Question: Management is interested in increasing the
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 customers were randomly selected and their purchase order processing times are shown after the process improvement changes.
(a) Find the mean, standard deviation, skewness coefficient, kurtosis coefficient, and interquartile range of the processing time prior to process changes and comment on the values.
(b) Find the mean, standard deviation, skewness coefficient, kurtosis coefficient, and interquartile range of the processing time after the process changes and comment on the values.
(c) Find a 95% confidence interval for the mean processing time prior to process changes.
(d) Can we conclude that the mean processing time, before the process changes, is less than 10.5 days? Use α= 0.02. What is the p-value? If α = 0.10, what is your decision? What does this imply?
(e) Can we conclude that the mean processing time, after the process changes, is less than 8.5 days? Use α = 0.05. What is the p-value? Explain.
(f) Is there a difference in the variabilities of processing times before and after process changes? Use α= 0.05.
(g) Can we conclude that the process changes have been effective in reducing the mean processing time? Use α = 0.05. What assumptions do you need to make for? conducting the test?
> 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.
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> Consider the hospitality industry. Describe special causes and common causes in this setting and discuss the role of quality control and quality improvement.
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> 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
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> 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
> 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
> 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
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> 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
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> 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
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> 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
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> 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
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> 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
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> 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
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> 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
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> 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
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> 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
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> 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
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> 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 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 failu
> 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
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> 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
