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 will be selected from each plant, what should the sample size be if the bound on the error of estimation is 40 minutes with a probability of 0.90? (b) If the unit sampling costs are less in plant 1 compared to plant 2 such that a sample that is twice as large could be selected from plant 1, what are the respective sample sizes? (c) Suppose that it is desired to detect a difference of 30 minutes in the lost time with a probability of 0.80. Assume that there is no significant difference in the standard deviations of lost time. For a chosen level of significance of 0.10, what should the sample size be assuming samples of equal size from both plants?
> Refer to Exercise 7-46. Construct an exponentially weighted moving-average chart using a weighting constant of 0.2 for the decision-making process and comment. Is the existing process capable of meeting a goal value of 12 weeks? Data from Exercise 7-46:
> Refer to Exercise 7-46. Demonstrate if the existing process in making a decision on loan applications is capable of meeting a goal value of 12 weeks. Assuming a normal distribution of the decision-making time, what proportion of the applications will not
> The time to evaluate and make a decision on mortgage loan applications is being examined in a financial institution. Twenty-five mortgage applications are selected from the previous month and the decision-making times, in days, are shown in Table 7-30. C
> 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 cer
> 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 3-15. (a) Construct a Hotelling’s T2 -chart and comment on process stability. Whic
> 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
> 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
> 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 non-conformance rate of 4%. Determine the ac
> 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?
> The percentage of potassium in a compound is expected to be within the specification limits of 18–35%. Samples of size 4 are selected, and the mean and range of 25 such samples are shown in Table 7-27. It is desirable for the process no
> The time from product inception and design to marketing and sales is important for application software in mobile devices. For the last 20 products, Table 7-26 shows such times (in weeks) for a software organization. Construct an appropriate control char
> Consider the data on the waiting time (seconds) of customers before speaking to a representative at a call center, shown in Exercise 5-9. Data from Exercise 5-9: A random sample of 50 observations on the waiting time (in seconds) of customers before sp
> 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. Data from Table 4-6:
> 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 s
> 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 sho
> 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 7-23. Construct a chart for the moving range of two success
> Explain the rationale behind placing the control limits at three standard deviations from the mean.
> 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
> 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 have The specifications on the bore size are 4.4 ±0.
> 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
> 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 7-20. Construct appropriate control charts and comment on
> Explain the difference between common causes and special causes. Give examples of each.
> Consider the hospitality industry. Describe special causes and common causes in this setting and discuss the role of quality control and quality improvement.
> The turnaround time (TAT) for a certain blood test in a laboratory in a health care facility is of interest. The mean and standard deviation of a random sample of 100 such tests are found to be 120 minutes and 20 minutes, respectively. Find the 3σ contro
> 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 t
> 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 averag
> 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
> Suppose 3σ control limits are constructed for the average temperature in a furnace. Samples 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
> 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 de
> The length of industrial filters is a quality characteristic of interest. Thirty samples, each of size 5, are chosen from the process. The data yield an average length of 110 mm, with the process standard deviation estimated to be 4 mm. (a) Find the warn
> The diameter of a part 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 proc
> 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 3σ control limits are used?
> Explain some causes that would make the control chart pattern follow a gradually increasing trend.
> Consider Exercise 5-27 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 s
> 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:
> Management is exploring the possibility of adding more agents at the check-in counter of an airline to reduce the waiting time of customers. Based on available information, the standard deviation of the waiting times is approximately 5.2 minutes. If mana
> 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
> 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
> 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 th
> 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 SBA wants to
> Summary data on ratings of patient satisfaction and importance for the survey item “waiting time prior to being seen by a physician” is shown in Table 5-16 for a total of 400 patients. Perceived satisfaction was rated
> Consider Table 5-15 on the summary of patient satisfaction ratings. The percentages in each rating category are based on a response from a total of 200 patients from a prior year. For the item waiting time prior to being seen by a physician, consider the
> What are some reasons for a process to go out of control due to a sudden shift in the level?
