Exam 18: Statistical Applications in Quality Management

TABLE 18-7 A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes samples of size 5 from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below. Sheet Day 1 2 3 4 5 Mean Range 1 8 10 14 6 5 8.6 9 2 8 13 6 6 10 8.6 7 3 10 12 7 7 9 9.0 5 4 5 9 12 7 10 8.6 7 5 8 3 8 9 10 7.6 7 6 9 7 9 6 9 8.0 3 7 10 10 5 7 6 7.6 5 8 10 9 10 6 5 8.0 5 9 6 10 6 9 9 8.0 4 10 6 9 8 6 8 7.4 3 11 8 5 6 10 10 7.8 5 12 6 4 7 7 12 7.2 8 13 7 5 7 6 9 6.8 4 14 5 8 8 7 6 6.8 3 15 7 12 10 6 10 9.0 6 16 7 11 4 7 8 7.4 7 17 8 4 5 4 7 5.6 4 18 11 4 11 11 10 9.4 7 19 6 10 6 10 10 8.4 4 20 6 12 12 6 8 8.8 6 She also decides that the upper specification limit is 10 blemishes. -Referring to Table 18-7, what is the value of d₂ factor?

TABLE 18-3 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. Day ( in minutes ) R 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 18-3, suppose the analyst constructs an $\bar{X}$ chart to see if the production process is in-control. What is the center line for this chart?

TABLE 18-4 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. Hour R 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 18-4, 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?

TABLE 18-4 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. Hour R 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 18-4, what is the value of d2 factor?

TABLE 18-6 The maker of a packaged candy wants to evaluate the quality of her production process. On each of 16 consecutive days, she samples 600 bags of candy and determines the number in each day's sample that she considers to be of poor quality. The data that she developed follows. Day Number Poor Proportion Poor 1 33 0.0550000 2 29 0.0483333 3 31 0.0516667 4 32 0.0533333 5 43 0.0716667 6 45 0.0750000 7 46 0.0766667 8 48 0.0800000 9 48 0.0800000 10 46 0.0766667 11 28 0.0466667 12 32 0.0533333 13 28 0.0466667 14 32 0.0533333 15 31 0.0516667 16 24 0.0400000 -Referring to Table 18-6, the estimate of the proportion of poor quality bags of candy is_______

TABLE 18-9 The manufacturer of cat 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 Range Number XBar Range 1 3.05072 0.0215 16 3.04646 0.073 2 3.01228 0.087 17 3.03868 0.0696 3 3.03558 0.0851 18 3.03338 0.0329 4 3.01014 0.0674 19 3.03322 0.0455 5 3.00858 0.0983 20 3.05078 0.0215 6 3.02704 0.0527 21 3.04808 0.0396 7 3.04268 0.0508 22 3.05348 0.0581 8 3.01052 0.0791 23 3.05516 0.0682 9 3.03464 0.0663 24 3.03426 0.0325 10 3.02034 0.0538 25 3.0516 0.0641 11 3.03764 0.0584 26 3.05562 0.0809 12 3.0409 0.0434 27 3.04402 0.0374 13 3.0519 0.0762 28 3.06458 0.0284 14 3.03994 0.0833 29 3.0544 0.0738 15 3.03788 0.0601 -Referring to Table 18-9, an X chart is to be used for the weight. The lower control limit for this data set is_____ , while the upper control limit is_____ .

TABLE 18-1 A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every day. The owner decides to record the number of papers delivered on time for a 10-day period and construct a p chart to see whether the percentage is too erratic. Number of Papers Day Delivered on Time 1 46 2 45 3 46 4 45 5 43 6 48 7 46 8 49 9 48 10 47 -Referring to Table 18-1, what is the numerical value of the lower control limit for the p chart?

TABLE 18-8 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. Day Range Mean Std.Dev. 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 18-8, an X chart is to be used for the time required to register. The lower control limit for this data set is , while the upper control limit is__________ .

TABLE 18-1 A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every day. The owner decides to record the number of papers delivered on time for a 10-day period and construct a p chart to see whether the percentage is too erratic. Number of Papers Day Delivered on Time 1 46 2 45 3 46 4 45 5 43 6 48 7 46 8 49 9 48 10 47 -Referring to Table 18-1, what is the numerical value of the center line for the p chart?

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

Once the control limits are set for a control chart, one attempts to

TABLE 18-4 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. Hour R 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 18-4, 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?

TABLE 18-3 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. Day (in minutes) R 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 18-3, suppose the analyst constructs an R chart to see if the variability in production times is in-control. What is the center line of this R chart?

Cpk > 1 indicates that the process average is exactly 3 standard deviations away from the closest specification limit.

Which of the following is not one of Deming's 14 points?

TABLE 18-9 The manufacturer of cat 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 Range Number XBar Range 1 3.05072 0.0215 16 3.04646 0.073 2 3.01228 0.087 17 3.03868 0.0696 3 3.03558 0.0851 18 3.03338 0.0329 4 3.01014 0.0674 19 3.03322 0.0455 5 3.00858 0.0983 20 3.05078 0.0215 6 3.02704 0.0527 21 3.04808 0.0396 7 3.04268 0.0508 22 3.05348 0.0581 8 3.01052 0.0791 23 3.05516 0.0682 9 3.03464 0.0663 24 3.03426 0.0325 10 3.02034 0.0538 25 3.0516 0.0641 11 3.03764 0.0584 26 3.05562 0.0809 12 3.0409 0.0434 27 3.04402 0.0374 13 3.0519 0.0762 28 3.06458 0.0284 14 3.03994 0.0833 29 3.0544 0.0738 15 3.03788 0.0601 -Referring to Table 18-9, based on the $\bar{X}$ chart, it appears that the process is in control.

The control chart

TABLE 18-8 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. Day Range Mean Std.Dev. 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 18-8, an R chart is to be constructed for the time required to register. The center line of this R chart is located at _____.

A process capability is estimated by the percentage of product or service that fall outside the specification limits.

TABLE 18-5 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. Day Bad \% Bad 1 9 0.037500 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 18-5, the process seems to be in control.