MGMT 425 Chapter 8: Measuring and Controlling Quality

Control limits are often confused with a. pre-control lines. b. center lines. c. specification limits. d. three sigma limits.

C

If the process mean and variance do not change over time, the process is a. in statistical control. b. normally distributed. c. stable. d. capable.

C

Process capability indexes can be computed from data in an -chart. a. True b. False

True

The center line for the np-chart is the average number of nonconforming items per sample. a. True b. False

True

A measurement system may be precise but not necessarily accurate at the same time. a. True b. False

True

Attribute measurement requires a much larger sample size than variable measurement to obtain the same amount of statistical information. a. True b. False

True

A machined part has a lower specification limit of 3.5 inches and an upper specification limit of 3.9 inches. The range for the pre-control green zone is a. 3.6 inches to 3.8 inches. b. 3.8 inches to 3.9 inches. c. less than 3.5 inches. d. 3.5 inches to 3.9 inches.

A

A precision parts manufacturer produces bolts for use in military aircraft. The specifications for bolt length are 37.50 ± 0.25 cm. The company has established an -chart and an R-chart using samples of size five. The center lines for the -chart and R-chart are set at 37.35 cm and 1.05 cm, respectively. Which of the following is the value of Cpk for this process? a. 0.07 b. 0.28 c. 0.75 d. 0.03

A

If the lower limit for a p-chart computes to a number less than zero, this indicates that a. the lower limit should be set at zero. b. the process is out of control. c. an attribute measure is incorrectly used. d. a calculation error has been made.

A

In determining whether a process is in statistical control, the _____ should be analyzed first. a. R-chart b. upper and lower control limits c. -chart d. center line

A

The _____ is used to monitor the centering of the process. a. -chart b. R-chart c. p-chart d. np-chart

A

The control chart most appropriate for plotting the daily percentage of students that wait longer than 5 minutes in line at the undergraduate admissions office is a(n) a. p-chart. b. np-chart. c. x-chart. d. -chart.

A

Twenty samples of size 6 were collected for a variable measurement. Which of the following is the upper control limit (UCL) and lower control limit (LCL) for an R-chart if the sum of the sample ranges equals 88.0? a. UCL = 8.8176; LCL = 0.0000 b. UCL = 9.3016; LCL = 0.3344 c. UCL = 13.2000; LCL = 0.0000 d. UCL = 29.3921; LCL = 0.0000

A

Which of the following is NOT an indication of an out-of-control process? a. Five consecutive points fall on one side of the center line. b. Four of five consecutive points fall within the outer two-thirds region between the center line and one of the control limits. c. Two of three consecutive points fall in the outer one-third region between the center line and one of the control limits. d. A single point falls above the upper control limit.

A

Which of the following is a likely cause of the control chart pattern known as a trend? a. Aging of equipment b. Maintenance schedules c. New process operator d. Sudden power surge

A

At the Midwest pharmaceutical company, how was the -chart interpreted by the second shift operators of the syringe assembly process after the machine had been adjusted three times by the technician? How did the statistical consultants interpret it?

ANSWER: After the maintenance technician made three attempts to adjust the machine, the second shift operators continued sampling and collected 15 additional samples of size 5, at 15-minute intervals. They plotted these results on the -chart, but because no values were beyond the control limits, they concluded that the process was under statistical control and took no action. It was at this point that the statistical consultants reviewed what had transpired. They determined that the 15 points showed a process not under statistical control. The string of 15 points of the -chart were all above the center line and hence they concluded that the process mean had shifted.

The featured distributor of electrical automation and power transmission products implemented a total quality program. Describe its effect on the distributor's receiving process.

ANSWER: An analysis of the control chart showed that the average error rate gradually improved. To a large extent, this improvement was due to the recognition of problems in the receiving process and enhanced communication among the constituents.

Discuss the differences between attributes and variables measurement.

ANSWER: An attribute measurement characterizes the presence or absence of nonconformances in a unit of work, or the number of nonconformances in a unit of work. Attribute measurements often are collected by visual inspection and expressed as proportions and counts. Variable measurements apply to dimensional quantities such as length, weight, and time, or any value on a continuous scale of measurement. Variable measurements are generally expressed with statistical measures such as averages and standard deviations. Collecting attribute data is usually easier than collecting variable data because the assessment can usually be done more quickly by a simple inspection or count, whereas variable data require the use of some type of measuring instrument. However, in a statistical sense, attributes measurement is less efficient than variables measurement; that is, attribute measurement requires a much larger sample size than variable measurement to obtain the same amount of statistical information. This difference can become significant when inspection of each item is time-consuming or expensive.

