Exam 18: Statistical Applications in Quality Management

Instruction 18-5 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. 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 Instruction 18-5,a p control chart is to be constructed for these data.The estimate of the standard error of the sample proportion is _______.

Instruction 18-3 A political pollster randomly selects a sample of 100 voters each day for eight successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favouring the incumbent candidate is too erratic. Sample (Day) Number Favouring Incumbent Candidate 1 57 2 57 3 53 4 51 5 55 6 60 7 56 8 59 -Referring to Instruction 18-3,which expression best characterises the p 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,the chart is to be used for the number of blemishes.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 18-16 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 CPL index?

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.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 _______.

Changes in the system to reduce common cause variation are the responsibility of management.

The smaller the capability index,the more capable a process is of meeting customer requirement.

One of the morals of the red bead experiment 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,estimate the percentage of the cans whose weight is inside the specification limit.

A company's management must listen to customers and translate their needs and expectations into easily measured _______variables,also known as CTQ variables.

Instruction 18-3 A political pollster randomly selects a sample of 100 voters each day for eight successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favouring the incumbent candidate is too erratic. Sample (Day) Number Favouring Incumbent Candidate 1 57 2 57 3 53 4 51 5 55 6 60 7 56 8 59 -Referring to Instruction 18-3,what is the numerical value of the lower control limit for the p chart?

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.Which expression best describes this chart?

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

CPL >1 implies that the process mean is more than three standard deviations away from the lower specification limit.

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.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 _______.

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

Instruction 18-9 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 18-9,based on the chart,it appears that the process is in control.

Instruction 18-9 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 18-9,based on the R chart,it appears that the process is out of control.

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,a p control chart is to be made for these data.The centre line of the control chart is _______.