Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Chapter 12, Problem 70AP
Summary Introduction
Interpretation: Process control needs to be analyzed using a 3-sigma p chart with the help of given data.
Concept Introduction: P-chart helps to analyze the process control when no. of defective products and helps organizations makes better improvement decisions.
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You work for Raider Data Systems where thousands of insurance records are entered by clerks each day for a variety of client firms. You are in charge of setting control limits to include 99.73% of the random variation in the data entry process when it is in control. Samples that you collected from 20 employees are shown below. You carefully examine 100 records entered by each employee and count the number of errors entered by each clerk. You also compute the proportion defective in each sample. Using a p-chart, what are the upper and lower control limits?
Sample
Errors Made
Proportion Defective
1
4
0.04
2
5
0.05
3
6
0.06
4
3
0.03
5
8
0.08
7.
An ad agency tracks the complaints, by week received, about the billboards in its city:
Week
No. of Complaints
1
3
2
6
3
4
4
12
5
2
6
9
This exercise contains only parts a, b, and c.
Part 2
a) The type of control chart that is best to monitor this process is
c minus chart ______
.
Part 3
b) Using z =
3,
the control chart limits for this process are (assume that the historical complaints rate is unknown):
UCLc
= ________ complaints per week (round your response to two decimal places).
The upper control limit is: ________
The lower control limit is: _________
The central limit is ___________
Steps to monitor using the control charts:
Now monitor the process. An additional ten days of data have been collected, see table labeled “1st 10 Days of Monitoring Reservation Processing Time” in the Data File.
Develop Xbar and R charts for the 1st 10 days of monitoring. Plot the data for the 1st 10 days on the Xbar and R charts.
Is the process in control? If the control chart indicates an out-of-control process, note which days, the pattern, and whether it is the Xbar or R chart.
Now that we have set up the control charts using enough data from a stable process, the 30 days of data, we will monitor the process. While monitoring the process, what will we use as the upper control limit for the X-bar Chart to compare against our new x-bar values? Enter your response to three decimal places. You do not need to include the units (minutes), ONLY the numeric value.
USE DATA TO GET UPPER CONTROL LIMIT
Chapter 12 Solutions
Production and Operations Analysis, Seventh Edition
Ch. 12.1 - Prob. 2PCh. 12.1 - Prob. 3PCh. 12.1 - Prob. 4PCh. 12.1 - Prob. 5PCh. 12.1 - Prob. 6PCh. 12.2 - Prob. 7PCh. 12.2 - Prob. 8PCh. 12.2 - Prob. 9PCh. 12.2 - Prob. 10PCh. 12.2 - Prob. 11P
Ch. 12.2 - Prob. 12PCh. 12.2 - Prob. 13PCh. 12.3 - Prob. 14PCh. 12.3 - Prob. 15PCh. 12.3 - Prob. 16PCh. 12.3 - Prob. 17PCh. 12.4 - Prob. 18PCh. 12.4 - Prob. 19PCh. 12.4 - Prob. 20PCh. 12.4 - Prob. 21PCh. 12.5 - Prob. 22PCh. 12.6 - Prob. 23PCh. 12.6 - Prob. 24PCh. 12.6 - Prob. 25PCh. 12.6 - Prob. 26PCh. 12.6 - Prob. 27PCh. 12.6 - Prob. 28PCh. 12.9 - Prob. 29PCh. 12.9 - Prob. 30PCh. 12.9 - Prob. 31PCh. 12.9 - Prob. 32PCh. 12.9 - Prob. 33PCh. 12.10 - Prob. 34PCh. 12.10 - Prob. 35PCh. 12.10 - Prob. 37PCh. 12.10 - Prob. 38PCh. 12.10 - Prob. 39PCh. 12.10 - Prob. 40PCh. 12.11 - Prob. 41PCh. 12.11 - Prob. 42PCh. 12.11 - Prob. 43PCh. 12.11 - Prob. 44PCh. 12.12 - Prob. 46PCh. 12.12 - Prob. 47PCh. 12.12 - Prob. 48PCh. 12 - Prob. 49APCh. 12 - Prob. 50APCh. 12 - Prob. 51APCh. 12 - Prob. 52APCh. 12 - Prob. 53APCh. 12 - Prob. 54APCh. 12 - Prob. 55APCh. 12 - Prob. 57APCh. 12 - Prob. 58APCh. 12 - Prob. 59APCh. 12 - Prob. 60APCh. 12 - Prob. 61APCh. 12 - Prob. 62APCh. 12 - Prob. 63APCh. 12 - Prob. 64APCh. 12 - Prob. 65APCh. 12 - Prob. 66APCh. 12 - Prob. 67APCh. 12 - Prob. 68APCh. 12 - Prob. 69APCh. 12 - Prob. 70AP
