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.