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mathematics
statistics

Questions and Answers of Statistics

A sampling plan is desired to have a producer's risk of 0.05 at AQL = 0.9% and a consumer's risk of 0.10 at LQL = 6.5% nonconforming. Find the single sampling plan that meets the consumer's
A sampling plan is desired to have a producer's risk of 0.05 at AQL= 1.3% nonconforming and a consumer's risk of 0.10 at LQL = 7.1% nonconforming. Find the single sampling plan that meets the
A sampling plan is desired to have a producer's risk of 0.05 at AQL = 2.0% nonconforming and a consumer's risk of 0.10 at LQL = 7% nonconforming. Find the single sampling plan with the largest sample
What is the importance of the OC curve in the selection of sampling plans? Describe the impact of the sample size and the acceptance number on the OC curve. What is the disadvantage of having an
Consider a double sampling plan given by the following parameters: N = 1200, n1 = 50, c1 = 1, r1 = 4, n2 = 110, c2 = 5, r2 = 6. Find the probability of accepting lots that are 4% nonconforming. What
Consider a double sampling plan given by the following parameters: N=2200, n1 = 60, c1 = 0, r1= 5, n2 = 100, c2 = 6, r2 = 7. Find the probability of accepting lots that are 3% nonconforming. What is
Refer to Exercise 10-30. What is the average sample number of incoming lots that are 2% nonconforming? What is the average total inspection for this quality level of 2% nonconforming? In Exercise
A double sampling plan is desired that has a producer's risk of 0.05 at AQL = 1.8% nonconforming and a consumer's risk of 0.10 at LQL = 8.5% nonconforming. The lot size is 1500, and the sample sizes
It is desired to accept lots that are 9.5% nonconforming with a probability of 0.10 and to accept lots that are 2.3% nonconforming with a probability of 0.95. Find a double sampling plan for a lot
Refer to Exercise 10-33. Find the double sampling plan if the second sample is to be twice as large as the first sample and the consumer's stipulation is to be satisfied exactly. In Exercise 10.33 A
Refer to Exercise 10-33. Find the sampling plan if it is desired to accept batches that is 5% nonconforming with a probability of 0.5. In Exercise 10.33 A double sampling plan is desired that has a
Find a Dodge-Romig single sampling plan if the lot size is 900, LQL = 5% nonconforming, and the process average is 0.8% nonconforming. What is the AOQL for the plan? Interpret it.
Find a Dodge-Romig single sampling plan if the lot size is 2200 and LQL = 5.0%. Determine and interpret the AOQL for the plan.
Find a Dodge-Romig single sampling plan if the lot size is 600, the process average is 1.4% nonconforming, and AOQL = 3%. Determine and interpret the LQL for the plan.
Discuss the relative advantages and disadvantages of single, double, and multiple sampling plans.
A chain sampling plan is used with a sample size of 5 and a parameter i of 3. If lots have a proportion nonconforming of 0.06, find the probability of accepting such lots.
A sequential sampling plan is to be used. It is desirable to have a producer's risk of 0.05 at AQL = 0.008 and a consumer's risk of 0.07 at LQL = 0.082. Determine the equations for the acceptance and
The initial inspection of transmission systems in automobiles is estimated to cost $0.50 per unit. If a nonconforming transmission is allowed in the assembly, the unit cost to eventually disassemble
In Exercise 10-43 if the initial inspection costs of the transmission systems are $ 1.00 per unit, what inspection policy should be followed using Deming's kp rule? In Exercise 10.43 The initial
Refer to Exercise 10-43. Suppose that the monthly production is 3000 units. What is the average savings in total inspection costs per month when using the policy found from Deming's kp rule as
Refer to Exercise 10-44. If the monthly production is 2000 units, what is the average savings in total inspection costs when using Deming's kp rule as opposed to 100% inspection?
In the construction industry, the initial inspection of tie beams is estimated to cost $0.20 per unit. If, however, a nonconforming beam is allowed for construction purposes, the unit cost of
The upper specification limit for the resistance of coils is 30 Ω. The distribution of coil resistance is known to be normal with a standard deviation of 5 Ω. It is preferred to reject batches that
The lower specification limit for the breaking strength of yarns is 25 g. The distribution of the breaking strength of yarns is normal with a variance of 6. It is desirable that lots with a mean such
Distinguish between average outgoing quality and acceptable quality level. Explain the meaning and importance of the average outgoing quality limit.
