EBK OM
6th Edition
ISBN: 9781305888210
Author: Collier
Publisher: YUZU
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Chapter 16, Problem 4PA
Summary Introduction
Interpretation: Control chart using the Excel
Concept Introduction: x-bar chart is used to measure the statistical data of the industry. It is also one type of shewhart chart. The main process of the x-bar chart is to invigilate the arithmetic means of the given samples of the constant size.
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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
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…
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
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…
The weights of boxes of Oat Flakes within a large production lot are sampled each hour. Managers want to set control limits that include 99.73% of the sample means, and given is the population (process) standard deviation, which is 1.13.
You are in charge of randomly selecting four boxes each hour, for three hours. The data you collected is located in the table below:Using an Xbar Chart, what are the upper and lower control limits?
Sample
Avg. of 4 boxes
1
16.8
2
17.1
3
17.2
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- The weights of boxes of Oat Flakes within a large production lot are sampled each hour. Managers want to set control limits that include 99.73% of the sample means and given is the population (process) standard deviation, which is 1.13. You are in charge of randomly selecting four boxes each hour, for three hours. The data you collected is in the table below: Using an R Chart, what are the upper and lower control limits? Sample Lightest Obs. (n=4) Heaviest Obs. (n=4) Range (Ri) in difference 1 15.00 17.00 2.00 2 15.30 16.90 1.60 3 15.20 16.70 1.50arrow_forwardSteps 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 LIMITarrow_forwardIf a process is neither capable nor in control, which of the following is the first step to be taken? 1) Redesign the equipment 2) Remove sources of special causes of variation 3) Determine the process capability index 4) Remove common causes of variationarrow_forward
- A green belt is going to monitor the process by collecting more than 10 samples per group. Which of the following control charts would be most appropriate ? a. I-MR b. Xbar R c. X bar S d. np chart (Don't Hand writing in solution) .arrow_forwardSpecifications for a metal shaft are much wider than the machine used to make the shafts is capableof. Consequently, the decision has been made to allow the cutting tool to wear a certain amountbefore replacement. The tool wears at the rate of .004 centimeter per piece. The process has a naturalvariation, σ, of .02 centimeter and is normally distributed. Specifications are 15.0 to 15.2 centimeters.A three-sigma cushion is set at each end to minimize the risk of output outside of the specifications.How many shafts can the process turn out before tool replacement becomes necessary?arrow_forwardControl charts for X-bar and R, using a subgroup size of 5, are to be applied to control thecritical dimension of a certain manufacturing process. Specifications call for a nominal dimension of1,250.000 + 0.050 mm. The process is believed to have a σ of 0.015 mm Determine appropriate control limits for the X-bar and R charts. a) After 12 subgroups have been drawn and X-bar and R plotted on the charts, a computation of X-double bar give 1,250.015. b1) What is the probability that a value of X-bar will fall within the limits if this is the true value of the mean setting? b2) What is the probability that all 12values fall within the control limits? b) Make the necessary calculations to determine if the process can meet specifications by solvingfor Cp, Cpu, CpL, Cpk . Assume a normal distribution of product output. Illustrate how the processwould look like relative to the result of the computations of the process capability analysis.arrow_forward
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