Define pre-control, and explain under what conditions pre-control can be used.

ANSWER: Pre-control is a simple technique for ensuring that a process that has relatively good capability remains in control. The idea behind pre-control is to divide the tolerance range into zones by setting two pre-control lines halfway between the center of the specification and the upper and lower specification limits. The center zone, called the green zone, comprises one-half of the total tolerance. Between the pre-control lines and the specification limits are the yellow zones. Outside the specification limits are the red zones. Pre-control should only be used when process capability is no greater than 88 percent of the tolerance, or equivalently, when Cp is at least 1.14. If the process mean tends to drift, then Cp should be higher. If managers or operators are interested in detecting process shifts even though the product output falls within specifications, pre-control should not be used because it will not detect such shifts.

Define the term "statistical process control." Outline the steps for setting up a control chart to monitor a process.

ANSWER: Statistical process control (SPC) is a methodology for monitoring a process to identify special causes of variation and to signal the need to take corrective action when it is appropriate. The following steps are required to develop and use control charts: 1. Prepare a. Choose the variable or attribute measurement. b. Determine the basis, size, and frequency of sampling. 2. Collect data a. Record the sample observations. b. Calculate relevant statistics: averages, ranges, proportions, and so on. c. Plot the statistics on the chart(s). 3. Determine initial control limits a. Compute the upper and lower control limits. b. Draw the center line (average) and control limits on the chart. 4. Analyze the chart a. Determine if it is in control. b. Identify and eliminate out-of-control points and recompute control limits. 5. Use for ongoing control a. Continue collecting data and plotting on the chart(s). b. Stop the process when an out-of-control condition is identified and make necessary corrections or adjustments.

At the Midwest pharmaceutical company, what conclusions were drawn by the statistical consultants using the R-chart?

ANSWER: The consultants examined the R-chart along with the -chart. The last 14 points of R were all on one side of the center line, indicating a lack of statistical control. Careful examination of both charts revealed that the points of R were below the center and were indicating that the overall variation had been reduced by what the maintenance technician had done. Yet, in reading the -chart (after examining the R-chart), the length of the syringes seemed to have increased.

Construct a flowchart that illustrates the decision process for selecting the appropriate control chart(s) for monitoring a given process.

ANSWER: The decision flowchart for proper control chart selection is as follows. The key decision variable that should begin the flowchart is determination of whether the quality characteristic represents variable or attribute data. Pic in doc

State the conclusion drawn by the operators in the capability study of the tacking operation at the Midwest pharmaceutical company.

ANSWER: The process was minimally capable and could indeed produce the length desired.

Identify the trade-offs associated with the s-chart instead of the R-chart.

ANSWER: The s-chart utilizes the sample standard deviation, which is a more sensitive and better indicator of process variability than the range. It is desirable when tight control of variability in the process is required. However, a larger sample size is desirable (in order to estimate the standard deviation) and calculation of a standard deviation is more complex than finding the range.

What did the statistical consultants recommend to the managers of the Midwest pharmaceutical company after the maintenance technician explained the reason for the increased length of the syringes? Was the recommendation implemented? What was the result?

ANSWER: The statistical consultants recommended to the managers that the threaded stud on which the height adjustment stop moved should be replaced. The repair work needed a special part that was fairly expensive and necessitated some downtime for the manufacturing process. The recommendation was implemented based on the strength of the control chart data and the explanation of the maintenance technician and the consultants. Upon replacement of the threaded stud, waste and rework from the final step dropped to virtually zero over the period of many weeks.

A specification is 50.0 cm ± 10.0 cm. Sketch and label the pre-control zones for this specification. Include the following values on your sketch: nominal, upper and lower specification limits, and end points of the green zone.

