SUPPLEMENT 6: STATISTICAL PROCESS CONTROL

The X-bar chart indicates that a gain or loss of uniformity has occurred in dispersion of a production process.

False

The acceptable quality level (AQL) is the average level of quality we are willing to accept.

False

The probability of rejecting a good lot is known as consumer's risk.

False

The purpose of process control is to detect when natural causes of variation are present.

False

The x-bar chart, like the c-chart, is based on the exponential distribution.

False

To measure the voltage of batteries, one would sample by attributes.

False

X-bar charts are used when we are sampling attributes.

False

A c-chart is appropriate to plot the number of flaws in a bolt of fabric.

True

A process range chart illustrates the amount of variation within the samples.

True

Acceptance sampling accepts or rejects an entire lot based on the information contained in the sample.

True

An acceptance sampling plan must define "good lots" and "bad lots" and specify the risk level associated with each one.

True

Averages of small samples, not individual measurements, are generally used in statistical process control.

True

In acceptance sampling, a manager can reach the wrong conclusion if the sample is not representative of the population it was drawn from.

True

In statistical process control, the range often substitutes for the standard deviation

True

Mean charts and range charts complement one another, one detecting shifts in process average, the other detecting shifts in process dispersion.

True

Mistakes stemming from workers' inadequate training represent an assignable cause of variation

True

Some degree of variability is present in almost all processes.

True

The Central Limit Theorem states that when the sample size increases, the distribution of the sample means will approach the normal distribution.

True

The Cpk index measures the difference between desired and actual dimensions of goods or services produced.

True

A manager wishes to build a 3V range chart for a process. The sample size is five, the mean of sample means is 16.01, and the average range is 5.3. From Table S6.1, the appropriate value of D3 is 0, and D4 is 2.115. The UCL and LCL for this range chart are a. 33.9 and 11.2 b. 33.9 and 0 c. 11.2 and 0 d. 6.3 and 0 e. 31.91 and 0.11

c. 11.2 and 0

A Cpk index of 1.00 equates to a defect rate of a. five percent b. 3.4 defects per million c. 2.7 per 1,000 items d. 97.23 percent e. one percent

c. 2.7 per 1,000 items

If x = 23 ounces, V = 0.4 ounces, and n = 16, the r3V control limits will be a. 21.8 to 24.2 ounces b. 23 ounces c. 22.70 to 23.30 ounces d. 22.25 to 23.75 ounces e. none of the above

c. 22.70 to 23.30 ounces

Which of the following is true regarding the relationship between AOQ and the true population percent defective? a. AOQ is greater than the true percent defective. b. AOQ is the same as the true percent defective. c. AOQ is less than the true percent defective. d. There is no relationship between AOQ and the true percent defective. e. The relationship between these two cannot be determined.

c. AOQ is less than the true percent defective.

Which of the following statements on acceptance sampling is true? a. Acceptance sampling draws samples from a population of items, tests the sample, and accepts the entire population if the sample is good enough, and rejects it if the sample is poor enough. b. The sampling plan contains information about the sample size to be drawn and the critical acceptance or rejection numbers for that sample size. c. The steeper an operating characteristic curve, the better its ability to discriminate between good and bad lots. d. All of the above are true. e. All of the above are false.

d. All of the above are true.

Assignable causes a. are not as important as natural causes b. are within the limits of a control chart c. depend on the inspector assigned to the job d. are also referred to as "chance" causes e. are causes of variation that can be identified and removed

e. are causes of variation that can be identified and removed

The statistical process chart used to control the number of defects per unit of output is the a. x -chart b. R-chart c. p-chart d. AOQ chart e c-chart

e. c-chart

The mean and standard deviation for a process for which we have a substantial history are x = 120 and V = 2. For the variable control chart, a sample size of 16 will be used. What is the mean of the sampling distribution? a. 1/8 (0.125) b. 0.5 c. 2 d. 40 e. none of the above

e. none of the above

If the process average is in control, then the process range must also be in control.

False

A lot that is accepted by acceptance sampling is free of defects.

False

A normal distribution is generally described by its two parameters: the mean and the range.

False

A p-chart is appropriate to plot the number of typographic errors per page of text.

False

A process is said to be in statistical control when assignable causes are the only sources of variation.

False

A process that is in statistical control will always yield products that meet their design specifications.

False

The higher the process capability ratio, the greater the likelihood that process will be within design specifications.

True

The steeper an OC curve, the better it discriminates between good and bad lots.

