Assignment: SPC
1. Leah's Toys guarantees to ship customer orders in 24 hours or less. The following chart contains results for five samples of nine customer orders each:
|
SAMPLE CUSTOMER ORDERS SAMPLE (HOURS TO SHIP)
|
|
1
|
3
|
5
|
21
|
4
|
15
|
9
|
7
|
3
|
6
|
|
|
2
|
22
|
16
|
8
|
16
|
11
|
38
|
11
|
25
|
15
|
|
|
3
|
9
|
2
|
5
|
17
|
2
|
19
|
4
|
2
|
4
|
|
|
4
|
6
|
7
|
18
|
9
|
16
|
18
|
7
|
10
|
1
|
|
|
5
|
11
|
10
|
20
|
18
|
1
|
6
|
3
|
18
|
9
|
|
a. Based on these results, estimate the p and Sp values.
b. A student comments, "Time is a continuous variable. We should really be looking at the X and R values." Do you agree or disagree? Explain your rationale.
2. A lumber company makes plywood for commercial construction. A key quality measure is the thickness of the plywood. Every two hours, five pieces of plywood (n = 5) are selected, and the thicknesses are measured. The data (in inches) for the first 20 samples are as follows:
|
Two-Hour Period
|
Plywood 1
|
Plywood 2
|
Plywood 3
|
Plywood 4
|
Plywood 5
|
|
1
|
0.642
|
0.612
|
0.659
|
0.691
|
0.689
|
|
2
|
0.705
|
0.584
|
0.644
|
0.685
|
0.618
|
|
3
|
0.63
|
0.599
|
0.594
|
0.621
|
0.628
|
|
4
|
0.586
|
0.634
|
0.639
|
0.656
|
0.64
|
|
5
|
0.641
|
0.64
|
0.693
|
0.649
|
0.646
|
|
6
|
0.636
|
0.713
|
0.678
|
0.725
|
0.631
|
|
7
|
0.703
|
0.602
|
0.668
|
0.679
|
0.711
|
|
8
|
0.649
|
0.635
|
0.672
|
0.64
|
0.675
|
|
9
|
0.607
|
0.625
|
0.604
|
0.64
|
0.65
|
|
10
|
0.652
|
0.641
|
0.72
|
0.597
|
0.629
|
|
11
|
0.572
|
0.696
|
0.612
|
0.631
|
0.675
|
|
12
|
0.666
|
0.679
|
0.67
|
0.609
|
0.617
|
|
13
|
0.673
|
0.662
|
0.622
|
0.644
|
0.656
|
|
14
|
0.669
|
0.656
|
0.623
|
0.71
|
0.667
|
|
15
|
0.654
|
0.677
|
0.678
|
0.632
|
0.623
|
|
16
|
0.686
|
0.614
|
0.603
|
0.674
|
0.671
|
|
17
|
0.72
|
0.696
|
0.692
|
0.655
|
0.652
|
|
18
|
0.666
|
0.651
|
0.619
|
0.596
|
0.677
|
|
19
|
0.665
|
0.671
|
0.658
|
0.62
|
0.69
|
|
20
|
0.642
|
0.625
|
0.626
|
0.638
|
0.637
|
a. develop an x chart to determine if the process is stable or not.
b. develop an R chart to determine if the process is stable or not.
3. A company randomly selects 50 shipping records every day to determine the number of orders that are shipped late. The following are the most recent 20 days of samples. The company wants to use the sampled data to develop a p chart to monitor the proportion of late shipments. Using the data below, develop a p chart to monitor this process. Does the process appear to be in control?
|
Sample
|
n = Sample Size
|
Number of Late Shipments
|
Number defective (p)
|
|
1
|
50
|
3
|
0.06
|
|
2
|
50
|
5
|
0.1
|
|
3
|
50
|
2
|
0.04
|
|
4
|
50
|
4
|
0.08
|
|
5
|
50
|
6
|
0.12
|
|
6
|
50
|
4
|
0.08
|
|
7
|
50
|
4
|
0.08
|
|
8
|
50
|
2
|
0.04
|
|
9
|
50
|
4
|
0.08
|
|
10
|
50
|
5
|
0.1
|
|
11
|
50
|
2
|
0.04
|
|
12
|
50
|
3
|
0.06
|
|
13
|
50
|
5
|
0.1
|
|
14
|
50
|
3
|
0.06
|
|
15
|
50
|
6
|
0.12
|
|
16
|
50
|
4
|
0.08
|
|
17
|
50
|
5
|
0.1
|
|
18
|
50
|
4
|
0.08
|
|
19
|
50
|
5
|
0.1
|
|
20
|
50
|
2
|
0.04
|
4. A machine is designed to fill bottles to between 16.01 and 15.98 ounces. Thirty samples of bottles filled by the machine were randomly selected from the process. The sample bottles yielded a mean (mu) of 15.99 and a standard deviation of 0.0025. Calculate the process capability index for the bottle filling machine and comment on its capability.