ANSWER: ​ Red zone Yellow zone Green zone Yellow zone Red zone 40.0 LSL 45.0 50.0 Nominal 55.0 60.0 USL

A process fills boxes with detergent. Construct an appropriate set of control limits to monitor the filling process. Historical data for fill weight (in ounces) of 10 samples are presented in the table that follows. A sample size of six was used. Sample Sample Mean Sample Range 1 15.80 0.42 2 16.10 0.38 3 16.02 0.08 4 15.95 0.15 5 16.12 0.42 6 16.18 0.23 7 15.87 0.36 8 16.20 0.40 9 16.07 0.28 10 15.94 0.36

ANSWER: ​ The fill weight of the boxes is a variable measure, so use an -chart and an R-chart. X- - = 16.025 and R - = 0.308. For n = 6, D3 = 0, D4 = 2.004, and A2 = 0.483 ​ R-chart: UCLR = D4 R - = 2.004(0.308) = 0.617 Center line = R - = 0.308 LCLR = D3 R - = 0(0.308) = 0.000 ​ X - chart: UCL x - = x - - + A2 R - = 16.025 + 0.483(0.308) = 16.174 Center line = x - - = 16.025 LCL x - = x - - - A2 R - = 16.025 - 0.483(0.308) = 15.876

A bank recently took 32 random samples of size 600 to determine the accuracy of its customer records. A customer record was nonconforming if any portion of the record was left blank. The sample data are presented in the table that follows. Determine the control limits for an np-chart. Cont in doc

Answer in doc

A quality engineer took 40 samples of 100 transistors each from the output of an assembly line. Each transistor was tested, and the number of defectives in each sample is recorded in the table that follows. Determine the control chart limits for a p-chart. Cont in doc

Answer in doc

Coils of synthetic rope are monitored for defects. Each coil contains 1,200 feet of rope. There were 26 coils selected, and the number of defects found in each coil is presented in the table that follows. Identify an appropriate control chart, and determine the chart's control limits. Cont in doc

Answer in doc

Define each of the following control chart patterns. Include a sketch for patterns b through f with your definition. a. One point outside the control limits b. Sudden shift in the process average c. Cycles d. Trends e. Hugging the center line f. Hugging the control limits

Answer in doc

In the production of vitamin capsules, the proportion of calcium in each capsule has a specification of 48 ± 18 parts per million (ppm). An initial random sample of 100 capsules revealed a sample average calcium content of 44.5 ppm and a sample standard deviation of 3.2 ppm. Management uses - and R-charts to monitor the calcium amount using samples of size 4 for each. The charts depict an in-control process. The center line of the R-chart is 6.7 and the center line of the -chart is 44.8. ​ a. Compute Cp for this process using estimates of the process mean and standard deviation derived from the random sample. b. Compute Cp for this process using estimates of the process mean and standard deviation derived from the control chart parameters. c. Compute Cpk for this process using estimates of the process mean and standard deviation derived from the random sample. d. Compute Cpk for this process using estimates of the process mean and standard deviation derived from the control chart parameters. e. What do the differences between the values of Cp and Cpk tell you?

Answer in doc

RM Industries wishes to monitor its end-of-week accounts receivable balance. To do so, the end-of-week balances for the previous 25 weeks were recorded and are shown in the table that follows. Establish an x-chart and a moving range (using n = 2) chart for this process. Cont in doc

Answer in doc

A better alternative to using the R-chart to monitor variation is the a. np-chart. b. s-chart. c. c-chart. d. p-chart.

B

A company wishes to monitor the variation in the length of time it takes to process and send a bill to a customer. Seven bills will be randomly selected each day for a 60-day period and the length of time it takes to process and send the bill to a customer will be recorded for each bill. The appropriate control chart is a(n)

B

A precision parts manufacturer produces bolts for use in military aircraft. The specifications for bolt length are 37.50 ± 0.25 cm. The company has established an -chart and an R-chart using samples of size five. The center lines for the -chart and R-chart are set at 35.25 cm and 1.08 cm, respectively. Which of the following is the value of Cp for this process? a. 1.333 b. 0.179 c. 0.301 d. 0.166

B

A process is said to be out of control when a. common causes are present. b. special causes are present. c. the process is not capable of meeting specifications. d. the upper and lower control limits cannot be computed.

B

After the featured distributor of electronic automation and power transmission products consolidated the types of packing slip errors into five categories, a _____ was performed. a. price evaluation b. Pareto analysis c. qualification standard d. quantification

B

All else being constant, if the sample size in a p-chart increases from 100 to 120, the upper and lower control limits will a. move farther apart. b. move closer together. c. not be affected. d. both shift upward.

B

Assuming 25 samples of size 100 were collected and a total of 96 nonconforming items were found, the upper control limit for the p-chart would be a. 0.083. b. 0.096. c. 0.137. d. 0.254.

B

Defects per million opportunities (dpmo) = a. (Number of defects discovered)/Opportunities for error × 100,000. b. (Number of defects discovered)/Opportunities for error × 1,000,000. c. (Opportunities for error × Number of defects discovered)/1,000,000. d. (Opportunities for error/Number of defects discovered) × 10,000,000.