The tensile strength of an alloy has double specification limits. If the process average tensile strength is below 800 kg/cm2 or above 1200 kg/cm2, it is desired to accept such lots with a
The length of connector pins has an upper specification limit of 45 mm and a lower specification limit of 40 mm. It is desirable that lots with a mean such that 8% of the product is nonconforming,
The proportion of carbon monoxide in exhaust gases has an upper specification limit of 0.30. Emission control devices are being tested to meet such requirements. We wish that devices with an average
Refer to Exercise 10-52 regarding the proportion of carbon monoxide in exhaust gases, which has an upper specification limit of 0.30. If the average carbon monoxide content is 1 standard deviation
Unleaded gasoline must meet certain federal standards. The octane number for a particular brand must be at least 89. The standard deviation of the octane number is estimated to be 4. It is preferred
A dairy has to control the amount of butterfat in its low-fat milk. The upper specification limit of the fat content is 4 g for 4-L containers. The standard deviation of the fat content for these
The thickness of silicon wafers is an important characteristic in microelectronic circuits. The upper specification limit for the thickness is 0.015 mm. It is estimated that the standard deviation of
A cereal manufacturer who claims to meet certain mineral and vitamin requirements has a minimum specification of 25% for the iron content. The standard deviation of the iron content is estimated to
If you were interested in protection for acceptance of a single lot from a vendor with whom you do not expect to conduct much business, what criteria would you select, and why?
Explain the difference between average sample number and average total inspection. State any assumptions made.
If rectification inspection is used, discuss possible criteria to use in choosing sampling plans.
Discuss the context in which minimizing the average sample number would be a feasible criterion. Which type of sampling plan (single, double, or multiple) would be preferable, and what factors would
Define reliability. Explain its role in quality control and improvement.
Refer to Exercise 11-10. Each component has a time to failure that is exponentially distributed, with a mean time to failure of 3000 hours. Find the reliability of the subassembly for 2500 hours of
Consider the seven-component system shown in Figure 11-10. The reliabilities of the components are as follows: RA = 0.96, RB = 0.92, RC = 0.94, RD = 0.89, RE = 0.95, RF = 0.88, RC = 0.90. Find the
Consider the seven-component system shown in Figure 11-10. Assume that the time to failure for each component has an exponential distribution. The failure rates are as follows: λA = 0.0005/hour, λB
A standby system has a basic unit with four standby components. The time to failure of each component has an exponential distribution with a failure rate of 0.008/hour. For a 400 hour operation
Refer to Exercise 11-13 and the system shown in Figure 11-10. Suppose that component B is a standby component. Find the reliability of the system after 1000 hours. What is the mean time to failure?
Construct the OC curve for the life testing plan n = 6, T = 900 hours, c = 3. For a producer's risk of 0.05, what is the associated quality of batches as indicated by their mean life? For a
A sample of 20 diodes is chosen for life testing. The time to failure of the diodes is exponentially distributed. The test is terminated after six failures, with no replacement of the failed items.
Refer to Exercise 11-17. Assume that each failed item is replaced with an identical unit. Estimate the mean time to failure and the failure rate. Find a 90% confidence interval for the mean time to
A sample of 25 relays is chosen for life testing. The time to failure of a relay is exponentially distributed. The test is terminated after 800 hours, with 5 failures being observed at times 610,
Describe the life cycle of a product. What probability distributions would you use to model each phase?
A life testing plan is to be terminated after the eighth failure. It should reject a lot that has an acceptable mean life of 900 hours with a probability of 0.10. Items that fail during the test are
Refer to Exercise 11 -20. Assume that failed items are immediately replaced during the test. Using Handbook H-108, what is your recommendation on the lot?
A life testing plan is to be terminated after the third failure. It should accept a lot that has an acceptable mean life of 600 hours with a probability of 0.99. Failed items are not replaced during
A time-terminated life testing plan is to be found that will reject lots with a mean life of 1500 hours with a probability 0.05 and accept lots with a mean life of 600 hours with a probability of
Refer to Exercise 11-23. Suppose that items that fail during the test are immediately replaced with similar items. Determine the life testing plan using Handbook H-108.