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- At Webster Chemical Company, lumps in the caulking compound could cause difficulties in dispensing a smooth bead from the tube. Even when the process is in control, an average of four lumps per tube of caulk will remain. Testing for the presence of lumps destroys the product, so an analyst takes random samples. The following results are obtained: Tube No. Lumps Tube No. Lumps Tube No. Lumps 1 6 5 6 9 5 2 5 6 4 10 0 3 0 7 1 11 9 4 4 8 6 12 2 Determine the c-chart two-sigma upper and lower control limits for this process. Is the process in statistical control?arrow_forwardThe Watson Electric Company produces incandescent light bulbs. The following data on the number of lumens for 40-watt light bulbs were collected when the process was in control. The standard deviation of the process is 15. Calculate control limits for an x-bar chart with 3-sigma limit and draw the chart. Since these data were collected, some new employees were hired. A new sample obtained the following readings: 625, 592, 612, and 650. Is the process still in control?arrow_forwardWrite a paragraph to your coworker explaining why you take 3 samples of size 5 and find the mean of each sample instead of randomly choosing and measuring the amounts in 15 vials individually to check the machine's setting.arrow_forward
- One of the stages in the process of making denim cloth at the Southern Mills Company is to spin cotton yarn onto spindles for subsequent use in the weaving process. Occasionally the yarn breaks during the spinning process, and an operator ties it back together. Some number of breaks is considered normal; however, too many breaks may mean that the yarn is of poor quality. In order to monitor this process, the quality-control manager randomly selects a spinning machine each hour and checks the number of breaks during a 15-minute period. Following is a summary of the observations for the past 20 hours. Construct a c-chart using 3 limits for this process and indicate if the process was out of control at any time.arrow_forwardAbout the OC curve for p chart, which statement is INCORRECT? Select one: a. None of those listed b. There is one particular point on the OC curve at which β=1-α c. The y-axis of the OC curve is β d. The maximum β exists when p is equal to the center line of the control chart e. β is computed based on binomial distributionarrow_forwardpoint on a control chart falls outside one of the controllimits, this suggests that the process variation is non random and should be investigated . a FALSE b TRUEarrow_forward
- At Quick Car Wash, the wash process is advertised to take less than 7 minutes. Consequently, management has set a target average of 390 seconds for the wash process. Suppose the average range for a sample of 10 cars is 11 seconds. Use the accompanying table to establish control limits for sample means and ranges for the car wash process. The UCL Subscript x overbar equals seconds and the LCL Subscript x overbar equals seconds. (Enter your responses rounded to two decimal places.)arrow_forwardAt Quick Car Wash, the wash process is advertised to take less than 7 minutes. Consequently, management has set a target average of 390 seconds for the wash process. Suppose the average range for a sample of 9 cars is 8 seconds. Use the accompanying table to establish control limits for sample means and ranges for the car wash process. LOADING... Click the icon to view the table of factors for calculating three-sigma limits for the x overbarx-chart and R-chart. Factors for calculating three-sigma limits for the x overbarx-chart and R-chart Size of Sample (n) Factor for UCL and LCL for x overbarx-chart (Upper A 2A2) Factor for LCL for R-Chart (Upper D 3D3) Factor for UCL for R-Chart (Upper D 4D4) 2 1.8801.880 00 3.2673.267 3 1.0231.023 00 2.5752.575 4 0.7290.729 00 2.2822.282 5 0.5770.577 00 2.1152.115 6 0.4830.483 00 2.0042.004 7 0.4190.419 0.0760.076 1.9241.924 8 0.3730.373…arrow_forwardAt Quick Car Wash, the wash process is advertised to take less than 7 minutes. Consequently, management has set a target average of 390 seconds for the wash process. Suppose the average range for a sample of 9 cars is 8 seconds. Use the accompanying table to establish control limits for sample means and ranges for the car wash process. LOADING... Click the icon to view the table of factors for calculating three-sigma limits for the x overbarx-chart and R-chart. Factors for calculating three-sigma limits for the x overbarx-chart and R-chart Size of Sample (n) Factor for UCL and LCL for x overbarx-chart (Upper A 2A2) Factor for LCL for R-Chart (Upper D 3D3) Factor for UCL for R-Chart (Upper D 4D4) 2 1.8801.880 00 3.2673.267 3 1.0231.023 00 2.5752.575 4 0.7290.729 00 2.2822.282 5 0.5770.577 00 2.1152.115 6 0.4830.483 00 2.0042.004 7 0.4190.419 0.0760.076 1.9241.924 8 0.3730.373…arrow_forward
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