Exam 18: Statistical Applications in Quality Management

Instruction 18-11 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 eight 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 Instruction 18-11,an R chart is to be constructed for the time required to register.The upper control limit for this data set is _______

Instruction 18-15 The manufacturer of canned food constructed control charts and analysed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 kg. The table below provides the range and mean of the weights of five cans tested every 15 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 Instruction 18-16,the chart is to be used for the time required to register.One way to obtain the control limits is to take the grand mean and add and subtract the product of A₂ times the average of the sample ranges.For this data set,the value of A₂ is _______.

Instruction 18-11 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 eight 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 Instruction 18-11,an R chart is to be constructed for the time required to register.The centre line of this R chart is located at _______

Instruction 18-12 The manufacturer of canned food constructed control charts and analysed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 kg. The table below provides the range and mean of the weights of five cans tested every 15 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 Instruction 18-12,an R chart is to be constructed for the weight.The upper control limit for this data set is _______

The CPL and CPU indices are used to measure a process's actual performance rather than its potential.

Instruction 18-7 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 five individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below. She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively. Hour 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 -Referring to Instruction 18-7,suppose the supervisor constructs an R chart to see if the variability in collection times is in control.This R chart is characterised by which of the following?

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

Instruction 18-16 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 five individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below. She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively. -Referring to Instruction 18-16,what is the value of the C_p index?

Instruction 18-4 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 Instruction 18-4,the best estimate of the mean proportion of disks with bad sectors is _______.

Instruction 18-1 Below is the number of defective items from a production line over 20 consecutive morning shifts. Day Nonconf. Day Nonconf. 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 Note: Nonconf. = Nonconformances -Referring to Instruction 18-1,based on the c chart,no opportunity appears to be present to render an improvement in the process.

Instruction 18-8 A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes a sample size of five 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. She also decides that the upper specification limit is 10 blemishes. 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 -Referring to Instruction 18-8,based on the chart for the number of blemishes,it appears that the process is out of control.

Instruction 18-7 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 five individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below. She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively. Hour 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 -Referring to Instruction 18-7,suppose the supervisor constructs an R chart to see if the process is in control.What are the lower and upper control limits of this chart?

Instruction 18-10 A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes a sample size of five 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. She also decides that the upper specification limit is 10 blemishes. 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 -Referring to Instruction 18-10,an R chart is to be constructed for the number of blemishes.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 _______.

Instruction 18-15 The manufacturer of canned food constructed control charts and analysed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 kg. The table below provides the range and mean of the weights of five cans tested every 15 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 Instruction 18-15,construct an R chart for the time required to register.

Instruction 18-16 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 five individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below. She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively. -Referring to Instruction 18-16,what percentage of the time it takes workers to complete an important production task will fall inside the specification limits?

Instruction 18-10 A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes a sample size of five 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. She also decides that the upper specification limit is 10 blemishes. 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 -Referring to Instruction 18-10,the chart is to be used for the number of blemishes.The centre line of this chart is located at _______.

Instruction 18-7 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 five individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below. She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively. Hour 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 -Referring to Instruction 18-7,suppose the sample mean and range data were based on six observations per hour instead of five.How would this change affect the lower and upper control limits of an R chart?

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

Instruction 18-11 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 eight 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 Instruction 18-11,the 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 _______

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