Exam 18: Statistical Applications in Quality and Productivity Management

Which of the following best measures the ability of a process to consistently meet specified customer-driven requirement?

Special or assignable causes of variation are signalled by individual fluctuations or patterns in the data.

The C_pk is a one-sided specification limit.

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

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

Instruction 18-13 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. sheet Day 1 2 3 4 5 1 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 18-13,an R chart is to be constructed for the number of blemishes.The centre line of this R chart is located at ________.

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

Instruction 18-13 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. sheet Day 1 2 3 4 5 1 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 18-13,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 ________.

C_p >1 indicates that if the process mean can be centred,then more than 99.73% of the observations will fall inside the specification limits.

Instruction 18-9 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. -Referring to Instruction 18-9,suppose the analyst constructs an chart to see if the production process is in control.What is the upper control limit (UCL)for this chart?

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. Number Proportion Day Poor 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,the estimate of the proportion of poor quality bags of candy 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 kilograms.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 3 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,an chart is to be used for the weight.One way to obtain the control limits is to take the grand mean and add and subtract the product of A₂ times the mean of the sample ranges.For this data set,the value of A₂ 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,what is the numerical value of the lower control limit for the p chart?

Which of the following is a method for breaking a process into a series of steps in order to eliminate defects and produce near perfect results?

Instruction 18-17A 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 18-17A,what percentage of the time it takes workers to complete an important production task will fall inside the specification limits?

The control chart

The p chart is a control chart used for monitoring the proportion of items in a batch that meet given specifications.

________ causes of variation are correctable without modifying the system.

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 upper control limit for the p chart?

Instruction 18-14 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 22875 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 12875 9.3723 -Referring to Instruction 18-14,an R chart is to be constructed for the time required to register.The upper control limit for this data set is ________.