Suppose that the prevention cost function is as given in Exercise 1-21. However, the unit appraisal cost is $2, with the cost function being linear in 1 q, implying a decrease in appraisal costs as quality improves. Further, the rework and external failure cost functions are given by Cr=5(1 q)/q and Ce= 85(1q)/q, respectively. Construct the total cost function as a function of q and graph it for levels of q in the range 0.80–0.98. What is the desirable operational level of quality? Data from Exercise 1-21: Suppose that the prevention and appraisal cost functions are given by Cp= 50q2 and Ca=10q, respectively, where q represents the degree of quality level (0< q< 1). The cost of reworking a unit is $5, and the cost of a customer obtaining a nonconforming product is $85. Assume that these cost functions are linear in 1 q. What is the desirable operational level of quality for this static situation? Discuss the appropriateness of the cost functions.
> 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
> Suppose that the prevention and appraisal cost functions are given by Cp= 50q2 and Ca=10q, respectively, where q represents the degree of quality level (0< q< 1). The cost of reworking a unit is $5, and the cost of a customer obtaining a nonconforming pr
> In the production of a part for a printer, four sequential operations are involved. Unit processing costs for the operations are $10, $6, $15, and $20, respectively. The first pass yields for each operation are 0.95, 0.90, 0.95, and 0.85, respectively. U
> The following data (in $/m^3) were obtained from a company that makes insulation for commercial buildings: direct labor, 20; direct materials, 30; indirect labor and materials, 30% of direct labor; fixed expenses, 25; administrative costs, 25; selling co
> A pharmaceutical company has obtained the following cost information (per 1000 tablets) based on the production of a drug in the past year: material, $150; direct labor, $100; energy, $50; overhead, 40% of direct labor and material. Presently, the proces
> Consider the hardware company in Exercise 1-15. The company is contemplating outsourcing of its complex monitor M2. Assume that all other information remains as given in Exercise 1-15. Information from Exercise 1-15: An assemble-to-order hardware company
> The settling of unwanted material in a mold is causing some defects in the output. Based on recent data, it is estimated that 5% of the output has one or more defects. In spot checking some parts, an inspector randomly selects two parts. Find the probabi
> An assemble-to-order hardware company has two types of central processing units (CPUs), C1 and C2, and two types of display monitors, M1 and M2. Unit C2 is slightly more complex than C1, as is M2 compared to M1. The annual production volume and direct co
> 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?
> Based on historical data, it is estimated that 12% of new products will obtain a profitable market share. However, if two products are newly introduced in the same year, there is only a 5% chance of both products becoming profitable. A company is plannin
> 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 5-11 shows the number who selected each plan. Th
> 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 α= 0.05. (b) Is ther
> The pH values of a dye for 30 samples taken consecutively over time are listed row wise: (a) Can we conclude that the sequence of pH values over time is non-random? Use α = 0.05. (b) Assume that dyes are produced in batches, with 10 random
> Using the call waiting time of customer data in Exercise 5-9, construct a stem-and-leaf plot. Construct a box plot and comment on the distribution. Are there any outliers? Construct a 95% confidence interval for the median. Data from Exercise 5-9: A ran
> 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 m
> A remote control unit has 40 components in series. The reliability of each component is 0.9994. What is the reliability of the remote control unit? If a redesign has 25 components in series, what is the reliability of the unit?
> A retail company has information on the time taken (in days) to fulfil an order, the value of the order (in $10,000), the number of different types of products in the order, and the store location. The data are shown in Table 13-8. (a) Find a simple regr
> Refer to the data in Table 13-9 on diabetic patients and the development of retinopathy. (a) Develop a regression model to predict the probability of development of retinopathy based on years of diabetes and gender of person. Is the model significant at
> Table 13-9 shows data on diabetic patients and the development of retinopathy. The gender of the person, number of years that the person has been diagnosed with diabetes (labelled as Years), and whether the person has developed retinopathy (Y = Yes; N =
> A financial institution is contemplating the offering of three different types of savings accounts. Its elects 100 customers randomly and obtains a response on which account each person would select. What statistical test would you use to determine if cu
> Refer to the data in Table 13-6 on obesity, gender, and occurrence of a heart attack. (a) Develop a regression model to predict the chance of a heart attack based on weight. Interpret the model coefficients. (b) Is the model significant using Î&plu
> Refer to the data in Table 13-8 on order fulfilment time. (a) You believe that there are differences, in general, in the value of orders by location of the store. Consequently, its impact on order fulfilment time may be influenced as such. Find the model
> Refer to the data in Table 13-8 on order fulfilment time. (a) You decide to develop a regression model using order value, number of products, and location of the retailer as predictors. Find the model equation. Is it significant at α =0.05?
