500 câu trắc nghiệm Kinh tế lượng – 13C

5) A machine is supposed to fill cans that contain 12 oz. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below.

S	A	M	R
1	11.2 11.7 11.8 11.7	11.6	0.6
2	11.8 11.3 11.6 11.6	11.575	0.5
3	11.3 12.0 11.8 11.7	11.7	0.7
4	12.1 11.6 12.1 12.0	11.95	0.5
5	11.8 11.8 11.9 11.9	11.85	0.1
6	12.0 11.9 11.8 11.7	11.85	0.3
7	11.6 12.0 11.9 11.8	11.825	0.4
8	11.5 12.1 11.9 12.0	11.875	0.6
9	12.1 12.1 11.7 11.9	11.95	0.4
10	11.7 12.0 11.6 11.9	11.8	0.4
11	12.1 12.4 11.9 12.2	12.15	0.5
12	12.5 12.0 12.4 12.3	12.3	0.5
13	12.5 12.0 12.1 12.1	12.175	0.5
14	12.4 12.0 12.0 12.4	12.2	0.4
15	12.4 12.4 12.6 12.1	12.375	0.5

Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-control criteria apply.
6) A control chart for \({\bar x}\) is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.

Process mean is not within statistical control. There are points above and below the control limits. There is a shift upward.
7) A control chart for R is shown below. Determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation.

Process variation appears to be out of statistical control . There is an upward trend indicating that variation is increasing. There are points above the upper control limit. There are more than 8 consecutive points below the center line.
8) A run chart for individual values is shown below. Does there appear to be a pattern suggesting that the process is not within statistical control? If so, describe the pattern.

Process appears to be out of statistical control. There is a cyclical pattern
9)


Use the given process data to construct a control chart for p.
10) A drugstore considers a wait of more than 5 minutes to be a defect. Each week 100 customers are randomly selected and timed at the checkout line. The numbers of defects for 20 consecutive weeks are given below.
4 4 5 5 5 5 5 6 6 6 6 12 6 6 6 7 6 7 8 7

Solve the Problem.
11) A control chart for atrributes is to be constructed. Which process would have wider control limits, a process which has been having a 5% rate of nonconforming items, or a process which has been having a 10% of nonconforming items? Assume that both processes have the same sample sizes. For a given sample size, would it be easier to detect a shift from 5% to 10% or a shift from 10% to 15%? Explain your reasoning.
The process which has been having a 10% of nonconforming items would have wider control limits. It would be easier to detect a shift from 5% to 10% than a shift from 10% to 15%, because at a 5% rate of nonconforming items, the control limits are narrower, and it thus takes a smaller shift before the proportion falls outside the control limits.