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Fundamentals of quality control and improvement 3rd edition Amitava mitra - Solutions
Explain why a p- or c-chart is not appropriate for highly conforming processes.
Distinguish between 3ó limits and probability limits. When would you consider constructing probability limits?
Meeting customer due dates is an important goal. What attribute or variables control charts would you select to monitor? Discuss the underlying assumptions in each case.
Explain the setting under which a U-chart would be used. How does the U-chart incorporate the user's perception of the relative degree of severity of the different categories of defects?
Which type of control chart (p-, np-, c-, u-, U-, or charts for highly conforming processes) is most appropriate to monitor the following situations?· (a) Number of potholes in highways (b) Proportion of customers who are satisfied with the operation of the local housing authority (c) Satisfaction
Every employee in a check-processing department goes through a four-month training period, after which the employee is responsible for their operation. The work of one employee who has been on the job for eight months is being studied. Table 8-15 shows the number of errors and the number of items
The number of customers who are not satisfied with the service provided in a retail store is found for 20 samples of size 100 and is shown in Table 8-16. Construct a control chart for the proportion of dissatisfied customers. Revise the control limits, assuming special causes for points outside the
Refer to Exercise 8-18. Management believes that the dissatisfaction rate is 3%, so establish control limits based on this value. Comment on the ability of the store to meet this standard. If management were to set the standard at 2%, can the store meet this goal? What actions would you
What are the advantages and disadvantages of control charts for attributes over those for variables?
Health care facilities must conform to certain standards in submitting bills to Medicare/Medicaid for processing. The number of bills with errors and the number sampled are shown in Table 8-17. Construct an appropriate control chart and comment on the performance of the billing department. Revise
Observations are taken from the output of a company making semiconductors. Table 8-18 shows the sample size and the number of nonconforming semiconductors for each sample. Construct ap-chart by setting up the exact control limits for each sample. Are any samples out of control? If so, assuming
Refer to Exercise 8-21 and the data shown in Table 8-18. Construct a standardized p-chart and discuss your conclusions.TABLE 8-18
The quality of service in a hospital is tracked by determining the proportion of medication errors; this is done by dividing the number of medication errors by 1000 patient-days for each observation. The results of 25 such samples (in percentage of medication errors) are shown in Table 8-19.
A health care facility is interested in monitoring the primary C-section rate. Monthly data on the number of primary C-sections collected over the last two and a half years is shown in Table 8-20.(a) Is the process in control?(b) There is pressure to make these data public. Can we conclude that the
Refer to Exercise 8-18 and the data shown in Table 8-16. Construct a control chart for the number of dissatisfied customers. Revise the chart, assuming special causes for points outside the control limits.TABLE 8-16
The number of processing errors per 100 purchase orders is monitored by a company with the objective of eliminating such errors totally. Table 8-21 shows samples that were selected randomly from all purchase orders. The company is in the process of testing the effects of a new purchase order form
The number of dietary errors is found from a random sample of 100 trays chosen on a daily basis in a health care facility. The data for 25 such samples are shown in Table 8-22.(a) Construct an appropriate control chart and comment on the process.(b) How many dietary errors do you predict if no
A building contractor subcontracts to a local merchant a job involving hanging wallpaper. To have an idea of the quality level of the merchant's work, the contractor randomly selects 300 m2 and counts the number of blemishes. The total number of blemishes for 30 samples is 80. Construct the
The number of imperfections in bond paper produced by a paper mill is observed over a period of several days. Table 8-23 shows the area inspected and the number of imperfections for 25 samples. Construct a control chart for the number of imperfections per square meter. Revise the limits if
Discuss the significance of an appropriate sample size for a proportion-nonconforming chart.
Refer to Exercise 8-29. If we want to control the number of imperfections per 100 m2, how would this affect the control chart? What would the control limits be? In terms of decision making, would there be a difference between this problem and Exercise 8-29, depending on which chart is constructed?
