Operations Management
17th Edition
ISBN: 9781259142208
Author: CACHON, Gérard, Terwiesch, Christian
Publisher: Mcgraw-hill Education,
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Chapter 9, Problem 4PA
Summary Introduction
To determine: The probability that the tire will either be too wide or too narrow.
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Webster Chemical’s nominal weight for filling tubes of caulk is 8.00 ounces ± 0.60 ounces. The target process capability ratio is 1.33. The current distribution of the filling process is centered on 8.054 ounces with a standard deviation of 0.192 ounces. Compute the process capability ratios Cp and Cpk to assess whether the filling process is capable and set properly.
The specifications for a gasket that installs between two engine parts calls for a thickness of 6.0 mm ± .2 mm. The standard deviation of the process is estimated to be 0.05 mm. The process is known to operate at a mean thickness of 6.1 mm
What are the upper and lower specification limits for the gasket?
What are the Cp and Cpk values for this process?
Is this process capable of producing the desired part?
SCENARIO B:
A woodcutting operation has a target (nominal) value of 200 inches and consistently averages 200.1 inches with a standard deviation of .05 inches. The design engineers
have established an upper specification limit of 200.25 and a lower specification limit of 199.75 inches.
Chapter 9 Solutions
Operations Management
Ch. 9 - Prob. 1CQCh. 9 - Prob. 2CQCh. 9 - Prob. 3CQCh. 9 - Prob. 4CQCh. 9 - Prob. 5CQCh. 9 - Prob. 6CQCh. 9 - Prob. 7CQCh. 9 - Prob. 8CQCh. 9 - Prob. 9CQCh. 9 - Prob. 10CQ
Ch. 9 - Prob. 11CQCh. 9 - Prob. 12CQCh. 9 - Prob. 13CQCh. 9 - Prob. 14CQCh. 9 - Prob. 15CQCh. 9 - Prob. 16CQCh. 9 - Prob. 17CQCh. 9 - Prob. 18CQCh. 9 - Prob. 1PACh. 9 - Prob. 2PACh. 9 - Prob. 3PACh. 9 - Prob. 4PACh. 9 - Prob. 5PACh. 9 - Prob. 6PACh. 9 - Prob. 7PACh. 9 - Prob. 8PACh. 9 - Prob. 9PACh. 9 - Prob. 10PACh. 9 - Prob. 11PACh. 9 - Prob. 12PACh. 9 - Prob. 1CCh. 9 - Prob. 2C
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- You are a food specialist in a company that specializes inrefrigerated delicacies, and one of your brands requires beingmaintained at a temperature of 5°C. You determine averagewater activity (aw) at this temperature to be 0.2. One day, you are informed that the cooling systems onone of the delivery trucks carrying your company’s productsmalfunctioned while en route to its destination and it would notbe fixed until the next delivery. The driver has informed you thatthe temperature in the delivery bay of the truck is averaging55°C. You estimate a heat of sorption (Q) of 19 kJ/mol. Calculate the water activity of the brand at this elevatedtemperature and comment on it’s integrity. Should the deliverystill push through? Or should the products be recalled anddisposedarrow_forwardSuppose that material hardness is normally distributed with a mean of 52 and a standard deviation of 1. Specification limits for hardness are from 45 to 55. What is Cp?arrow_forwardA metal fabricator produces connecting rods with an outer diameter that has a 1± 0.02 inch specification. A machine operator takes several sample measurements over time and determines the sample mean outer diameter to be 1.005 inches with a standard deviation of 0.003 inch. Calculate the process capability index for this example. Note: Round your answer to 3 decimal places. Process capability indexarrow_forward
- C-Spec, Incorporated is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 4 ± 0.003 inch. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 4.001 inches with a standard deviation of 0.002 inch. Calculate the capability index ( Cpk��� ) for this machine. Note: Round your answer to 3 decimal places. Should C-Spec use this machine to produce this part? multiple choice Yes Noarrow_forwardElon Corporation manufactures parts for an aircraft company. It uses a computerized numerical controlled (CNC) machining center to produce a specific part that has a design (nominal) target of 1.275 inches with tolerances of ±0.024 inch. The CNC process that manufactures these parts has a mean of 1.281 inches and a standard deviation of 0.008 inch. Which of the following statements is