Exam 17: Statistical Applications in Quality Management

TABLE 17-3 A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day. 1 58.5 5.1 2 47.6 7.8 3 64.3 6.1 4 60.6 5.7 5 63.7 6.2 6 57.5 6.0 7 55.0 5.4 8 54.9 6.1 9 55.0 5.9 10 62.7 5.0 11 61.9 7.1 12 60.0 6.5 13 58.3 5.9 14 52.0 5.2 -Referring to Table 17-3, suppose the analyst constructs an $\bar { X }$ chart to see if the production process is in-control. What is the lower control limit (LCL)for this chart?

TABLE 17-10 Below is the number of defective items from a production line over twenty consecutive morning shifts. Day Nonconformances Day Nonconformances 1 26 11 22 2 27 12 26 3 23 13 21 4 21 14 22 5 26 15 19 6 20 16 17 7 35 17 21 8 30 18 18 9 21 19 16 10 25 20 17 -Referring to Table 17-10, based on the c chart, it appears that the process is out of control.

Which of the following situations suggests a process that appears to be operating in a state of statistical control?

TABLE 17-8 Recently, a university switched to a new type of computer-based registration. The registrar is concerned with the amount of time students are spending on the computer registering under the new system. She decides to randomly select 8 students on each of the 12 days of the registration and determine the time each spends on the computer registering. The range, mean, and standard deviation of the times required to register are in the table that follows. 1 10 5.250 3.4949 2 31 15.250 10.3060 3 13 20.375 4.9262 4 21 22.875 8.3911 5 35 8.500 11.3767 6 18 7.875 6.9372 7 25 11.250 8.5815 8 30 7.875 9.5235 9 17 10.250 6.3640 10 22 9.500 7.8740 11 27 7.875 8.7086 12 26 12.875 9.3723 -Referring to Table 17-8, an R chart is to be constructed for the time required to register. The center line of this R chart is located at ________.

TABLE 17-4 A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below. 1 18.4 25 2 16.9 27 3 23.0 30 4 21.2 23 5 21.0 24 6 24.0 25 7 19.3 12 8 15.8 14 9 20.0 13 10 23.0 11 She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively. -Referring to Table 17-4, suppose the sample mean and range data were based on 6 observations per hour instead of 5. How would this change affect the lower and upper control limits of an R chart?

Common causes of variation represent variation due to the inherent variability in the system.

TABLE 17-8 Recently, a university switched to a new type of computer-based registration. The registrar is concerned with the amount of time students are spending on the computer registering under the new system. She decides to randomly select 8 students on each of the 12 days of the registration and determine the time each spends on the computer registering. The range, mean, and standard deviation of the times required to register are in the table that follows. 1 10 5.250 3.4949 2 31 15.250 10.3060 3 13 20.375 4.9262 4 21 22.875 8.3911 5 35 8.500 11.3767 6 18 7.875 6.9372 7 25 11.250 8.5815 8 30 7.875 9.5235 9 17 10.250 6.3640 10 22 9.500 7.8740 11 27 7.875 8.7086 12 26 12.875 9.3723 -Referring to Table 17-8, an $\bar { X }$ chart is to be used for the time required to register. The center line of this chart is located at ________.

Which of the following is not part of the Shewhart-Deming cycle?

TABLE 17-5 A manufacturer of computer disks took samples of 240 disks on 15 consecutive days. The number of disks with bad sectors was determined for each of these samples. The results are in the table that follows. 2 7 0.029167 3 4 0.016667 4 6 0.025000 5 8 0.033333 6 3 0.012500 7 6 0.025000 8 10 0.041667 9 16 0.066667 10 24 0.100000 11 15 0.062500 12 9 0.037500 13 4 0.016667 14 8 0.033333 15 6 0.025000 -Referring to Table 17-5, the best estimate of the mean proportion of disks with bad sectors is ________.