The director of the pharmacy department is interested in benchmarking the level of operations in the unit. The director has defined medication errors as being any one of the following: wrong medication; wrong dose; administered to the wrong patient; administered at the wrong time; incorrectly
Nonconformities in automobiles fall into three categories: serious, major, and minor. Twenty-five samples of five automobiles are chosen, and the total number of nonconformities in each category is reported. Table 8-25 shows the results. Assuming a weighing system of 50,10, and 1 for serious,
The Joint Commission on Accreditation of Healthcare Organizations (JCAHO) requires an accounting of significant medication errors. Data collected over the last 25 months, shown in Table 8-26, indicate the number of orders filled and the number of significant medication errors. Each order is
Refer to Exercise 8-18. Construct an OC curve for the p-chart. If the process proportion of dissatisfied customers were to rise to 7%, what is the probability of not detecting this shift on the first sample drawn after the change has taken place? What is the probability of detecting the shift by
Refer to Exercise 8-18. Construct an OC curve for the p-chart. If the process proportion of dissatisfied customers were to rise to 7%, what is the probability of not detecting this shift on the first sample drawn after the change has taken place? What is the probability of detecting the shift by
Refer to Exercise 8-27. Construct an OC curve for the c-chart. If the process average number of dietary errors per 100 trays increases to 10, what is the probability of detecting this on the first sample drawn after the change?TABLE 8-22
Refer to Exercise 8-36. Set up 2σ control limits. What is the probability of detecting a change in the process average number of dietary errors per 100 trays to 8 on the first sample drawn after the change? Explain under what conditions you would prefer to have these 2σ
The number of heart surgery complications is rare. To monitor the effectiveness of such surgeries, data are recorded on the number of such procedures until a complication occurs. These complications occur independently with a constant probability of occurrence and follow a geometric distribution.
Consider Exercise 8-38. If you were interested in detecting an improvement in the process using a one-sided limit, what should the minimum sample size be for an a of 0.005? What should it be for an a of 0.05? What conclusions can you draw from these results?TABLE 8-27
The CEO of a company has been charged with reducing the proportion nonconforming of the product output. Discuss which control charts should be used and where they should be placed.
Consider Exercise 8-38 under the assumption that the complication rate is 0.1%. If you were to construct ap-chart using two-sided 3ó limits, what would the minimum sample size be to detect an improvement in the process?TABLE 8-27
Consider Exercise 8-38. Determine the sensitivity of the control limits on the complication rate, using values of 0.2% and 0.5%.TABLE 8-27
Consider Exercise 8-38 under the assumption that the complication rate is 0.1 % and a type I error of 0.005. If you reduced the upper control limit to half of its previous value, what type of process complication rates, on average, will this new limit be able to detect improvements?TABLE 8-27
Consider Exercise 8-38. However, now assume that the interval between complications follows an exponential distribution. Construct an appropriate control chart and comment on the process assuming a type I error rate of 0.005.
JCAHO has standards pertaining to patient restraint use. A checklist has been developed that is to be used each time a restraint is used. The checklist contains five items, all of which should be checked. Table 8-28 shows data collected for 25 months that indicate the number of patients restrained
How does changing the sample size affect the centerline and the control limits of a p-chart?
What are the advantages and disadvantages of the standardized p-chart as compared to the regular proportion-rionconforming chart?
Discuss the assumptions that must be satisfied to justify using ap-chart. How are they different from the assumptions required for a c-chart?
Is it possible for a process to be in control and still not meet some desirable standards for the proportion nonconforming? How would one detect such a condition, and what remedial actions would one take?
Discuss the role of the customer in influencing the proportion-nonconforming chart. How would the customer be integrated into a total quality systems approach?
Explain the difference between specification limits and control limits. Is there a desired relationship between the two?
Discuss the importance of identifying an appropriate distribution of the quality characteristic in process capability analysis. Address this in the context of waiting time for service in a fast-food restaurant during lunch hour.
Discuss how the precision of a measurement system affects the process potential in the context of measuring unloading times of supertankers. What bounds exist on the observed process potential?
Distinguish between gage repeatability and gage reproducibility in the context of measuring unloading times of supertankers.
A pharmaceutical company producing vitamin capsules desires a proportion of calcium content between 40 and 55 ppm. A random sample of 20 capsules chosen from the output yields sample mean calcium content of 44 ppm with a standard deviation of 3 ppm. Find the natural tolerance limits of the process.
For Exercise 9-13, find the Cp index. Comment on the ability of the process to meet specifications. What proportion of the specification range is used up by the process? If it is easier to change the process mean than to change its variability, to what value should the process mean be set to
The emergency service unit in a hospital has a goal of 3.5 minutes for the waiting time of patients before being treated. A random sample of 20 patients is chosen and the sample average waiting time is found to be 2.3 minutes with a sample standard deviation of 0.5 minutes. Find an appropriate
Refer to Exercise 9-13. Find the process capability index Cpk, and comment on process performance. If the target value is 47.5 ppm, find the Cpm, and Cpmk indices and comment on their values. If the process center is shifted to the midpoint between the specification limits, what proportion of the
The diameter of a forged part has specifications of 120 ± 5mm. A sample of 25 parts chosen from the process gives a sample mean of 122 mm with a sample standard deviation of 2 mm. (a) Find the Cpk index for the process, and comment on its value. What is the proportion of nonconforming parts
The waiting time in minutes before being served in a local post office is observed for50 randomly chosen customers:(a) Test for normality using a = 0.05. What inferences can you draw?(b) Estimate the mean and standard deviation of the waiting times.(c) If the goal of the post office is for the
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 of those customers has to wait (in minutes) while having his or her car
Explain the difference between natural tolerance limits and specification limits. How does a process capability index incorporate both of them? What assumptions are made in constructing the natural tolerance limits?