True

A Type I error occurs when a. a good lot is rejected b. a bad lot is accepted c. the number of defectives is very large d. the population is worse than the AQL e. none of the above

a. a good lot is rejected

To set x -chart upper and lower control limits, one must know the process central line, which is the a. average of the sample means b. total number of defects in the population c. percent defects in the population d. size of the population e. average range

a. average of the sample means

The usual purpose of an R-chart is to signal whether there has been a a. gain or loss in dispersion b. change in the percent defective in a sample c. change in the central tendency of the process output d. change in the number of defects in a sample e. none of the above

a. gain or loss in dispersion

If a sample of items is taken and the mean of the sample is outside the control limits the process is a. out of control and the cause should be established b. in control, but not capable of producing within the established control limits c. within the established control limits with only natural causes of variation d. monitored closely to see if the next sample mean will also fall outside the control limits e. producing high quality products

a. out of control and the cause should be established

A manager wants to build 3V control limits for a process. The target value for the mean of the process is 10 units, and the standard deviation of the process is 6. If samples of size 9 are to be taken, the UCL and LCL will be

b. 16 and 4

Which of the following is true regarding the process capability index Cpk? a. A Cpk index value of 1 is ideal, meaning all units meet specifications. b. The larger the Cpk, the more units meet specifications. c. The Cpk index can only be used when the process centerline is also the specification centerline. d. Positive values of the Cpk index are good; negative values are bad. e. None of the above is true.

b. The larger the Cpk, the more units meet specifications.

A sample of parts is measured. The mean of this sample is in the middle of the control limits, but some individual parts measure too low for design specifications and other parts measure too high. Which of the following is true? a. The process is out of control, and the cause should be established. b. The process is in control, but not capable of producing within the established control limits. c. The process is within the established control limits with only natural causes of variation. d. The process is outside the established control limits with only natural causes of variation. e. The process is in control, and there is nothing to worry about.

b. The process is in control, but not capable of producing within the established control limits.

If the Cpk index exceeds 1 a. the AQL must be smaller than the LTPD b. Vmust be less than one-third of the difference between the specification and the process mean c. the x-bar chart must indicate that the process is in control d. the process is capable of Six Sigma quality e. the process is characterized as "not capable"

b. Vmust be less than one-third of the difference between the specification and the process mean

A Type II error occurs when a. a good lot is rejected b. a bad lot is accepted c. the population is worse than the LTPD d. the proportion of defectives is very small e. none of the above

b. a bad lot is accepted

The type of inspection that classifies items as being either good or defective is a. variable inspection b. attribute inspection c. fixed inspection d. all of the above e. none of the above

b. attribute inspection

The local newspaper receives several complaints per day about typographic errors. Over a sevenday period, the publisher has received calls from readers reporting the following number of errors: 4, 3, 2, 6, 7, 3, and 9. Based on these data alone, what type of control chart(s) should the publisher use? a. p-chart b. c-chart c. x -chart d. R-chart e. x - and R-charts

b. c-chart

The c-chart signals whether there has been a a. gain or loss in uniformity b. change in the number of defects per unit c. change in the central tendency of the process output d. change in the percent defective in a sample e. change in the AOQ

b. change in the number of defects per unit

Statistical process control charts a. display the measurements on every item being produced b. display upper and lower limits for process variables or attributes, and signal when a process is no longer in control c. indicate to the process operator the average outgoing quality of each lot d. indicate to the operator the true quality of material leaving the process e. none of the above

b. display upper and lower limits for process variables or attributes, and signal when a process is no longer in control

Assignable variation a. is a sign that a process is under control b. is to be identified and eliminated c. is the same as random variation d. is variation that cannot be traced to a specific cause e. leads to a steep OC curve

b. is to be identified and eliminated

A manufacturer uses statistical process control to control the quality of the firm's products. Samples of 50 of Product A are taken, and a defective/acceptable decision is made on each unit sampled. For Product B, the number of flaws per unit is counted. What type(s) of control charts should be used?

b. p-chart for A, c-chart for B

. Producer's risk is the probability of a. accepting a good lot b. rejecting a good lot c. rejecting a bad lot d. accepting a bad lot e. none of the above

b. rejecting a good lot

The Central Limit Theorem a. is the theoretical foundation of the c-chart b. states that the average of assignable variations is zero c. allows managers to use the normal distribution as the basis for building some control charts d. states that the average range can be used as a proxy for the standard deviation e. controls the steepness of an operating characteristic curve

c. allows managers to use the normal distribution as the basis for building some control charts

Control charts for variables are based on data that come from a. acceptance sampling b. individual items c. averages of small samples d. averages of large samples e. the entire lot

c. averages of small samples

A nationwide parcel delivery service keeps track of the number of late deliveries (more than 30 minutes past the time promised to clients) per day. They plan on using a control chart to plot their results. Which type of control chart(s) would you recommend? a. x - and R-charts b. p-charts c. c-charts d. x -, but not R-charts e. both p- and c-charts

c. c-charts

The purpose of an X chart is to determine whether there has been a a. gain or loss in uniformity b. change in the percent defective in a sample c. change in the central tendency of the process output d. change in the number of defects in a sample e. change in the AOQ

c. change in the central tendency of the process output

The x-bar chart tells us whether there has been a a. gain or loss in dispersion b. change in the percent defective in a sample c. change in the central tendency of the process output d. change in the number of defects in a sample e. none of the above

c. change in the central tendency of the process output

An operating characteristics curve shows a. upper and lower product specifications b. product quality under different manufacturing conditions c. how the probability of accepting a lot varies with the population percent defective d. when product specifications don't match process control limits e. how operations affect certain characteristics of a product

c. how the probability of accepting a lot varies with the population percent defective