B

For variables data, the sample means are assumed to be a. exponentially distributed. b. normally distributed. c. Poisson distributed. d. binomially distributed.

B

In pre-control, which of the following zones covers the nominal specifications of a process? a. Gray zone b. Green zone c. Red zone d. Yellow zone

B

Process capability calculations make little sense if the process a. data were taken over time. b. is not in statistical control. c. variations are due to common causes. d. is not initiated.

B

Short, repeated patterns in a control chart, with alternating high peaks and low valleys, are known as a. trends. b. cycles. c. shifts. d. runs.

B

Six samples of size 10 were collected. The data are provided in the following table: Sample number 1 2 3 4 5 6 Sample mean 4.80 4.62 4.81 4.55 4.92 4.65 Sample standard deviation 0.35 0.33 0.31 0.35 0.37 0.39 ​ The upper control limit (UCL) and lower control limit (LCL) for an s-chart are a. LCL = 0.2840, UCL = 1.7160. b. LCL = 0.0994, UCL = 0.6006. c. LCL = 4.6256, UCL = 5.3256. d. LCL = 3.6750, UCL = 5.7750.

B

The output of a process is stable and normally distributed. If the process mean equals 23.5, the percentage of output expected to be less than or equal to the mean a. is less than 25 percent. b. is 50 percent. c. is greater than 75 percent. d. cannot be determined without knowing the standard deviation value.

B

The s-chart is recommended when a. the control chart calculations need to be performed by hand. b. tight control of variability in the process is required. c. the -chart is not associated with an R-chart. d. the sample size for each sample needs to be reduced.

B

To form rational subgroups for an -chart, the goal is to choose samples that are as _____ as possible. a. heterogeneous b. homogeneous c. large d. systematic

B

Which of the following charts is used to monitor the average number of nonconformances per unit when sample sizes vary? a. -chart b. u-chart c. p-chart d. c-chart

B

Which of the following is NOT one of the basic applications of a control chart? a. To establish a state of statistical control. b. To calculate the average range. c. To monitor a process to identify special causes of variation. d. To determine process capability.

B

Which of the following statements regarding an x-chart is true? a. Individual data require averaging before being plotted on it. b. It is less sensitive to many conditions that can be detected by the -chart and R-chart. c. Specification limits cannot be drawn on the chart for direct comparison with the control limits. d. The assumption of normality of observations is less critical than for the -chart and R-chart.

B

_____ is measured as the amount of error in a measurement in proportion to the total size of the measurement. a. Precision b. Accuracy c. Systematic bias d. Capability

B

A c-chart is based on the _____ probability distribution. a. normal b. binomial c. Poisson d. exponential

C

A delivery company defines a defect as a package delivered later than the promised delivery time. Management wants to monitor the proportion of such defect packages per week and plans to sample 120 packages every week. The appropriate control chart is a(n) a. -chart. b. R-chart. c. p-chart. d. np-chart.

C

A preliminary analysis involving data entry at the featured distributor of electrical automation and power transmission products revealed that packing slips contained errors; to remedy this problem, a _____ was constructed for each day to track the number of defects found. a. Quality Assurance Committee b. sampling strategy c. u-chart d. new production process

C

A(n) _____ measurement characterizes the presence or absence of nonconformances in a unit of work. a. variable b. indicator c. attribute d. error

C

Because of high test costs, a sample of single wastewater sludge is tested daily for dissolved oxygen content. The appropriate control chart(s) would be a. -chart and R-chart. b. u-chart. c. x-chart and moving range chart. d. x-chart and R-chart.

C

Collecting _____ data is usually easier than collecting _____ data because the assessment can usually be done more quickly by a simple inspection or count. a. variable; attribute b. conformances; nonconformances c. attribute; variable d. simple; complex

C

Compared to variable measurement, attributes measurement requires _____ to obtain the same amount of statistical information about the quality of the product. a. a more distributed population b. more nonconformances c. a much larger sample size d. a smaller sample size

C

If a process is neither capable nor in control, the appropriate first step is to a. remove common causes of variation. b. redesign the equipment. c. remove special causes of variation. d. determine the process capability index.

C

If the variation in the process is due to common causes alone, the process is said to be a. out of control. b. in pre-control. c. in statistical control. d. out of capability.

C

In service applications, the term _____ is generally used to describe a nonconformance. a. cycle b. unit c. error d. trend

C

Statistical process control relies on a. process capability studies. b. dashboards. c. control charts. d. metrology.