> Consider Table 5-15 on the summary of patient satisfaction ratings on survey items related to timeliness of operations. Suppose the percentages are based on a response from a total of 200 patients. Regarding the item on timeliness of nurse visits, can we
> Consider the five items on timeliness of operations as listed in Table 5-7. A summary of the survey responses on patient satisfaction for each item, by the percentage in each rating category, is shown in Table 5-15. Construct a stacked bar chart and disc
> Refer to Table 5-7 and the patient satisfaction survey form with 22 items. Data from Table 5-7: Patients were asked to rate their perceived level of satisfaction on a five-point ordinal Likert scale as shown. Additionally, patients were asked to rate t
> 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 1–5 was used with the following guidelines: 1, poor; 2, below
> 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 Ta
> A local hospital estimates that the number of patients admitted daily to the emergency room has a Poisson probability distribution with a mean of 4.0. What is the probability that on a given day: (a) only 2 patients will be admitted? (b) at most 6 patien
> In a lot of 200 electrical fuses, 20 are known to be nonconforming. A sample of 10 fuses is selected. (a) What is the probability distribution of the number of nonconforming fuses in the sample? What are its mean and standard deviation? (b) Using the bin
> The guidance system design of a satellite places several components in parallel. The system will function as long as at least one of the components is operational. In a particular satellite, 4 such components are placed in parallel. If the probability of
> A process is known to produce 5% nonconforming items. A sample of 40 items is selected from the process. (a) What is the distribution of the nonconforming items in the sample? (b) Find the probability of obtaining no more than 3 nonconforming items in th
> The probability of an electronic sensor malfunctioning is known to be 0.10. A random sample of 12 sensors is chosen. Find the probability that: (a) at least 3 will malfunction. (b) no more than 5 will malfunction. (c) at least 1 but no more than 5 will m
> State and explain each rule for determining out-of-control points.
> A university has purchased a service contract for its computers and pays $20 annually for each computer. Maintenance records show that 8% of the computers require some sort of servicing during the year. Furthermore, it is estimated that the average expen
> A company involved in making solar panels estimates that 3% of its product are nonconforming. If a random sample of 5 items is selected from the production output, what is the probability that none are nonconforming? That 2 are nonconforming? The cost of
> A pharmaceutical company making antibiotics has to abide by certain standards set by the Food and Drug Administration. The company performs some testing on the strength of the antibiotic. In a case of 25 bottles, 4 bottles are selected for testing. If th
> The following times (in minutes) to process hot-rolled steel are observed for a random sample of size 10: (a) Find the mean, median, and mode of the processing times. Interpret the differences between them. (b) Compute the range, variance, and standard d
> Two types of defects are observed in the production of integrated circuit boards. It is estimated that 6% of the boards have solder defects and 3% have some surface-finish defects. The occurrences of the two types of defects are assumed to be independent
> The number of times a Web server is accessed per minute is known to follow a Poisson distribution. A random sample of size 8, each over a minute, shows the number of times that the server is accessed as follows: 5, 3, 2, 0, 6, 1, 1, 2. Find a 90% confide
> 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
> 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
> 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 to
> 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, certa
> What are the benefits of using control charts?
> 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 characteri
> A company is investigating two potential vendors on the timeliness of their deliveries. A random sample of size10fromthefirstvendor produced an average delay time of 4.5 days with a standard deviation of2.3 days. A random sample of size 12 from the secon
> 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 o
> 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 i
> 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
> 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 captu
> Consider the data in Exercise 4-17 on the time (in minutes) to process hot-rolled steel for a sample of size 10. Data from Exercise 4-17: The following times (in minutes) to process hot-rolled steel are observed for a random sample of size 10: (a) Find
> 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 of8 natural fibers yields an average breaking strength of 540 kg with a standard deviati
> 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
> 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 emp
> Explain why it is important to obtain feedback from customers on both perceived satisfaction and importance of specified survey items.
