Supplement 6 Statistical Process Control

What is the primary objective of a statistical process control (SPC) system?

A process producing boxes of oatmeal is designed to have a mean weight of 14 ounces with a standard deviation of 0.1 ounce. If samples of 36 boxes are taken, what are the 3-sigma upper and lower control limits for the x-chart?

Which statement best describes the central limit theorem as it applies to statistical process control?

An insurance claims process has an upper specification of 213 minutes and a lower specification of 207 minutes. The process standard deviation is 0.516 minutes. What is the process capability ratio (Cp)?

To monitor the number of flaws in a bolt of cloth, which type of control chart is the most appropriate choice?

A quality manager is setting up an R-chart for a process where the sample size is 7 and the average range (R-bar) across all samples is 10. Using the standard factors for 3-sigma limits, what are the Upper Control Limit (UCLR) and Lower Control Limit (LCLR) for the range?

A new machine cuts insoles with a process mean of 0.250 inches and a standard deviation of 0.0005 inches. The upper specification limit is 0.251 inches and the lower specification limit is 0.249 inches. What is the process capability index (Cpk) for this machine?

In a data entry process, 20 samples of 100 records each were examined, and a total of 80 records with errors were found. What is the value of p-bar, the center line for the p-chart?

What is the key difference between an x-chart and a p-chart?

In acceptance sampling, what does the Acceptable Quality Level (AQL) represent?

A Red Top Cab Company owner receives the following number of complaints over a 9-day period: 3, 0, 8, 9, 6, 7, 4, 9, 8. What are the 3-sigma upper and lower control limits for the c-chart monitoring these complaints?

What is the primary difference between assignable variation and natural variation in a process?

On a control chart, what does a run of 5 points all above the center line typically indicate?

For a process with an average range of 0.25 ounces and a sample size of 5, a manager wants to set up an x-chart. Using the factors from standard tables, what would the term 'A2*R-bar' be, which represents the 3-sigma distance from the center line?

In acceptance sampling, the mistake of rejecting a good lot is known as what?

A process has an upper specification limit of 8.12 grams and a lower specification limit of 7.88 grams. The process mean is 8.01 grams and the process standard deviation is 0.03 grams. What is the Cpk for this process?

Which of these five steps is performed LAST when building x-bar and R-charts?

An operating characteristic (OC) curve is used in acceptance sampling to illustrate the relationship between what two factors?

A process monitoring the diameter of auto pistons has an overall mean (x-double-bar) of 155 mm and an average range (R-bar) of 4.5 mm. If the sample size is 10, what are the 3-sigma upper and lower control limits for the x-chart?

If a process has a capability ratio (Cp) of 2.0, what quality level does this correspond to?

What is a primary advantage of using the range (R) instead of the standard deviation to calculate control limits for an x-chart?

An Altman Distributors takes samples of 100 catalog orders each day. The average defect rate (p-bar) was found to be 0.05. What are the 3-sigma upper and lower control limits for the p-chart?

In the context of control charts, what is a run test used for?

The average number of misplaced bags on America South Airlines flights over the past 6 weeks has been 10 bags per week. What is the 3-sigma upper control limit for the c-chart monitoring misplaced bags?

What is the key difference between the process capability ratio (Cp) and the process capability index (Cpk)?

A process has an overall average of 705 cc and an average range of 6 cc. If a sample size of 10 is used, what are the upper and lower control limits for the mean (x-chart)?

What does it mean if a process is 'in statistical control'?

A manufacturing process for precision-cut wire has an average range (R-bar) of 1.05 inches across 24 hourly samples. The sample size is 4. What are the upper and lower control limits for the R-chart?

What is the statistical term for the probability of rejecting a good lot, also known as producer's risk?

A process filling bottles with baby formula has a target of 3 ounces plus or minus 0.150 ounce. Samples showed the process average is 3.042 ounces with a standard deviation of 0.034 ounce. What is the Cpk of this process?

When are p-charts or c-charts used instead of x-charts and R-charts?

In a sampling plan, the lot tolerance percentage defective (LTPD) is 7 percent and the consumer's risk (beta) is 10 percent. What does this mean?

If the defective rate for a product has historically been 1.5 percent, what are the 3-sigma upper and lower control limits for a p-chart with a sample size of 500?

According to the five steps for building control charts, what should be done immediately after graphing the sample data and determining that points fall outside the acceptable limits?

An acceptance sampling plan for lots of 500 pieces uses a sample size of 60. The plan has a 57 percent probability of accepting lots when the incoming quality is 4 percent defective. What is the average outgoing quality (AOQ) under these conditions?

Which of the following patterns on a control chart would require investigation, even if all points are within the control limits?

A computer chip production process yields chips with an average life of 1,800 hours and a standard deviation of 100 hours. The specification limits are 1,600 hours and 2,400 hours. Is this process capable of meeting the specifications?

Which of the following is an example of an observation for a p-chart?

An ad agency is tracking weekly complaints about its billboards. The historical average is 4 complaints per week. What would be the 3-sigma upper and lower control limits for a c-chart to monitor this?

Why must two charts, an x-chart and an R-chart, be used together to monitor variables?

The difference between the upper and lower specification for a process is 0.6 inches, and the standard deviation is 0.1 inches. What is the process capability ratio (Cp)?

For which of the following situations would an R-chart be most useful?

An acceptance sampling plan has lots of 2,000 units and a sample size of 100. The incoming lots are 3 percent defective, and the probability of acceptance (Pa) is 0.55. What is the Average Outgoing Quality (AOQ)?

What is represented by the solid line in the distribution graph in Figure S6.1b, which shows samples of cereal boxes?

A school board introduced a new math program and is evaluating test errors. The number of errors from 5 schools were: 52, 27, 35, 44, and 55. What is the center line for a c-chart to monitor these test errors?

If a process has 3-sigma control limits, what percentage of the sample averages are expected to fall within these limits if the process only has natural variations?

A process has an upper specification limit of 0.6 inches, a lower specification limit of 0.4 inches, and a process standard deviation of 0.025 inches. The process is centered, with a mean of 0.5 inches. What is the Cpk of this process?

How does increasing the sample size (n) affect the sampling distribution of means?

An inspection of 10 samples of 100 DNA samples each found the following number of defective samples per day: 7, 6, 6, 9, 5, 6, 0, 8, 9, 1. What is the center line (p-bar) for a p-chart?

If a process is in control but has a Cp of 0.8, what does this indicate?