C

The sample size for an x-chart a. should be between 25 and 30. b. is larger than that for an -chart. c. is equal to one. d. should be greater than one.

C

The x-chart is used for a. averages of variables data. b. individual attributes data. c. individual variables data. d. averages of attributes data.

C

Which of the following statements regarding a major advantage of np-charts is true? a. They can be used for variable sample sizes. b. They are more accurate than p-charts. c. They are easier to understand for production personnel than p-charts. d. The control limits are based on binomial distribution.

C

_____ is a study of variation in a measurement system using statistical analysis. a. A metrology study b. An SPC study c. A repeatability and reproducibility (R&R) study d. A calibration study

C

A _____ is the result of some cause that gradually affects the measurement and causes the points on a control chart to gradually move up or down from the center line. a. defect b. process shift c. cycle d. trend

D

A canning company defines a "nonconformance" as an orange juice can whose diameter is beyond the upper specification limit. A manager at the canning company wants to monitor the number of such orange juice cans produced per day. Each day, an employee will randomly select 120 cans over a period of four weeks. The employee then determines and plots the number of nonconformance cans in each sample. The appropriate control chart is a(n) a. u-chart. b. R-chart. c. p-chart. d. np-chart.

D

A(n) _____ monitors the fraction of nonconforming units. a. c-chart b. u-chart c. np-chart d. p-chart

D

Each day, a manufacturing company producing circuit boards will randomly sample 60 circuit boards for a period of 25 days and then determine and plot the number of defects contained in each of these boards. The appropriate control chart is a(n) a. u-chart. b. p-chart. c. np-chart. d. c-chart.

D

For statistical process control, a good sampling method should always a. use samples of random measurements over a long period of time. b. minimize sampling cost. c. maximize sample size. d. use rational subgroups.

D

In an attempt to solve the problem of tacked syringes at a Midwest pharmaceutical product manufacturer, statistical consultants recommended _____ for the purpose of improving the tacking operation. a. ANOVA b. pre-control c. measurement system evaluation d. statistical process control (SPC)

D

Which of the following pairs of charts are used together? a. -chart and p-chart b. R-chart and p-chart c. R-chart and s-chart d. -chart and R-chart

D

A "hugging the center line" pattern in a control chart can be the result of taking each sample from a different process but not mixed together. a. True b. False

False

A better alternative to the -chart to monitor variation is to compute and plot the standard deviation s of each sample. a. True b. False

False

A c-chart is based on the binomial distribution. a. True b. False

False

A histogram of data that resembles the normal distribution indicates that the process is in control. a. True b. False

False

Common and special causes of variation must be eliminated before process capability can be determined. a. True b. False

False

Control limits for the s-chart are given by: LCLs = B3s and UCLs = B4s, where B3 and B4 are constants. a. True b. False

False

For variable data, the two important quality measures are the proportion nonconforming and nonconformances per unit. a. True b. False

False

Histograms allow you to distinguish between common and special causes of variation. a. True b. False

False

If all sample averages on an -chart fall within the control limits, all output will be conforming. a. True b. False

False

In determining the method of sampling, samples should be chosen to be as heterogeneous as possible so that each sample reflects the system of common causes or assignable causes that may be present at that point in time. a. True b. False

False

A p-chart is used with the attribute data. a. True b. False

True

Control limits for variables and attributes data utilize different mathematical formulas. a. True b. False

True

If most of the points on a control chart fluctuate randomly between the control limits with no recognizable pattern, then the process is in statistical control. a. True b. False

True

If points on a control chart are determined to be the result of special causes, the points should be eliminated, and new control limits should be computed. a. True b. False

True

If the cost of investigating an operation to identify the cause of an apparent out-of-control condition is low, narrower control limits should be selected. a. True b. False

True

Pre-control should only be used when process capability is no greater than 88 percent of the tolerance. a. True b. False

True

Rolled throughput yield is the proportion of conforming units that results from a series of process steps. a. True b. False

True

The frequency of sampling in pre-control is often determined by dividing the time period between two successive out-of-control signals by six. a. True b. False

True

The larger the sample size, the narrower the control limits. a. True b. False

True

The total observed variation in production output is the sum of the true process variation plus variation due to measurement. a. True b. False

True

When constructing a u-chart, the standard deviation of each sample varies because the size of the sampling unit varies. a. True b. False

True

A nonconforming unit of work is one that has no defects or errors. a. True b. False

False

Variable data are a. discrete. b. not measurable. c. continuous. d. nonrandom.

C