> 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
> The mean time to assemble a product as found from a sample of size 40 is 10.4 minutes. The standard deviation of the assembly times is known to be 1.2 minutes. (a) Find a two-sided 90% confidence interval for the mean assembly time and interpret it. (b)
> Reinforced concrete beams are used in bridges. However, cracks develop in these beams and it has an accumulation effect over time. The time to failure of such bridges, in days, is modelled by a lognormal distribution, where the mean of the natural logari
> Refer to the electronic switch in Exercise 4-40. In order to improve the reliability of a system, three such additional switches are used on a standby basis. This means that only when a switch fails, another is activated, and so on. The system operates a
> An electronic switch has a constant failure rate of (10)-3 per hour. (a) What is the expected life of the switch? (b) What is the standard deviation of the life of the switch? (c) Find the probability that the switch will last at least 1200 hours. (d) Wh
> Vendor quality control is an integral part of a total quality system. A soft drink bottling company requires its vendors to produce bottles with an internal pressure strength of at least 300 kg/cm2. A vendor claims that its bottles have a mean strength o
> Refer to Exercise 4-37. Suppose that the machine is considered to be out of statistical control if the average diameter of a sample of 36 bearings is less than 34.75 mm or greater than 35.25 mm. (a) If the true mean diameter of all bearings produced is 3
> The diameter of bearings is known to have a mean of 35 mm with a standard deviation of 0.5 mm. A random sample of 36 bearings is selected. What is the probability that the average diameter of these selected bearings will be between 34.95 and 35.18 mm?
> The time to failure of a mechanical component under friction may be modelled by a Weibull distribution with γ= 20 days, β= 0.2, and α = 35 days. (a) What proportion of these components will fail within 30 days? (b) What is the expected life of the compon
> The time to failure of an electronic component can be described by a Weibull distribution with γ= 0, β= 0.25, and α= 800 hours. (a) Find the mean time to failure. (b) Find the standard deviation of the time to failure. (c) What is the probability of the
> A fast-food restaurant in an urban area experiences a higher traffic rate during the early morning and lunch hours. In order to conduct a customer satisfaction survey, discuss possible sampling procedures.
> A limousine service catering to a large metropolitan area has found that the time for a trip (from dispatch to return) is exponentially distributed with a mean of 30 minutes. (a) What is the probability that a trip will take more than an hour? (b) If a l
> The time to repair an equipment is known to be exponentially distributed with a mean of 45 min. (a) What is the probability of the machine being repaired within half an hour? (b) If the machine breaks down at 3 P.M. and a repairman is available immediate
> A component is known to have an exponential time-to-failure distribution with a mean life of 10,000 hours. (a) What is the probability of the component lasting at least 8000 hours? (b) If the component is in operation at 9000 hours, what is the probabili
> A company has been able to restrict the use of electrical power through energy conservation measures. The monthly use is known to be normal with a mean of 60,000 kWh (kilowatt-hour) and a standard deviation of 400 kWh. (a) What is the probability that th
> The specifications for the thickness of nonferrous washers are 1.0±0.04 mm. From process data, the distribution of the washer thickness is estimated to be normal with a mean of 0.98 mm and a standard deviation of 0.02 mm. The unit cost of rework is $0.10
> The breaking strength of a cable is known to be normally distributed with a mean of 4000 kg and a standard deviation of 25 kg. The manufacturer prefers that at least 95%of its product meet a strength requirement of 4050 kg. Is this requirement being met?
> The outside diameter of a part used in a gear assembly is known to be normally distributed with a mean of 40 mm and standard deviation of 2.5 mm. The specifications on the diameter are (36, 45), which means that part diameters between 36 and 45 mm are co
> The number of bank failures per year among those insured by the Federal Deposit Insurance Company has a mean of 7.0. The failures occur independently. What is the probability that: (a) there will be at least 4 failures in the coming year? (b) there will
> In an auto body shop, it is known that the average number of paint blemishes per car is 3. If 2 cars are randomly chosen for inspection, what is the probability that: (a) the first car has no more than 2 blemishes? (b) each of the cars has no more than 2
> The enter for Medicare and Medicaid Services (CMS) reimburses health care facilities at a fixed rate for patients of a certain diagnosis-related group (DRG). The facility must also demonstrate an acceptable level of performance at the aggregate level. Fo
> 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?
> An urban health care facility is interested in providing quality care at an affordable price to all patients. On average, the facility serves 500 patients monthly, with the average net contribution to profit being $400 per patient. Recently, a quality im
> Consider Exercise 1-22. Suppose that market share is strongly influenced by the level of quality, with the revenue function given by 90q2. What is the net profit function? What is the minimum desirable quality level to break even? Data from Exercise 1-2
