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A local bank wants to study waiting times of customers. A sample of four customers is selected on successive days, and the time is measured from the point each customer enters the line to when he or she reaches the teller window. The results are shown in the data table. a. Construct a control chart for x. b. Is the process within statistical control? Click the icon to view the data. Click the icon to view a table of control chart factors.

A local bank wants to study waiting times of customers. A sample of four customers is selected on successive days, and the time is measured from the point each customer enters the line to when he or she reaches the teller window. The results are shown in the data table. a. Construct a control chart for x. b. Is the process within statistical control? Click the icon to view the data. Click the icon to view a table of control chart factors.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Educational Content on Control Charts** A local bank is analyzing customer waiting times by observing samples of four customers over several days. The waiting time is recorded from the moment a customer lines up until they reach the teller. The goal is to determine if the process is under statistical control using a control chart for the mean (\(\overline{x}\)). --- ### Task 1: Construct a Control Chart for \(\overline{x}\) **Step:** Choose the correct graph from the options. - **Graph Options:** - **A** - **B** - **C** - **D** Each graph shows the sample mean on the y-axis against the sample number on the x-axis, with upper control limit (UCL) and lower control limit (LCL) marked. --- ### Task 2: Is the Process Within Statistical Control? **Choose the Correct Explanation:** - **A.** No, there is at least one point lying outside the UCL and LCL. - **B.** No, there are eight consecutive points either all above or below the centerline. - **C.** Yes, no criteria are violated. - **D.** No, there is a noticeable trend or pattern. The correct choice considers the presence of points violating control limits or patterns. --- ### Table of Control Chart Factors **View the Table:** A table named **"Table 14-2 Control Chart Constants"** provides constants for constructing R, \(\overline{x}\), and s charts. It lists values based on the number of observations in each subgroup, useful for setting control limits. --- **Instructions:** - Click the icon to view the data for deeper analysis. - Click the icon to view detailed control chart factors. This exercise aims to enhance understanding of monitoring processes for quality control by interpreting control charts and identifying deviations from statistical norms.
Transcribed Image Text:**Educational Content on Control Charts** A local bank is analyzing customer waiting times by observing samples of four customers over several days. The waiting time is recorded from the moment a customer lines up until they reach the teller. The goal is to determine if the process is under statistical control using a control chart for the mean (\(\overline{x}\)). --- ### Task 1: Construct a Control Chart for \(\overline{x}\) **Step:** Choose the correct graph from the options. - **Graph Options:** - **A** - **B** - **C** - **D** Each graph shows the sample mean on the y-axis against the sample number on the x-axis, with upper control limit (UCL) and lower control limit (LCL) marked. --- ### Task 2: Is the Process Within Statistical Control? **Choose the Correct Explanation:** - **A.** No, there is at least one point lying outside the UCL and LCL. - **B.** No, there are eight consecutive points either all above or below the centerline. - **C.** Yes, no criteria are violated. - **D.** No, there is a noticeable trend or pattern. The correct choice considers the presence of points violating control limits or patterns. --- ### Table of Control Chart Factors **View the Table:** A table named **"Table 14-2 Control Chart Constants"** provides constants for constructing R, \(\overline{x}\), and s charts. It lists values based on the number of observations in each subgroup, useful for setting control limits. --- **Instructions:** - Click the icon to view the data for deeper analysis. - Click the icon to view detailed control chart factors. This exercise aims to enhance understanding of monitoring processes for quality control by interpreting control charts and identifying deviations from statistical norms.
### Analysis of Customer Waiting Times #### Context A local bank is studying the waiting times of customers. Each day, four customers are sampled, and their time spent waiting from entering the line to reaching the teller is recorded. The goal is to determine if the process is within statistical control using control charts. #### Construction of Control Charts **Objective:** Construct a control chart for the mean waiting time (\(\bar{x}\)). - **Graph Options:** - Graph A: Shows variation with one point outside control limits. - Graph B: Shows a different set of variations. - Graph C: Another variety of control chart visual. - Graph D: Depicts a control chart with distinct data points. #### Question: Is the Process Within Statistical Control? **Answer Choices:** - **A:** No, because there is at least one point lying outside the region between the upper and lower control limits. - **B:** No, because there are eight consecutive points all above or all below the centerline. - **C:** Yes, because none of the criteria are satisfied. - **D:** No, because there is a trend, pattern, or cycle that is obviously not random. **Correct Selection:** Choice A is selected, indicating an out-of-control point as one data point lies outside the control limits. #### Customer Waiting Times Data Table **Data Summary:** - **Columns Include:** - **Day:** Sequence from 1 to 20. - **Time in Minutes:** Recorded for each of the four customers. - **Mean:** Average waiting time for the day. - **Range:** Difference between highest and lowest times. **Sample Data:** (Day 1 Example) - Times: 7.6, 8.4, 7.7, 8.8 - Mean: 8.125 - Range: 1.2 #### Conclusion The customer waiting times undergo regular inspection using a control chart to determine variability. The response indicates the process is currently not in control due to certain points falling outside control limits, suggesting potential improvements in process efficiency.
Transcribed Image Text:### Analysis of Customer Waiting Times #### Context A local bank is studying the waiting times of customers. Each day, four customers are sampled, and their time spent waiting from entering the line to reaching the teller is recorded. The goal is to determine if the process is within statistical control using control charts. #### Construction of Control Charts **Objective:** Construct a control chart for the mean waiting time (\(\bar{x}\)). - **Graph Options:** - Graph A: Shows variation with one point outside control limits. - Graph B: Shows a different set of variations. - Graph C: Another variety of control chart visual. - Graph D: Depicts a control chart with distinct data points. #### Question: Is the Process Within Statistical Control? **Answer Choices:** - **A:** No, because there is at least one point lying outside the region between the upper and lower control limits. - **B:** No, because there are eight consecutive points all above or all below the centerline. - **C:** Yes, because none of the criteria are satisfied. - **D:** No, because there is a trend, pattern, or cycle that is obviously not random. **Correct Selection:** Choice A is selected, indicating an out-of-control point as one data point lies outside the control limits. #### Customer Waiting Times Data Table **Data Summary:** - **Columns Include:** - **Day:** Sequence from 1 to 20. - **Time in Minutes:** Recorded for each of the four customers. - **Mean:** Average waiting time for the day. - **Range:** Difference between highest and lowest times. **Sample Data:** (Day 1 Example) - Times: 7.6, 8.4, 7.7, 8.8 - Mean: 8.125 - Range: 1.2 #### Conclusion The customer waiting times undergo regular inspection using a control chart to determine variability. The response indicates the process is currently not in control due to certain points falling outside control limits, suggesting potential improvements in process efficiency.
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