1. The following sample information was obtained by taking four doughnuts per hour for twelve hours from Fawcett Bakery's doughnut process and weighing them:
|
Hour
|
WEIGHTS (GRAMS)
|
|
1
|
110, 105, 98, 100
|
|
2
|
79, 102, 100, 104
|
|
3
|
100, 102, 100, 96
|
|
4
|
94, 98, 99, 101
|
|
5
|
98, 104, 97, 100
|
|
6
|
104, 97, 99, 100
|
|
7
|
89, 102, 101, 99
|
|
8
|
100, 101, 98, 96
|
|
9
|
98, 95, 101, 100
|
|
10
|
99, 100, 97, 102
|
|
11
|
102, 97, 100, 101
|
|
12
|
98, 100, 100, 97
|
For the data shown above,
a) Find the x- and R for each sample.
b) Find the x-and R- for the twelve samples.
c) Find the 3-sigma UCL for the mean and range charts.
d) Does the process appear to be in statistical control. Why or why not?
2. Ten customers per hour were asked by the cashier at Stanley's Deli if they liked their meal, and the fraction that said "no" are shown below, for a twelve-hour period.
|
Hour
|
Fraction Defective
|
|
1
|
0
|
|
2
|
0.2
|
|
3
|
0.4
|
|
4
|
0.1
|
|
5
|
0.1
|
|
6
|
0.2
|
|
7
|
0.1
|
|
8
|
0
|
|
9
|
0
|
|
10
|
0.2
|
|
11
|
0
|
|
12
|
0.1
|
For the data shown above, find
a) P-
b) σp.
c) The 3-sigma UCL and LCL.
d) Does customer satisfaction at Stanley's appear to be in statistical control? How could we improve the analysis?
3. Roberto's Steakhouse tracks customer complaints every day and then follows up with its customers to resolve problems. For the past thirty days, it received a total of twenty complaints from unhappy customers. Using this information, calculate the 3-Sigma control limits.