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Fundamentals of quality control and improvement 3rd edition Amitava mitra - Solutions

A company that dumps its industrial waste into a river has to meet certain restrictions. One particular constraint involves the minimum amount of dissolved oxygen that is needed to support aquatic life. A random sample of 10 specimens taken from a given location gives the following results of
The Occupational Safety and Health Administration (OSHA) mandates certain regulations that have to be adopted by corporations. Prior to the implementation of the OSHA program, a company found that for a sample of 40 randomly selected months, the mean employee time lost due to job-related accidents
Refer to Exercise 4-45. Suppose that the standard deviations of the values of lost time due to accidents before and after use of the OSHA program are unknown but are assumed to be equal. The first sample of size 40 gave a mean of 45 hours with a standard deviation of 3.8 hours. Similarly, the
A company is experimenting with synthetic fibers as a substitute for natural fibers. The quality characteristic of interest is the breaking strength. A random sample of 8 natural fibers yields an average breaking strength of 540 kg with a standard deviation of 55 kg. A random sample of 10 synthetic
Consider the data in Exercise 4-17 on the time (in minutes) to process hot-rolled steel for a sample of size 10. (a) Find a 98% confidence interval for the mean time to process hot-rolled steel. What assumptions do you have to make to solve this problem? (b) Find a 95% confidence interval for the
Price deregulation in the airline industry has promoted competition and a variety of fare structures. Prior to deciding on a price change, a particular airline is interested in obtaining an estimate of the proportion of the market that it presently captures for a certain city. A random sample of
Explain the different types of measurement scales, and give examples in the following situations:(a) Gallons of water to put out a fire by the fire department(b) Response time of an ambulance(c) Test score in an examination(d) Customer product preference expressed on a scale of 1 to 5(e)
An advertising agency is judged by the increase in the proportion of people who buy a particular product after the advertising campaign is conducted. In a random sample of 200 people prior to the campaign, 40 said that they prefer the product in question. After the advertising campaign, out of a
Two machines used in the same operation are to be compared. A random sample of 80 parts from the first machine yields 6 nonconforming ones. A random sample of 120 parts from the second machine shows 14 nonconforming ones.(a) Can we conclude that there is a difference in the output of the machines?
The precision of equipment and instruments is measured by the variability of their operation under repeated conditions. The output from an automatic lathe producing the diameter (in millimeters) of a part gave the following readings for a random sample of size 10:(a) Find a 90% confidence interval
A company is investigating two potential vendors on the timeliness of their deliveries. A random sample of size 10 from the first vendor produced an average delay time of 4.5 days with a standard deviation of 2.3 days. A random sample of size 12 from the second vendor yielded an average delay time
Twenty five patients of a certain diagnosis-related group were randomly selected, and their systolic blood pressure, blood glucose level, and total cholesterol level were measured. Upon administration of a certain drug, after 6 months the same characteristics were measured for the selected
Management is interested in increasing the efficiency of processing purchase orders. The time to process purchase orders, in days, was observed for 31 randomly selected customers and is shown in Table 4-6. Following a detailed study of the process, certain recommendations were adopted. Twenty-six
An insurance company wants to estimate the premium to be charged for a $200,000 homeowner's policy that covers fire, theft, vandalism, and natural calamities. Flood and earthquakes are not covered. The company has estimated from historical data that a total loss may happen with a probability of
An insertion machine in printed circuit board manufacturing has an insertion rate of 5000 parts per hour. From historical data, it is known that the error rate is 300 parts per million parts inserted. The errors occur randomly and independently. (a) What is the probability of observing no more than
A wave soldering process is used in printed circuit boards. It is known that the error rate is 200 per million solders, where errors occur randomly and independently. A given board requires 5000 solders. (a) What is the probability of 3 or more errors in a circuit board? (b) Find the probability of
Distinguish between the use of the mean, median, and mode in quality control applications. When do you prefer to use the trimmed mean?
State the null and alternative hypotheses in the following situations by defining the parameters used. Also, state any assumptions that you need to make to conduct the test: (a) The Postal Service wishes to prove that the mean delivery time for packages is less than 5 days. (b) A financial
Distinguish between a hypergeometric and a binomial random variable.
A 95% confidence interval for the mean thickness of a part in millimeters is (10.2, 12.9). Interpret this interval.
