
Please use Excel.

Random samples of five hundred units that were selected daily from a manufacturing process produced an overall defective rate of 3.5%. Calculate the loweranduppercontrollimits for a percentage control chart.

(Problem attached in excel file)
Sampling four pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results:
Hour X in " R in "
1 3.25 0.71
2 3.1 1.18
3 3.22 1.43
4 3.39 1.26
5 3.07 1.17
6 2.86 0.32
7 3.05 0.53
8 2.65 1.13
9 3.02 0.71
10 2.85

Computer upgrades have a nominal time of 80 minutes. Samples of five observations each have been taken, and the results are as listed. Using factors from table 10.3, determine upperandlowercontrollimits for mean and range charts, and decide if the process is in control.
Sample
1 2 3 4 5

We have taken 12 samples of 400 letters each from a typing pool and found the following proportions of defective letters: 01, .02, .02, .00, .01, .03, .02, .01, .00, .04, .03 and .02. A letter is considered defective when one or more errors are detected.
Questions:
1. Calculate the center line, upperandlowercontrol limi

Find the upperandlowercontrollimits for /x- and R-charts for the width of a chair seat when the sample grand mean (based on 30 samples of 6 observations each) is 27.0 inches, and the average range is 0.35 inches.

See attached file.
Factors for computing control chart limits (3 sigma) for this problem
Cordelia Barrera is attempting to monitor a filling process that has an overall average of 715 cm3
The average range R is 6 cm3
For a sample size of 10 the controllimits for 3-sigma x-bar chart are:
UpperControl Limit (UCL x-bar

Please help with the following problem. Provide step by step calculations.
In general, how will the upperandlowercontrollimits change if a 2-sigma control chart is used instead of a 3-sigma control chart?

The yield strength of a metal bolt has a mean of 6,050 pounds with a standard deviation of 100 pounds. Twenty samples of three bolts were tested, resulting in the means shown below.
(a) Construct upperandlowercontrollimits for the¯ x chart, using the given product parameters.
(b) Plot the data on the control chart.
(