Exam 17: Statistical Applications in Quality Management

The control chart

The R chart is a control chart used to monitor a process mean.

TABLE 17-2 A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favoring the incumbent candidate is too erratic. Sample (Day) Number Favoring Incumbent Candidate 1 57 2 57 3 53 4 51 5 55 6 60 7 56 8 59 -Referring to Table 17-2, what is the numerical value of the lower control limit for the p 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, suppose the supervisor constructs an $\bar { X }$ chart to see if the process is in-control. Which expression best describes this chart?

TABLE 17-2 A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favoring the incumbent candidate is too erratic. Sample (Day) Number Favoring Incumbent Candidate 1 57 2 57 3 53 4 51 5 55 6 60 7 56 8 59 -Referring to Table 17-2, what is the numerical value of the upper control limit for the p chart?

The Shewhart-Deming cycle plays an important role in which of the following Deming's 14 points for management?

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, construct an R chart for the time required to register.

TABLE 17-7 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 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 -Referring to Table 17-7, what is the value of the CPU index?

TABLE 17-6 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 follow. Number Proportion 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 17-6, a p control chart is to be constructed for these data. The lower control limit is ________, while the upper control limit is ________.

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 $\bar { X }$ chart is to be used for the weight. The center line of this chart is located at ________.

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, based on the R chart, it appears that the process is out of control.

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, construct a c chart for the number of defective items.

The Cp index measures the potential of a process, not its actual performance.

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. This R chart is characterized by which of the following?

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

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 R chart to see if the variability in production times is in-control. What is the center line of this R 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 upper control limit involves multiplying the mean of the sample ranges by D₄. For this data set, the value of D₄ is ________.

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. The upper control limit for this data set is ________.

TABLE 17-6 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 follow. Number Proportion 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 17-6, a p control chart is to be constructed for these data. The center line for the chart should be located at ________.

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