Light bulbs are tested for their luminance, with the intensity of brightness desired to be within a certain range. Random samples of 5 bulbs are chosen from the output and their luminance values measured. The sample mean X and standard deviation s are found. After 30 samples, the following summary
The amount of a preservative added to dairy products should not exceed certain levels of 23 ± 6 mg (set by the Food and Drug Administration). Samples of size 5 of processed cheese produced the values of the average and range shown in Table 9-6.(a) Construct appropriate control charts and
Consider the assembly of three components shown in Figure 9-19. The tolerances for these three components are given in Table 9-7. Assume that the tolerances on the components are independent of each other and that the lengths of the components are normally distributed with a capability ratio of 1.
In Exercise 9-22, suppose that the specifications for the gap are 1.05 ±0.15 cm. An assembly with a gap exceeding the upper specification limit is scrapped, whereas that with a gap less than the lower specification limit can be reworked to increase the gap dimension. The unit cost of rework is
Refer to the four-component assembly shown in Figure 9-14. Assume that the length of each component is normally and independently distributed with the means shown in Table 9-8. The specifications for the assembly length are 35 ± 0.5 cm. Assuming that the natural tolerances (or process spread) for
Refer to Exercise 9-24. Suppose that the specifications for the assembly length are 35 ± 0.3 cm and that the tolerances of A and C are equal, but those for B and D are each twice as large as that for A. In addition, assume that the specifications are barely equal to the natural tolerance limits.
Consider the two-component assembly shown in Figure 9-15. Suppose that the specifications for the dimension X2 are 5 ± 0.05 cm and those for X1 are 12 ± 0.15 cm. Find the specifications for the dimension K Assume that the specification limits equal the natural tolerance limits. For what
Consider the two-component assembly shown in Figure 9-15. Suppose that the mean lengths are given as μ1 = 14 cm and μ2 = 8 cm. Assuming that the specifications for Y are 6 ± 0.2 cm, what are the tolerances for X1 and X2? Assume that the variance of X1 is three times as large as that of X2
Four metal plates, each of thickness of 3 cm, are welded together to form a subassembly. The specifications for the thickness of each plate are 3 ± 0.2 cm. Assuming the weld thickness to be negligible, determine the tolerances for the assembly thickness.
Consider Figure 9-16, which shows the assembly of a shaft in a bearing. The specifications for the shaft diameter are 6 ± 0.06 cm, and those for the hole diameter are 6.2 ± 0.03 cm.(a) Find the probability of the assembly having a clearance fit.(b) What is the probability of the
What are statistical tolerance limits? Explain how they differ from natural tolerance limits.
The specifications for a shaft diameter in an assembly are 5 ± 0.03 cm, and those for the hole are 5.25 ± 0.08 cm. If the assembly is to have a clearance of 0.18 ± 0.05 cm, what proportion of the assemblies will be acceptable?
Refer to Exercise 9-30. If there is too much clearance between the hole and the shaft, a wobble will result. Clearances above 0.05 cm are not desirable and cause a wobble. Find the probability of a wobble.
In a piston assembly, the specifications for the piston diameter are 12 ± 0.5 cm, and those for the cylinder diameter are 12.10 ± 0.4 cm. Assume that the natural tolerance limits coincide with the specifications. A clearance fit is required for the assembly. What proportion of the assemblies will
A logistics firm has identified four operations, which are to be conducted in succession, for an order to be processed. The tolerances (in hours) are shown in Table 9-9. Assume that the tolerances are independent of each other and that the time in each phase is normally distributed. Further assume
Measurements on the pH values of a chemical compound are taken at random by two operators. Fifteen samples are randomly chosen, with each operator measuring each sample twice. The data are shown in Table 9-10. Specifications on pH are 6.5 ±0.05. Comment on the capability of the measurement
Consider the data on call waiting time of customers in a call center (Exercise 5-8). The call center has set a goal of waiting time not to exceed 35 seconds. (a) Test to see (using a = 0.05) if conducting capability analysis using normal distribution is appropriate. (b) If not, consider a Box-Cox
A cylindrical piece is used in an assembly in which the weight is to be controlled. The tolerances on diameter and height, on the basis of 5 observations, are 2 ± 0.06 cm and6 ± 0.06 cm, respectively assume that the dimensions are independent of each other and are each normally
In solar cells, the exposed surface area is the characteristic of interest. The tolerances on the length and width of the cells are 4 ± 0.06 cm and 5 ± 0.09 cm, respectively. Assuming these dimensions to be independent of each other and each normally distributed with a capability ratio of 1, what
The body mass index (BMI) is a measure of obesity and equals a person's weight (in kilograms) divided by the height (in meters) squared. For a certain diagnosisrelated group of 20 patients, the following natural tolerances were obtained on weight (60 ± 5 kg) and height (1.7 ± 0.09 m). Assume that
Find the sample size required for two-sided non-parameteric statistical tolerance limits for the viscosity of grease used as a lubricant. It should contain 99% of the population with a probability of 0.95. How will the interval be found?