An automobile manufacturing company is attempting to cope with rising health care costs of its employees. It offers three types of plans. Based on a random sample of 200 employees selected last year, Table 5-7 shows the number that selected each plan. The same table also shows, for a random sample
The impact of three different advertising techniques is being studied by a marketing firm. Sales, in thousand dollars, categorized in four groups are shown for each advertising technique for 200 randomly selected customers, exposed to each technique, in Table 5-8. Can we conclude that the
A survey asked customers to rate their overall satisfaction with a service company as well as the speed in responding to their requests. For both questions, a rating scale of 1 to 5 was used with the following guidelines: 1, poor; 2, below average; 3, above average; 4, good; and 5, excellent. Table
The Small Business Administration (SBA) wishes to estimate the mean annual sales of companies that employ fewer than 20 persons. Historical data suggest that the standard deviation of annual sales of such companies is about $5500 (a) If the SB A wants to estimate mean annual sales to within $1000
A company's quality manager wants to estimate, with a probability of 0.90, the copper content in a mixture to within 4%. (a) How many samples must be selected if no prior information is available on the proportion of copper in the mixture? (b) Suppose that the manager has made some changes in the
The personnel manager wants to determine if there is a difference in the average time lost, due to absenteeism, between two plants. From historical data, the estimated standard deviations of lost time are 200 and 250 minutes, respectively, for plants 1 and 2. (a) Assuming that equal sample sizes
By incorporating certain process improvement methods, a company believes that it has reduced the proportion of nonconforming product and wishes to test this belief. (a) If the operations manager selects an error bound for the difference in the proportion nonconforming before and after
The production of nonconforming items is of critical concern because it increases costs and reduces productivity. Identifying the causes behind the production of unacceptable items and taking remedial action are steps in the right direction. To begin, we decide to estimate the proportion of
It is desired to estimate the average consumer spending on durable goods, annually, in a defined geographical region. Spending patterns are influenced by disposable income. Based on county tax records, the population has been segmented into three groups: (1) annual income < $50,000; (2) between
Consider Exercise 5-21 and suppose that a cluster sample is chosen, where the randomly groups selected are (2) and (3). The total of all observations from group 2 is $7,100,000, while that from group 3 is $15,200,000. (a) Estimate the mean spending and its standard error. (b) Find a bound on the
Explain the relationship between a type I error, power, degree of difference that one wishes to detect in a parameter value, and sample size. How can a type I error be reduced and the power be increased, for a given difference in the parameter?
Explain type I and type II errors in the context of sampling from customers' accounts to identify billing errors in a large retail store. What are the associated costs of these two types of errors?
A random sample of 50 observations on the waiting time (in seconds) of customers before speaking to a representative at a call center is as follows:(a) Construct a histogram and comment on the process. (b) What assumptions are necessary to test if the mean waiting time is less than 32 seconds? (c)
Using the call waiting time of customers data in Exercise 5-8, construct a stem-andleaf plot. Construct a box plot and comment on the distribution. Are there any outliers? Construct a 95% confidence interval for the median.
Explain some specific parametric tests that require the distributional assumption of normality. What do you do if the assumption is not satisfied?
The pH values of a dye for 30 samples taken consecutively over time are listed rowwise:(a) Can we conclude that the sequence of pH values over time is nonrandom? Use Î± = 0.05. (b) Assume that dyes are produced in batches, with 10 random samples taken from each of three batches.
Percentage investment in new-product development is monitored for a pharmaceutical company, by quarter. The observations are listed row-wise:(a) Can we conclude that the sequence of investment percentages is random? Use Î± = 0.05. (b) Is there clustering? Is there a trend? Use a =
State and explain each rule for determining out-of-control points.
What is meant by an overall type I error rate? If Rules 1,2, and 3 of this chapter are used simultaneously, assuming independence, what is the probability of an overall type I error if 3ó control limits are used?
The diameter of cotter pins produced by an automatic machine is a characteristic of interest. Based on historical data, the process average diameter is 15 mm with a process standard deviation of 0.8 mm. If samples of size 4 are randomly selected from the process: (a) Find the 1σ and 2σ control
The length of industrial filters is a quality characteristic of interest. Thirty samples, each of size 5, are chosen from the process. The data yields an average length of 110 mm, with the process standard deviation estimated to be 4 mm. (a) Find the warning limits for a control chart for the
The tensile strength of nonferrous pipes is of importance. Samples of size 5 are selected from the process output, and their tensile strength values are found. After 30 such samples, the process mean strength is estimated to be 3000 kg with a standard deviation of 50 kg. (a) Find the 1σ and 2σ
Suppose 3σ control limits are constructed for the average temperature in a furnace. Sample of size 4 were selected with the average temperature being 5000°C and a standard deviation of 50°C. (a) Find the 3σ control charts. (b) Suppose that Rules 2 and 3 are used simultaneously to determine
A manager is contemplating using Rules 1 and 4 for determining out-of-control conditions. Suppose that the manager constructs 3σ limits. (a) What is the overall type I error probability assuming independence of the rules? (b) On average, how many samples will be analyzed before detecting a change
The time to deliver packaged containers by a logistics company is found from samples of size 4. The mean and standard deviation of delivery times is estimated to be 140 hours and 6 hours, respectively. (a) Find the 2σ and 3σ control limits for the average delivery time. (b) Explain a type I and
Explain the difference between common causes and special causes. Give examples of each.
