Operations Management
13th Edition
ISBN: 9781259667473
Author: William J Stevenson
Publisher: McGraw-Hill Education
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Chapter 10, Problem 16P
Summary Introduction
To determine: The number of replacement needed.
Introduction: Quality is a measure of excellence or a state of being free from deficiencies, defects and important variations. It is obtained by consistent and strict commitment to certain standards to attain uniformity of a product to satisfy consumers’ requirement.
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Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean
and the range of this diameter have been as follows:
a) What is the value of x?
=
x= 155.56 mm (round your response to two decimal places).
b) What is the value of R?
R 4.48 mm (round your response to two decimal places).
c) What are the UCL; and LCL; using 3-sigma?
Day
1
2
3
4
5
Upper Control Limit (UCL) = 156.94 mm (round your response to two decimal places).
Lower Control Limit (LCL-) = 154.18 mm (round your response to two decimal places).
d) What are the UCLR and LCLR using 3-sigma?
Upper Control Limit (UCL) = 7.96 mm (round your response to two decimal places).
Mean x
(mm)
154.9
153.2
155.6
155.5
158.6
Range R
(mm)
4.0
4.8
3.9
5.0
4.7
Lower Control Limit (LCL) = 1.00 mm (round your response to two decimal places).
e) If the true diameter mean should be 155 mm and you want…
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.
A metal fabricator produces connecting rods with an outer diameter that has a 1 ± 0.04 inch specification. A machine operator takes several sample measurements over time and determines the sample mean outer diameter to be 1.003 inches with a standard deviation of 0.020 inch. Calculate the process capability index.
Chapter 10 Solutions
Operations Management
Ch. 10.2 - A potato chip is a delicate thing Fragile A pound...Ch. 10.2 - A potato chip is a delicate thing Fragile A pound...Ch. 10.5 - It's estimated that more than 7 000 hospital...Ch. 10.5 - It's estimated that more than 7 000 hospital...Ch. 10 - Prob. 1DRQCh. 10 - Prob. 2DRQCh. 10 - Prob. 3DRQCh. 10 - Prob. 4DRQCh. 10 - Prob. 5DRQCh. 10 - Prob. 6DRQ
Ch. 10 - Prob. 7DRQCh. 10 - Prob. 8DRQCh. 10 - Prob. 9DRQCh. 10 - Prob. 10DRQCh. 10 - Prob. 11DRQCh. 10 - Prob. 12DRQCh. 10 - Prob. 13DRQCh. 10 - Prob. 14DRQCh. 10 - Prob. 15DRQCh. 10 - Prob. 16DRQCh. 10 - Prob. 1TSCh. 10 - Prob. 2TSCh. 10 - Prob. 3TSCh. 10 - Prob. 1CTECh. 10 - Prob. 2CTECh. 10 - Prob. 3CTECh. 10 - Prob. 4CTECh. 10 - Prob. 1PCh. 10 - Prob. 2PCh. 10 - Prob. 3PCh. 10 - Prob. 4PCh. 10 - Prob. 5PCh. 10 - Prob. 6PCh. 10 - Prob. 7PCh. 10 - Prob. 8PCh. 10 - Prob. 9PCh. 10 - Prob. 10PCh. 10 - Prob. 11PCh. 10 - Prob. 12PCh. 10 - Prob. 13PCh. 10 - Prob. 14PCh. 10 - Prob. 15PCh. 10 - Prob. 16PCh. 10 - Prob. 17PCh. 10 - A production process consists of a three-step...Ch. 10 - Prob. 19PCh. 10 - Prob. 20PCh. 10 - Prob. 21PCh. 10 - Prob. 22PCh. 10 - Prob. 23PCh. 10 - Prob. 24PCh. 10 - Prob. 25PCh. 10 - Prob. 26PCh. 10 - Prob. 27PCh. 10 - Prob. 28PCh. 10 - Prob. 29PCh. 10 - Prob. 1.1CQCh. 10 - Prob. 2.1CQCh. 10 - Prob. 2.2CQCh. 10 - Prob. 2.3CQCh. 10 - Prob. 2.4CQ
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- A company producing printed circuit boards is using a c-chart with an L = 2.75 to monitor the lamination process. The process is in-control and the data show that average number of defects per inspection unit of 100 boards is 2.5. Unknowingly the process mean shifts to 4.5. What is the probability the shift will be caught on the next process sample?arrow_forwardAt 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_forwardNorthshore hospital surgeon, Bill, wants to build 3-sigma x- bar control limits for the open heart surgery. The target value for the mean of the process (x-bar) is 10 units, and the standard deviation of the process is 8. If samples of size 16 are to be taken, what will be the upper and lower control limits, respectively? Question 33 options: 8 and 12 16 and 4 -8 and 28 18 and 6 16 and 4arrow_forward
- Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: a) What is the value of x? x= 156.76 mm (round your response to two decimal places). b) What is the value of R? Day 1 2 3 4 5 Mean x (mm) 158.9 155.2 155.6 157.5 156.6 R = 4.40 mm (round your response to two decimal places). c) What are the UCL and LCL using 3-sigma? Upper Control Limit (UCL) = mm (round your response to two decimal places). Range R (mm) 4.2 4.4 4.3 4.8 4.3 Çarrow_forwardAn insurance company samples claim forms for errors created by its employees as well as the amount of time it takes to process a claim. a. When the process is in control, the proportion of claims with an error is .033. A p chart has LCL = 0 and UCL = .068. Plot the following seven sample results: .035, .062, .055, .049, .058, .066, and .055. Comment on whether there might be concern about the quality of the process.arrow_forwardAn Insurance company samples claim forms for errors created by its employees as well as the amount of time it takes to process a claim. a. When the process is in control, the proportion of claims with an error is .033. A p chart has LCL = 0 and UCL = .068. Plot the following seven sample results: .035, .062, .055, .049, .058, .066, and .055. Comment on whether there might be concern about the quality of the process. Process should be Select All points are Select ; however, all points are also Select the process proportion defective. b. An 2 chart for the mean processing time has LCL = 22.2 and UCL = 24.5. The mean is μ = 23.35 when the claim process is in control. Plot the following seven sample results: 22.4, 22.6, 22.65, 23.2, 23.4, 23.85, and 24.1. Comment on whether there might be concern about the quality of the process. Process should be Select All points are Select yet the trend in points show a movement or shift toward UCL out-of-control point.arrow_forward
- Specifications for a part for a 3-D printer state that the part should weigh between 24 and25 ounces. The process that produces the parts has a mean of 24.5 ounces and a standard deviation of .2 ounce. The distribution of output is normal. What percentage of parts will not meet the weight specs? Within what values will 95.44 percent of the sample means of this process fall if samples of n = 16 are taken and the process is in control (random)? Using the control limits from part b, would the following sample means be in control? 24.52, 24.53, 24.44, 24.51, 24.41, 24.39 An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approxi- mately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations. Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control. Given the following sample means—1.005,…arrow_forwardSouthern Mills Company 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. Number of Number of Sample Breaks Sample Breaks 1 3 11 2 12 4 3 4 13 6 1 14 7 5 5 15 8 6 3 16 6 7 2 17 5 8 4 18 7 19 8 10 2 20 6arrow_forwardA can filling process at a beverage manufacturing factory is assumed to be in control with limits of 84 ±3 had sample averages for the x-bar chart of the following:87.1,87, 87.2, 89, 90, 88.5, 89.5, and 88. Which of the following statement ?below are correct Not enough information to determine .a O None is correct b O Process mean is in-control .c O Process mean is out-of-control .d O أخل اختياري 4) E ENG acerarrow_forward
- 50 motor generators are inspected per day from a stable process. The best estimate of the fraction of nonconforming is 0.076. Determine the centeral line and control limits. On a particular day, 5 nonconforming generators were discovered. Is this process in or out of control? For the information given in the problem, construct a np-chartarrow_forwardSpecifications for a metal shaft are much wider than the machine used to make shafts is capable of. Consequently, the decision has been made to allow the cutting tool to wear a certain amount before replacement. The tool wears at the rate of 0.004 centimeter per piece. The process has a natural variation, o, of 0.010 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. Wear rate 3σ 1 30 Starting Ending Lower specification process Upper specification process mean mean Number of shafts How many shafts can the process turn out before tool replacement becomes necessary? (See diagram.) (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Number of shafts piecesarrow_forwardThe specifications for a plastic liner for a concrete highway project calls for thickness of 5.0 mm ± 0.10 mm. The standard deviation of the process is estimated to be 0.02 mm. The upper specification limit for this product = mm (round your response to three decimal places).arrow_forward
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