Average outgoing quality (AOQ) usually a. worsens with inspection b. stays the same with inspection c. improves with inspection d. may either improve or worsen with inspection e. is the average quality before inspection

c. improves with inspection

Acceptance sampling a. is the application of statistical techniques to the control of processes b. was developed by Walter Shewhart of Bell Laboratories c. is used to determine whether to accept or reject a lot of material based on the evaluation of a sample d. separates the natural and assignable causes of variation e. all of the above

c. is used to determine whether to accept or reject a lot of material based on the evaluation of a sample

Up to three standard deviations above or below the centerline is the amount of variation that statistical process control allows for

c. natural variation

The normal application of a p-chart is in a. process sampling by variables b. acceptance sampling by variables c. process sampling by attributes d. acceptance sampling by attributes e. none of the above

c. process sampling by attributes

Jars of pickles are sampled and weighed. Sample measures are plotted on control charts. The ideal weight should be precisely 11 oz. Which type of chart(s) would you recommend? a. p-charts b. c-charts c. x - and R-charts d. x -, but not R-charts e. both p- and c-charts

c. x - and R-charts

. According to the text, the most common choice of limits for control charts is usually a. ± 1 standard deviation b. ± 2 standard deviations c. ± 3 standard deviations d. ± 3 standard deviations for means and ± 2 standard deviations for ranges e. none of the above

c. ± 3 standard deviations

Which of the following is true of a p-chart? a. The lower control limit is found by subtracting a fraction from the average number of defects. b. The lower control limit indicates the minimum acceptable number of defects. c. The lower control limit may be below zero. d. The lower control limit may be at zero. e. The lower control limit is the same as the lot tolerance percent defective.

d. The lower control limit may be at zero

An acceptance sampling plan's ability to discriminate between low quality lots and high quality lots is described by a. a Gantt chart b. the Central Limit Theorem c. a process control chart d. an operating characteristics curve e. a range chart

d. an operating characteristics curve

Acceptance sampling's primary purpose is to a. estimate process quality b. estimate lot quality c. detect and eliminate defectives d. decide if a lot meets predetermined standards e. determine whether defective items found in sampling should be replaced

d. decide if a lot meets predetermined standards

An operating characteristic (OC) curve describes a. how many defects per unit are permitted before rejection occurs b. the sample size necessary to distinguish between good and bad lots c. the most appropriate sampling plan for a given incoming product quality level d. how well an acceptance sampling plan discriminates between good and bad lots e. none of the above

d. how well an acceptance sampling plan discriminates between good and bad lots

Acceptance sampling is usually used to control a. the number of units output from one stage of a process which are then sent to the next stage b. the number of units delivered to the customer c. the quality of work-in-process inventory d. incoming lots of purchased products e. all of the above

d. incoming lots of purchased products

For an x-bar chart where the standard deviation is known, the Upper Control Limit a. is 3V below the mean of sample means for a 3V control chart b. is 3V above the mean of sample means for a 3V control chart c. is 3V n below the mean of sample means for a 3V control chart d. is 3V n above the mean of sample means for a 3V control chart e. cannot be calculated unless the average range is known

d. is 3V n above the mean of sample means for a 3V control chart

Natural variations a. are variations that are to be identified and eliminated b. are variations that can be traced to a specific cause c. are the same as assignable variations d. lead to occasional false findings that processes are out of control e. play no role in statistical process control

d. lead to occasional false findings that processes are out of control

The causes of variation in statistical process control are a. cycles, trends, seasonality, and random variations b. producer's causes and consumer's causes c. mean and range d. natural causes and assignable causes e. Type I and Type II

d. natural causes and assignable causes

A run test is used a. to examine variability in acceptance sampling plans b. in acceptance sampling to establish control c. to examine points in a control chart to check for natural variability d. to examine points in a control chart to check for nonrandom variability e. none of the above

d. to examine points in a control chart to check for nonrandom variability

The statistical definition of Six Sigma allows for 3.4 defects per million. This is achieved by a Cpk index of a. 0 b. 1 c. 1.33 d. 1.67 e. 2

e. 2

Acceptance sampling a. may involve inspectors taking random samples (or batches) of finished products and measuring them against predetermined standards b. may involve inspectors taking random samples (or batches) of incoming raw materials and measuring them against predetermined standards c. is more economical than 100% inspection d. may be either of a variable or attribute type, although attribute inspection is more common in the business environment e. All of the above are true.

e. All of the above are true.

Natural variations a. affect almost every production process b. are the many sources of variation that occur when a process is under control c. when grouped, form a pattern, or distribution d. are tolerated, within limits, when a process is under control e. All of the above are true.

e. All of the above are true.

Plots of sample ranges indicate that the most recent value is below the lower control limit. What course of action would you recommend? a. Since there is no obvious pattern in the measurements, variability is in control. b. One value outside the control limits is insufficient to warrant any action. c. Lower than expected dispersion is a desirable condition; there is no reason to investigate. d. The process is out of control; reject the last units produced. e. Variation is not in control; investigate what created this condition.

e. Variation is not in control; investigate what created this condition.