A health care facility is monitoring daily expenditures for a certain diagnosis-related group (DRG). Individual observations are selected. After 50 samples, the average and standard deviation of daily expenditures (in hundreds of dollars) are estimated to be 15 and 2, respectively. (a) Find the 3ó
Explain the rationale behind placing the control limits at 3 standard deviations from the mean.
Define and explain type I and type II errors in the context of control charts. Are they related? How does the choice of control limits influence these two errors?
What are warning limits, and what purpose do they serve?
What is the utility of the operating characteristic curve? How can the discriminatory power of the curve be improved?
Describe the role of the average run length (ARL) in the selection of control chart parameters. Explain how ARL influences sample size.
Discuss the relationship between ARL and type I and II errors.
How are rational samples selected? Explain the importance of this in the total quality systems approach.
What are the advantages and disadvantages of using variables rather than attributes in control charts?
A financial institution wants to improve proposal preparation time for its clients. Discuss the actions to be taken in reducing the average preparation time and the variability of preparation times.
Control charts are maintained on individual values on patient recovery time for a certain diagnosis-related group. What precautions should be taken in using such charts and what are the assumptions?
Explain the concept of process capability and when it should be estimated. What is its impact on nonconformance? Discuss in the context of project completion time of the construction of an office building.
What are the advantages and disadvantages of cumulative sum charts compared to Shewhart control charts?
What are the conditions under which a moving-average control chart is preferable? Compare the moving-average chart with the geometric moving-average chart.
Discuss the appropriate settings for using a trend control chart.
Discuss the appropriate setting for using a modified control chart and an acceptance control chart. Compare and contrast the two charts.
What is the motivation behind constructing multivariate control charts? What advantages do they have over control charts for individual characteristics?
A soft drink bottling company is interested in controlling its filling operation. Random samples of size 4 are selected and the fill weight is recorded. Table 7-17 shows the data for 24 samples. The specifications on fill weight are 350 ± 5 grams (g). Daily production rate is 20,000
Describe the use of the Pareto concept in the selection of characteristics for control charts.
A major automobile company is interested in reducing the time that customers have to wait while having their car serviced with one of the dealers. They select four customers randomly each day and find the total time that each customer has to wait (in minutes) while his or her car is serviced. From
Flight delays are of concern to passengers. An airline obtained observations on the average and range of delay times of flights (in minutes), each chosen from a sample of size 4, as shown in Table 7-18. Construct appropriate control charts, and comment on the performance level. What are the chances
In a textile company, it is important that the acidity of the solution used to dye fabric be within certain acceptable values. Data values are gathered for a control chart by randomly taking four observations from the solution and determining the average pH value and range. After 25 such samples,
The bore size on a component to be used in assembly is a critical dimension. Samples of size 4 are collected and the sample average diameter and range are calculated. After 25 samples, we haveThe specifications on the bore size are 4.4 ± 0.2 mm. The unit costs of scrap and rework are $2.40
The time to be seated at a popular restaurant is of importance. Samples of five randomly selected customers are chosen and their average and range (in minutes) are calculated. After 30 such samples, the summary data values are(a) Find the - and Ã„-chart control limits. (b) Find the
The thickness of sheet metal (mm) used for making automobile bodies is a characteristic of interest. Random samples of size 4 are taken. The average and standard deviation are calculated for each sample and are shown in Table 7-19 for 20 samples. The specification limits are 9.95 ± 0.3 mm. (a)
Light bulbs are tested for their luminance, with the intensity of brightness desired to be within a certain range. Random samples of five bulbs are chosen from the output, and the luminance is measured. The sample mean and the standard deviation s are found. After 30 samples, the following summary
The advertised weight of frozen food packages is 16 (oz) and the specifications are 16 ± 0.3 oz. Random samples are of size 8 are selected from the output and weighted. The sample mean and standard deviation are calculated. Information on 25 such samples yields the following(a) Determine the
The baking time of painted corrugated sheet metal is of interest. Too much time will cause the paint to flake, and too little time will result in an unacceptable finish. The specifications on baking time are 10 ± 0.2 minutes. Random samples of size 6 are selected and their baking times
The level of dissolved oxygen in water was measured every 2 hours in a river where industrial plants discharge processed waste. Each observation consists of four samples, from which the sample mean and range of the amount of dissolved oxygen in parts per million are calculated. Table 7-20 shows the
Discuss the preliminary decisions that must be made before you construct control chart. What concepts should be followed when selecting rational samples?