true concerning the process capability ratio and process capability index? O The process is off center and incapable. O The process is centered, but incapable. The process is capable and centered. O The process is capable, but off center.arrow_forwardBill Kime's bowling ball factory makes bowling balls of adult size and weight only. The standard deviation in the weight of a bowling ball produced at the factory is known to be 0.39 pounds. Each day for 24 days, the average weight, in pounds, of 9 of the bowling balls produced that day has been assessed as follows Day 1 2 3 4 5 6 Average (lb) 9.9 9.9 10.1 10.1 99 99 Day 7 8 9 10 11 12 Average (lb) Day Average (b) 13 14 15 16 17 18 10.1 10.0 10.0 10.1 10.1 10.0 9.9 10.1 10.1 10.0 10.1 10.1 Day 19 20 21 22 23 24 Average (lb) 99 10.0 10.1 9.9 10.0 10.0 a) Establish a control chart for monitoring the average weights of the bowling balls in which the upper and lower control limits are each two standard deviations from the mean What are the values of the control limits? Upper Control Limit (UCL)=b (Round your response to two decimal places)arrow_forward
- Discuss the basic differences between the mean absolute deviation and mean absolute percent error.arrow_forwardA manufacturing company produces steel rods. The length of these rods is critical to their customers. The company aims to manufacture rods with a mean length of 150 cm. However, due to variability in the manufacturing process, the lengths of the rods follow a normal distribution. The company's quality control department samples 30 rods and finds that they have a mean length of 151 cm and a standard deviation of 2 cm. Calculate the Process Capability Index (Cp) and the Process Performance Index (Ppk) for this process. Assume the customer's specification limits are 147 cm and 153 cm for the length of the rods.arrow_forwardDesign specifications require that a key dimension on a product measure 100kg plus and minus 3kg. If the value of the quality exceeds the target by the tolerance of 3kg on either side, the product will be likely to fail during the warranty period and cost $480 for repair. A process being considered for producing this product has a standard deviation of 1.5kg A) Compute the process capability ratio if the process is centered. Is it capable to meet the quality specification? Explain. B) Suppose the original process average shifts to 99kg, maintaining the current dispersion. Calculate the process capability index after the shift. Is it capable? C) What is the average loss per unit after the shift as in (part b)? Use Taguchi loss function for multi-products casearrow_forward
- Design specifications require that a key dimension on a product measure 100kg plus and minus 3kg. If the value of the quality exceeds the target by the tolerance of 3kg on either side, the product will be likely to fail during the warranty period and cost $480 for repair. A process being considered for producing this product has a standard deviation of 1.5kg A) Compute the process capability ratio if the process is centered. Is it capable to meet the quality specification? Explain. B) If the original process in (part A) is incapable, what should be the standard deviation of the process to make it capable? C) Suppose the original process average shifts to 99kg, maintaining the current dispersion. Calculate the process capability index after the shift. Is it capable? D) What is the average loss per unit after the shift as in (part c)? Use Taguchi loss function for multi-products casearrow_forwardA manufacturer is selling pharmaceuticals that have a weight specification 199.8 to 200.2 mg, with a target value of 200 mg. Before sending its next shipment, the company collects a large sample of product and determines the mean weight of the sample is 199.89 mg, with a standard deviation of 0.035 mg. The process capability index for the current process is ____. Round to three decimal places.arrow_forwardA manufacturing facility analyzes a lot-sample of 100 units out of a shipment of 10,000. The demodulator frequency is supposed to be within 53.5 and 54.5 MHz. The mean is 54.25 MHz with a standard deviation of 0.04 MHz. What is the CPK?arrow_forward
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