A time-terminated life testing plan is to be found that will reject lots that have a mean life of 1400 hours with a probability of 0.05. The rejection number is 7, with a sample size of 35. Determine
A time-terminated life testing plan is desired that will accept lots with a mean life of 6000 hours with a probability of 0.99, and will accept lots with a mean life of 2000 hours with a probability
In a time-terminated life testing plan, it is desired to reject lots with a mean life of 1500 hours with a probability of 0.95 and also to reject lots with a mean life of 7500 hours with a
Explain procedures that might improve the reliability of a system. How would you increase the availability of a system? Distinguish between a system with components in parallel and another with
Distinguish between failure-, time-terminated, and sequential tests for reliability and life testing.
A transistor has an exponential time-to-failure distribution with a constant failure rate of 0.00006/hour. Find the reliability of the transistor after 4000 hours of operation. What is the mean time
Refer to Exercise 11-8 concerning the redesigned remote control unit with 25 components in series. If it is desired that the remote unit has a reliability of 0.996 for 3000 hours of operation, what
Distinguish between factor, treatment, and treatment levels in the context of a health care facility.
What is the utility of contrasts in experimental design? What are orthogonal contrasts, and how are they helpful?
What are the features of a 2k factorial experiment? What are the features of a 2k-2 fractional factorial experiment, and how is it constructed?
Clearly distinguish between the principles of confounding and fractionalization.
What is the role of a defining contrast, or generator, in fractional factorial experiments? Distinguish between a principal fraction and an alternate fraction.
Discuss Taguchi's philosophy for quality improvement. Discuss his loss function and its contributions.
Compare and contrast Taguchi's loss functions for the situations target are best, smaller is better, and larger is better. Give examples in the hospitality industry.
Discuss the signal-to-noise ratio. How is it used in the Taguchi method? What is an adjustment parameter, and how is it used?
A large retail company has to deliver its goods to distributors throughout the country. It has been offered trial-run services by three transportation companies. To test the efficiency of these three
An airline is interested in selecting a software package for its reservation system. Even though the company would like to maximize use of its available seats, it prefers to bump as few passengers as
Three training programs are being considered for auditors in an accounting firm. The success of the training programs is measured on a rating scale from 0 to 100, with higher values indicating a
Explain the importance of experimental design in quality control and improvement for a financial institution.
A doctor is contemplating four types of diet to reduce the blood sugar levels of patients. Because of differences in the metabolism of patients, the doctor categorizes the patients into five age
A consulting firm wishes to evaluate the performance of four software packages (A, B, C, and D) as measured by the computational time. The experimenter wishes to control for two variables: the
Two controllable factors, temperature and pressure, are each kept at three levels to determine their impact on the ductility of an alloy being produced. The temperature levels are 150,250, and 300
Consider Example 12-4 concerning the efficiency of synthetic fuel for which the factors are an additive and a catalyst. The original data are given in Table 12-19. The experiment is conducted using
(a) Is there a difference between the mean degree of lateness of company 3 and that of the averages of companies 1 and 2? Test at the 5% level of significance. (b) Find a 90% confidence interval for
(a) Is there a difference in the mean number of passengers bumped using software packages 1 and 2 from those using software packages 3 and 4? Test at the 10% level of significance. (b) Find a 95%
Refer to Exercise 12-19. Find a 90% confidence interval for the difference in the mean effectiveness of program 1 and the average of those using programs 2 and 3.
Refer to Exercise 12-19. Consider the following two contrasts of totals: (1) difference between the totals for training programs 1 and 3; (2) difference between the totals for the sum of training
Consider the following three contrasts: (1) difference between the sum of the reduction in blood sugar levels using diet types 1 and 3 from that using diet types 2 and 4; (2) difference between the
Write out the treatment combinations for a 24 factorial experiment.
Explain the principles of replication, randomization, and blocking, and discuss their roles in experimental design in a semiconductor manufacturing company.
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
Consider a 24 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
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?In Exercise 12.31
Consider a 24 factorial experiment. Using BC as the defining contrast, find the treatment combinations in a 24 - 1 fractional factorial experiment. Find the aliases of the contrasts. How would it be
In a 25-2 fractional factorial experiment, using CDE and AB as the generators, find the treatment combinations. Find the aliases of the contrasts.
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
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
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.
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? In Exercise
Suppose the manufacturer has the ability to center 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
Explain the concept of interaction between factors, and give some examples in the entertainment industry.
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
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
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
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 x C and B x E are
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
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

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