> Refer to the data in Table 13-8 on order fulfilment time. (a) You decide to develop a regression model using order value and the number of products in the order as predictors. Find the model equation. Is it significant at α =0.05? (b) Find
> Refer to Exercise 13-9 and the corresponding data shown in Table 13-8. (a) Based on a scatterplot of order fulfillment time versus order value, you decide to fit a quadratic model in order value. What is the model equation? (b) What are values of R2 and
> Refer to Exercise 13-9 and the regression model of time to fulfil an order based on order value. Data from Exercise 13-9: A retail company has information on the time taken (in days) to fulfil an order, the value of the order (in $10,000), the number of
> Consider Exercise 12-50. Four factors (A, B, C, and D), each at three levels, are controlled in an experiment using an L9 orthogonal array. The output quality is classified as acceptable or unacceptable; unacceptable includes both the second-class and re
> In a textile processing plant the quality of the output fabric is believed to be influenced by four factors (A, B, C, and D), each of which can be controlled at three levels. The fabric is classified into three categories: acceptable, second-class, or re
> Consider Exercise 12-48. The design factors are A, B, C, and D, each at three levels. These are assigned to an orthogonal array (inner array) with the factors A, B, C, and D assigned to columns 1, 2, 3, and 4, respectively. Suppose that, in addition to t
> In a food processing plant, four design parameters, A, B, C, and D, each at three levels, have been identified as having an effect on the moisture content in packaged meat. Three noise factors, E, F, and G, each at two levels, are also to be investigated
> Data from a survey of customers are on an ordinal scale (1–7) regarding satisfaction with the services provided in a bank by three tellers. If we wish to determine if the degree of customer satisfaction is independent of the teller, what statistical test
> A travel agency is attempting to enter a market where several competitors currently exist. What are the various customer needs that they should address? How will quality be measured? As the company strives to improve its market share, discuss the impact
> Consider Exercise 12-46. With the assignment of factors, A, B, C, and D to columns 1, 2, 3, and 4, respectively, of an L9 orthogonal array, the output is as follows for another replication of the nine experiments: Determine the main effects. Plot the ave
> In a drilling operation, four factors (A, B, C, and D), each at three levels, are thought to be of importance in influencing the volume of crude oil pumped. Using an L9 orthogonal array, the factors A, B, C, and D are assigned to columns 1, 2, 3, and 4,
> A city library has established three factors (A, B, and C), each at three levels, that influence the satisfaction of their patrons. The library governance committee also believes that the interaction B × C is important. Using an orthogonal array, set up
> The tourism board of a large metropolitan area is seeking ways to promote tourism. They have identified five factors (A, B, C, D, and E) that they feel have an impact on tourist satisfaction. Factor C has four levels, and each of the other four factors h
> A baseball team manager believes that five factors (A, B, C, D, and E), each at two levels, are significant in affecting runs batted in. The manager believes that the interactions B× C and B × E are important. Show an experimental design using an orthogo
> The Environmental Protection Agency has identified four factors (A, B, C, and D), each at two levels, that are significant in their effect on the air pollution level at a photographic film production facility. The agency also feels that the interaction e
> Refer to Exercise 12-40. The restaurant is thinking of hiring more personnel to cut down the service time. However, the additional cost of increasing personnel is estimated to be $0.50 per customer. The results of sampling with the added personnel yield
> A restaurant believes that two of the most important factors that help it attract and retain customers are the price of the item and the time taken to serve the customer. Based on the price for similar items in other neighboring restaurants, it is estima
> Refer to Exercise 12-36. Suppose the manufacturer has the ability to centre the process such that the average thickness of the coating is at 0.005 mm, which is the target value. In doing so, the manufacturer estimates that the standard deviation of the p
> Refer to Exercise 12-36. Suppose that the manufacturer can rework the thickness prior to shipping the product at a cost of $2.00 per reel. What should the manufacturer’s tolerance be? Data from Exercise 12-36: A manufacturer of magnetic tapes is interes
> A county wishes to estimate the average income of people, where it is known that income levels vary quite a bit among the residents in sections of the county. What type of sampling scheme should be used?
> Refer to Exercise 12-36. The manufacturer is considering adopting a new process to reduce the variability in the thickness of coating. It is estimated that the additional cost for this improvement is $0.03 per linear meter. The annual production is 10,00
> A manufacturer of magnetic tapes is interested in reducing the variability of the thickness of the coating on the tape. It is estimated that the loss to the consumer is $10 per reel if the thickness exceeds 0.005 ±0.0004 mm. Each reel has 200 m of tape.
> Refer to Exercise 12-30. Factor A is the concentration of corn extract, factor B is the concentration of an ethylene-based compound, and factor C is the distillation temperature. Each factor will be controlled at two levels. Suppose the experimenter runs
> In a 2^5-2 fractional factorial experiment, using CDE and AB as the generators, find the treatment combinations. Find the aliases of the contrasts.
> Consider a 2^4 factorial experiment. Using BC as the defining contrast, find the treatment combinations in a 2^4–1 fractional factorial experiment. Find the aliases of the contrasts. How would it be possible to estimate the effect of the contrast BC? If
> In Exercise 12-31, use AB as the confounding factor to divide the experiment into two blocks. How would you estimate the effect of factor A? Data from Exercise 12-31: Consider a 2^4 factorial experiment. Set up a table of the coefficients for orthogonal
> Consider a 2^4 factorial experiment. Set up a table of the coefficients for orthogonal contrasts similar to Table 12-25. Write down the contrasts for estimating the main effects and the two-factor interactions. If the four-way interaction effect ABCD is
> In the search for a lower-pollution synthetic fuel, researchers are experimenting with three different factors, each controlled at two levels, for the processing of such a fuel. Factor A is the concentration of corn extract at 5% and 10%, factor B is the
> Write out the treatment combinations for a 2^4 factorial experiment.