Is it possible for a process to be in control and still produce nonconforming output? Explain. What are some corrective measures under these circumstances?
Refer to Exercise 9-39. Find the sample size needed to construct a one-sided lower nonparametric statistical tolerance limit. It should contain 90% of the population ith a probability of 0.95. How will the limit be found?
What are the advantages of having a process spread that is less than the specification spread? What should be the value of Cp be in this situation? Could Cpk be < 1 here?
Compare the capability indices Cpk, Cpm, and Cpmk, and discuss what they measure in the process. When would you use Cw?
What condition must exist prior to calculating the process capability? Discuss how process capability can be estimated through control charts.
Suppose that the time to complete a project is the sum of several independent operations. If the means and standard deviations of the independent operations are known, determine the mean and standard deviation of the project completion time. If the operations are not independent, what effect will
Suppose that the dimension of an assembly has to be within certain tolerances. Discuss how tolerances could be set for the components, given that the difference between two component dimensions comprises this assembly dimension. Assume that the inherent variability of each component is equal.
Discuss the advantages and disadvantages of sampling.
Compare and contrast chain sampling and sequential sampling plans. When are they used?
Discuss the assumptions made in Deming's kp rule. When would you use this rule?
What are the advantages and disadvantages of variable sampling plans over those for attributes?
What are the parameters of a variable sampling plan for which the process average quality is of interest? Explain the working procedure of such a plan when single and double specification limits are given.
Explain the difference between the decision-making procedure using Forms 1 and 2 for variable sampling plans that are designed to estimate the proportion of nonconforming items.
Consider a single sampling plan with a lot size of 1500, sample size of 150, and acceptance number of 3. Construct the OC curve. If the acceptable quality level is 0.05% nonconforming and the limiting quality level is 6% nonconforming, describe the protection offered by the plan at these quality
Consider Exercise 10-15. Answer the same questions for the sampling plan N = 1500, n = 200, c = 3. Discuss the degree of protection of this plan compared to that in Exercise 10-15.
Suppose that desirable producer's risk is 3% and consumer's risk is 6%. Which of the plans described in Exercises 10-15 and 10-16 are preferable? Discuss your choice.
For the sampling plan N = 1500, n = 150, c = 3, construct the average outgoing quality curve. What is the AOQL? Interpret it.
Construct the ATI curve for the sampling plan N = 1200, n = 50, c = 1. Suppose that the process average nonconforming rate is 3%. Explain the value of ATI for that level of nonconformance.
Distinguish between producer's risk and consumer's risk. In this context, explain the terms acceptable quality level and limiting quality level. Discuss instances for which one type of risk might be more important than the other.
For the double sampling plan N=2000, n1 =80, c1 = 1, r1 = 3, n2 = 100, c2 = 2, r2 = 3, construct and interpret the ASN curve. Suppose that process average nonconforming rate is 1.5%. Would you prefer the stated double sampling plan or a single sampling plan with n = 100, c = 2 in order to minimize
For the double sampling plan # = 2200, n1 = 60, c1 = 1, r1 = 5, n2 = 120, c2 = 4, r2 = 5, construct the ASN curve. Within what range of proportion nonconforming values would you prefer the stated double sampling plan over a single sampling plan with n = 85, c = 2 in order to minimize ASN?
A computer monitor manufacturer subcontracts its major parts to four vendors: A, B, C, and D. Past records show that vendors A and C provide 30% of the requirements each, vendor B provides 25%, and vendor D provides 15%. In a random sample of 10 parts, 4 were found to be nonconforming. It is known
A manufacturer is considering replacement of an existing machine that performs an operation on a part. The variable costs are $0.38 per piece on the existing machine and $0.05 per piece on the new machine. The cost of the new machine is $40,000, while the existing machine can be scrapped at a value
Determine the single sampling plans that will reject lots that are 1.3% nonconforming 8% of the time. Use acceptance numbers of 1, 3, and 5. From a consumer's point of view, which of these three plans would you choose?
Determine the single sampling plans that will accept lots that are 6% nonconforming 12% of the time. Use acceptance numbers of 1, 2, and 4. From a producer's point of view, which of these plans would you choose?
Determine single sampling plans that will accept lots that are 0.8% nonconforming with a probability of 0.96. Use acceptance numbers of 1, 3, and 4. If we desire batches that are 5% nonconforming to be accepted with a probability of no more than 0.04, which of the plans above would be preferable?
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