TABLE 17-5 A manufacturer of computer disks took samples of 240 disks on 15 consecutive days. The number of disks with bad sectors was determined for each of these samples. The results are in the table that follows. 2 7 0.029167 3 4 0.016667 4 6 0.025000 5 8 0.033333 6 3 0.012500 7 6 0.025000 8 10 0.041667 9 16 0.066667 10 24 0.100000 11 15 0.062500 12 9 0.037500 13 4 0.016667 14 8 0.033333 15 6 0.025000 -Referring to Table 17-5, a p control chart is to be made for these data. The upper control limit is ________, and the lower control limit is ________.

TABLE 17-4 A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below. 1 18.4 25 2 16.9 27 3 23.0 30 4 21.2 23 5 21.0 24 6 24.0 25 7 19.3 12 8 15.8 14 9 20.0 13 10 23.0 11 She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively. -Referring to Table 17-4, suppose the supervisor constructs an $\bar { X }$ chart to see if the process is in-control. What is the center line of the chart?

TABLE 17-9 The manufacturer of canned food constructed control charts and analyzed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 pounds. The table below provides the range and mean of the weights of five cans tested every fifteen minutes during a day's production. Number XBar Rang Number XBar Range 1 3.05072 0.0215 1 3.04646 0.073 3 3.01228 0.087 17 3.03868 0.0696 3 3.03558 0.0851 19 3.03338 0.0329 4 3.01014 0.0674 19 3.03322 0.0455 5 3.00858 0.0983 29 3.05078 0.0215 9 3.02704 0.0527 21 3.04808 0.0396 7 3.04268 0.0508 23 3.05348 0.0581 9 3.01052 0.0791 23 3.05516 0.0682 9 3.03464 0.0663 24 3.03426 0.0325 19 3.02034 0.0538 25 3.0516 0.064 11 3.03764 0.0584 29 3.05562 0.0809 12 3.0409 0.0434 27 3.04402 0.0374 13 3.0519 0.0762 29 3.06458 0.0284 14 3.03994 0.0833 29 3.0544 0.0738 15 3.03788 0.0601 -Referring to Table 17-9, an R chart is to be constructed for the weight. One way to create the lower control limit involves multiplying the mean of the sample ranges by D₃. For this data set, the value of D₃ is ________.

TABLE 17-4 A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below. 1 18.4 25 2 16.9 27 3 23.0 30 4 21.2 23 5 21.0 24 6 24.0 25 7 19.3 12 8 15.8 14 9 20.0 13 10 23.0 11 She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively. -Referring to Table 17-4, suppose the supervisor constructs an R chart to see if the variability in collection times is in-control. What are the lower and upper control limits for this R chart?

Cp > 1 indicates that if the process average can be centered, then more than 99.73% of the observations will fall inside the specification limits.

Which of the following situations suggests a process that appears to be operating out of statistical control?

It is not possible for the $\bar { X }$ chart to be out of control when the R chart is in control.

Determining the root causes of why defects can occur along with the variables in the process that cause these defects to occur involves which part of the DMAIC process?

TABLE 17-3 A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day. 1 58.5 5.1 2 47.6 7.8 3 64.3 6.1 4 60.6 5.7 5 63.7 6.2 6 57.5 6.0 7 55.0 5.4 8 54.9 6.1 9 55.0 5.9 10 62.7 5.0 11 61.9 7.1 12 60.0 6.5 13 58.3 5.9 14 52.0 5.2 -Referring to Table 17-3, suppose the analyst constructs an $\bar { X }$ chart to see if the production process is in-control. What is the upper control limit (UCL)for this chart?

TABLE 17-4 A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below. 1 18.4 25 2 16.9 27 3 23.0 30 4 21.2 23 5 21.0 24 6 24.0 25 7 19.3 12 8 15.8 14 9 20.0 13 10 23.0 11 She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively. -Referring to Table 17-4, what is the value of d₂ factor?

________ causes of variation are correctable without modifying the system.