EBK PRODUCTION AND OPERATIONS ANALYSIS
7th Edition
ISBN: 9781478628385
Author: Olsen
Publisher: WAVELAND PRESS (ECONTENT)
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Chapter 12, Problem 60AP
Summary Introduction
Interpretation:
Manufacturer who would be at advantage if the plan were adopted.
Concept Introduction: Poisson distribution is the probability distribution of discrete random variable series in which frequency of outcomes is calculated in a given period of time.
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In the past, Alpha Corporation has not performed incoming quality control inspections but has taken the word of its vendors. However, Alpha has been having some unsatisfactory experience recently with the quality of purchased items and wants to set up sampling plans for the receiving department to use. For a particular component, X, Alpha has a lot of tolerance percentage defective of 10 percent. Zenon Corporation, from which Alpha purchases this component, has an acceptable quality level in its production facility of 3 percent for component X. Alpha hasa consumer’s risk of 10 percent and Zenon has a producer’s risk of 5 percent.a. When a shipment of product X is received from Zenon Corporation, what sample size should the receiving department test?b. What is the allowable number of defects in order to accept the shipment?
In a sausage factory, quality managers are studying the compliance of the sausages with the requirements. Any sausage having pin holes, air pockets, deformation or breakage in its casings is counted as defective and total number of such defective sausages alone is noted in each shift. The following data represents the number of defective sausages in samples of 200 sausages taken from 10 shifts.
Sample
Defectives
Percent Defective
1
40
20%
2
28
14%
3
15
8%
4
23
(a)
5
20
10%
6
21
11%
7
19
10%
8
15
8%
9
16
8%
10
17
9%
Calculate the value for (a) in the table above.
Calculate p-bar based on the samples above.
What is the UCL and LCL for a p chart based on the data provided and a desired control level of 99.74%?
Use your control limits from part b along with the data provided to draw a p-chart.
Is the process in control? Why or why not? If not in control, suggest some potential reasons.
Using samples of 200 credit card statements, an auditor found the following:
Sample 1 2 3 4
Number with errors 4 2 5 9
a. Determine the fraction defective in each sample.
b. If the true fraction defective for this process is unknown, what is your estimate of it?
c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size?
d. What control limits would give an alpha risk of .03 for this process? Page 457
e. What alpha risk would control limits of .047 and .003 provide?
f. Using control limits of .047 and .003, is the process in control?
g. Suppose that the long-term fraction defective of the process is known to be 2 percent. What are the values of the mean and standard deviation of the sampling distribution?
h. Construct a control chart for the process, assuming a fraction defective of 2 percent, using two-sigma control limits. Is the process in control?
Can you show me the steps and formulas using excel
Chapter 12 Solutions
EBK PRODUCTION AND OPERATIONS ANALYSIS
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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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.Similar questions
- A company employs the following sampling plan: It draws a sample of 10 percentof the lot being inspected. If 1 percent or less of the sample is defective, the lot isaccepted. Otherwise the lot is rejected. c. If a lot contains 10,000 items of which 200 are defective, what is the probability that the lot is accepted?arrow_forwardWhy are convenience samples not desirable? Give ONE example of where a convenience sample may not be desirable.arrow_forwardJason's house was built in 1968. He's looking to sell his house in the next 6 months, but first wants to be sure there are no material defects with the house. What should Jason test for first? O Electrical charge in each outlet. Lead-based paint since his house was built prior to 1978. O Water temperatures in the bathrooms. • Argon gas since his house was built prior to 1988.arrow_forward
- Using samples of 200 credit card statements, an auditor found the following:Sample 1 2 3 4Number with errors 4 2 5 9a. Determine the fraction defective in each sample.b. If the true fraction defective for this process is unknown, what is your estimate of it?c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size?d. What control limits would give an alpha risk of .03 for this process?e. What alpha risk would control limits of .047 and .003 provide?f. Using control limits of .047 and .003, is the process in control?g. Suppose that the long-term fraction defective of the process is known to be 2 percent. What arethe values of the mean and standard deviation of the sampling distribution?h. Construct a control chart for the process, assuming a fraction defective of 2 percent, using twosigma control limits. Is the process in control?arrow_forwardA researcher wishes to estimate the proportion of fish in a certain lake that is inedible due to pollution of the lake. How large a sample should be tested in order to be 99% confident that the true proportion of inedible fish is estimated to within 8%?arrow_forwardA quality analyst wants to construct a sample mean chart for controlling a packaging process. Each day last week, he randomly selected four packages and weighed each. The raw data (in ounces) from that quality control activity appear below. Weight Day Package 1 Package 2 Package 3 Package 4 Monday 23 22 23 24 Tuesday 23 21 19 21 Wednesday 20 19 20 21 Thursday 18 19 20 19 Friday 18 20 22 20 What is the average of sample ranges in the random samples? Must compute each value in 2 dec pl.arrow_forward
- A sampling plan is desired to have a producer's risk of 0.10 at AQL -0.8% and a consumer's risk of 0.05 at LQL-7.5% nonconforming Find the single sampling plan that meets the consumer's stipulation and comes as close as possible to meeting the producer's stipulation.arrow_forwardA company employs the following sampling plan: It draws a sample of 10 percentof the lot being inspected. If 1 percent or less of the sample is defective, the lot isaccepted. Otherwise the lot is rejected.b. If a lot contains 1,000 items of which 20 are defective, what is the probabilitythat the lot is accepted?arrow_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_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_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_forwardDesign the Single Sampling Plan (SSP) that will accept 95% of the lots containing 2% defective parts and will accept only 5% of the lots containing 9% defective parts.arrow_forward
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