In a gasoline-blending plant, the quality of the output as indicated by its octane rating is measured for a sample taken from each batch. The observations from 20 such samples are shown in Table 7-21. Construct a chart for the moving range of two successive observations and a chart for
Automatic machines that fill packages of all-purpose flour to a desired standard weight need to be monitored closely. A random sample of four packages is selected and weighed. The average weight is then computed. Observations from 15 such samples are shown in Table 7-22. The desired weight of
The bending strength of the poles is a consideration to a manufacturer of fiberglass fishing rods. Samples are chosen from the process, and the average bending strength of four samples is found. The target mean bending strength is 30 kg, with a process standard deviation of 0.8 kg. Suppose that it
The average time (minutes) that a customer has to wait for the arrival of a cab after calling the company has been observed for random samples of size 4. The data for 20 such samples are shown in Table 7-23. Previous analysis gave the upper and lower control limits for an X-chart when the process
Consider Exercise 7-33 which deals with the average wait time for the arrival of a cab. Using the data in Table 7-23, construct a geometric moving-average control chart. Use a weighing factor of 0.10. What conclusions can you draw from the chart? How is it different from the moving-average control
Consider the data on purchase order processing time for customers shown in Table 4-6. Construct an individuals and a moving-range chart on the data before process improvement changes are made, and comment on process stability.
Consider the data on the waiting time (seconds) of customers before speaking to a representative at a call center, shown in Exercise 5-8. The data, in sequence, are to be read across the row, before moving to the next row. (a) Construct an individuals and moving-range chart, and comment on the
In an injection molding process, the die wears out gradually. To account for this wear, it is suggested that a trend chart be constructed for the outside diameter of the component produced. Samples of size 5 are selected and the sample average X and range R are found. The results of 20 such samples
The percentage of potassium in a compound is expected to be within the specification limits of 18 to 35%. Samples of size 4 are selected, and the mean and range of 25 such samples are shown in Table 7-25. It is desirable for the process nonconformance to be within 1.5%. If the acceptable level of
Refer to Example 7-13 and the data for the nitrogen content in a certain fertilizer mix. If it is desired that the proportion nonconforming be within 0.5% and the level of Type I error be limited to 0.025, find the modified control limits for the process mean.
Discuss specific characteristics that could be monitored through variables control charts, the form of data to collect, and the appropriate control chart in the following situations: (a) Waiting time to check in baggage at an airport counter (b) Product assembly time in a hardware company (c) Time
Refer to Exercise 7-38 and the data for the percentage of potassium content in a compound. Suppose that we wish to detect an out-of-control condition with a probability of 0.90 if the process is producing at a nonconformance rate of 4%. Determine the acceptance control chart limits
Refer to Example 7-14. If the nonconformance production rate is 2% and we wish to detect this with a probability of 0.98, what should be the acceptance control chart limits?
A component to be used in the assembly of a transmission mechanism is manufactured in a process for which the two quality characteristics of tensile strength (X1) and diameter (X2) are of importance. Twenty samples, each of size 4, are obtained from the process. For each component, measurements on
It is desired to monitor project completion times by analysts in a consulting company. The magnitude and complexity of the project influence the completion time. It is also believed that the variability in completion time increases with the magnitude of the completion time. Table 7-27 shows recent
Consider the data on the parameters in a chemical process of temperature, pressure, proportion of catalyst, and pH value of mixture as indicated in Table 3-16. (a) Construct a Hotelling's T2-chart and comment on process stability. Which process parameters, if any, would you investigate further? (b)
Consider the data on 25 patients, of a certain diagnosis-related group, on systolic blood pressure, blood glucose level, and total cholesterol level as shown in Table 4-5. The table shows values on these variables before and after administration of a certain drug. Assume that these variables are
What are some considerations in the interpretation of control charts based on standard values? Is it possible for a process to be in control when its control chart is based on observations from the process but to be out of control when the control chart is based on a specified standard? Explain.
A start-up company, promoting the development of new products, can afford only a few observations from each product. Thus, a critical quality characteristic is selected for monitoring from each product. What type of control chart would be suitable in this context? What assumptions are necessary?
Patient progress in a health care facility for a certain diagnosis-related group have a few vital characteristics (systolic blood pressure, diastolic blood pressure, total cholesterol, weight) monitored over time. The characteristics, however, are not independent of each other. Target values for
Explain the difference in interpretation between an observation falling below the lower control limit on an -chart and one falling below the lower control limit on an R-chait. Discuss the impact of each on the revision of control charts in the context of response time to fire alarms.
A new hire has been made in a management consulting firm and data are monitored on response time to customer queries. Discuss what the patterns on an - and /?-chart might look like as learning on the job takes place.
Distinguish between a nonconformity and a nonconforming item. Give examples of each in the following contexts: (a) Financial institution (b) Hospital (c) Microelectronics manufacturing (d) Law firm (e) Nonprofit organization
Discuss the impact of the control limits on the average run length and the operating characteristic curve.

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