Ch 10: Quality Control

If the number of standard deviations is not specified when computing control charts, what is an appropriate default value?

+/- 2 standard deviations

Run Tests

- RUN TEST: checks for patterns in a sequence of observations, or checks for nonrandomness. - RUN: a sequence of observations w/ a certain characteristic, followed by one or more observations w/ a diff characteristic. - RUN TEST 1: examination of the # of runs "up and down" - RUN TEST 2: runs "above and below" the median.

Control Charts for Attributes

- process characteristics are counted, not measured (ex. # of defective items) 1. P-Chart: used to monitor the proportion of defective items generated by a process. Theoretical basis is the binomial distribution. Use when (1) observations can be placed into one of 2 categories (pass/fail, good/bad, etc) or (2) the data consist of multiple samples of n observations each (ex. 15 samples of n=20 observations each) 2. C-Chart: for the # of defects per unit. use when only the # of occurrences per unit of measure can be counted; non-occurrences cannot be counted. (ex. scratches, ships dents, or errors per item)

Control Charts for Variables

- variable data are measured, usually on a continuous scale 1. Mean Control Chart (x-bar chart): based on a normal distribution. Sensitive to shifts in the process mean 2. Range Control Charts (R-charts): used to monitor process dispersion. They are sensitive to changes in process dispersion. Procedure for determining initial control limits: 1. Obtain 20-25 samples. Compute the appropriate sample statistics for each sample (ex. mean) 2. Establish preliminary control limits using the formulas 3. Determine if any points fall outside the control limits 4. Plot the data on the control chart and check for patterns 5. If no out-of-control signs are found, assume the process is in control. If any out-of-control signals are sound, investigate and correct causes of variation. Then, resume the process and collect another set of observations upon which control limits can be based

Basic Issues of Inspection

1) How much to inspect and how often 2) At what points in the process inspection should occur 3) Whether to inspect in a centralized or on-site location 4) Whether to inspect attributes or variables

The process capability index (Cpk) may mislead if (I) the process is not stable. (II) the process output is not normally distributed. (III) the process is not centered

1, 2 & 3

Data Types

1. Variables: data that are measures, interval or ratio-scaled data 2. Attributes: data that are counted

Limitations of Capability Indexes

1. the process may not be stable, in which case a capability index is meaningless 2. the process output may not be normally distributed, in which case inferences abt the fraction of output that isn't acceptable will be incorrect 3. the process is not centered, but the C(p) index is used, giving misleading results

Select the best definition of Quality Control.

A process that measures output relative to a standard and takes action when discrepancies occur.

Select the best definition of a control chart.

A time-ordered plot of sample statistics used to determine randomness or non-randomness.

What is the rationale and basis for statistical process control?

Acceptable variation within probability limits

Under which conditions would on-site inspection be better than off-site at a specialized test lab?

Alteration or contamination of samples during transfer to lab Need for quick inspection results due to delivery schedule

When is the nonrandom variation shown on a control chart a positive outcome?

An observation below the lower control limit on a p-chart. An observation below the lower control limit on a c-chart. An observation below the lower control limit on a R-chart.

What is the best synonym for inspection from the below list?

Appraisal

Managers must make a number of important decisions about the use of control charts. What are they?

At what points in the process to use control charts What type of control chart to use What size samples to take How often samples should be taken

What happens when a process is not stable?

Capability index is meaningless

When the results of quality control are unacceptable, what is the next step?

Corrective action

What is the formula for Cp?

Cp = Specification Width / Process Width

Which scenario would indicate the need for off-site testing at a centralized testing facility?

Customer specifications for satellite component require dust-free, no vibration test

Run tests can reveal non-random patterns in time-ordered data. Select three patterns that might be seen.

Cycles Trend Bias

What is the first step in the control process?

Define in sufficient detail what is to be controlled.

The Control Process

Effective control requires: 1. Define: define in sufficient detail what is to be controlled. Diff characteristics may require diff approaches for control purposes. 2. Measure: only those characteristics that can be counted or measured are candidates for control. 3. Compare: must be a standard or comparison that can be used to evaluate the measurements. This will relate to the level of quality being sought 4. Evaluate: mgmt must establish a definition of "out of control." Even a process that is functioning as it should will not yield output that conforms exactly to standard, simply bc of the natural variations inherent in all processes. 5. Correct: when a process is judged to be out of control, corrective action must be taken. Involves uncovering the cause of nonrandom variability and correcting it. 6. Monitor Results: to ensure corrective action is effective, the output of a process must be monitored for a sufficient period of time to verify that the problem has been eliminated.

Though process improvement initiatives come with a cost, benefits of more capable processes may outweigh and can include which of the following?

Fewer service complaints Less need for inspection Lower warranty costs

What are the different inspection points in manufacturing?

Finished goods after production Before a costly, irreversible or covering operation/process. Raw materials & purchased parts before production

Designing Quality into the Process

Greatly reduces the need for inspection or control efforts.

Where to Inspect in the Process

In manufacturing, the typical inspection points are: 1. Raw materials and purchased parts: little sense in paying for goods that don't meet quality standards and in expending time and effort on material that is bad to begin w/. Supplier certification programs can reduce or eliminate the need for inspection 2. Finished products: repairing or replacing products in the field is usually much more costly than doing it at the factory. Seller is usually responsible for shipping costs on returns, and payments for goods or service may be held up pending delivery or satisfactory goods or remedial service. 3. Before a costly operation: point is to not waste costly labor or machine time on items that are already defective 4. Before an irreversible process: items can be reworked up to a certain point, beyond that point they cannot. 5. Before a covering process: painting, plating, and assemblies often mask defects - measuring PROCESS YIELD: the ratio of output of good product to the total output

Acceptance Sampling

Quality assurance that relies primarily on inspection of lots (batches) of previously produced items

Which of the following statements is/are correct about the sampling distribution?

Sampling distribution is a plot of many sample means. Sampling distribution is narrower than the process distribution.

Which of the following statements is/are correct about Specifications?

Specifications are a range of values in which all units of output must fall to be acceptable. Specifications are tolerances established by Engineering and/or the Customer.

How do Specifications differ from Control Limits?

Specifications refer to the entire process and control limits are set on the sampling distribution.

Which of the following elements are part of the calculation for the capability analysis statistic Cpk?

Take the smaller of the two calculation values for Cpk. Calculate the distance from the mean to the upper tolerance then do the same to the lower.

How does Taguchi's belief about quality differ from the traditional view?

The cost of poor quality increases as the output approaches the specification limit.

Which of the following statements about inspection frequency are is/are correct?

The more lots being produced the more inspections are needed. A stable process will require less frequent checks than an unstable process.

In a control chart when a data point falls outside the control limits (upper and lower), what must be concluded?

The process appears non-random and should be checked.

Which of the following exemplify a capable process?

The range of process variability is much less than the width of customer specifications.

When comparing a sampling to a process distribution, what are the most important things to note?

They have the same means, are normally distributed, and sampling has less variability.

Why do statistical process control analysts perform run tests, even when control charts demonstrate all points within the limits?

To determine whether patterns can be detected.

Select the best definition of capability analysis.

To determine whether the variability of a stable process falls within tolerances.

What are some ways operations managers can improve process capability?

Upgrade or automate equipment Standardize process steps Reduce the process variability

When is the capability analysis statistic Cp used?

When a process is centered between the upper and lower specifications.

When is the capability analysis statistic Cpk used, instead of Cp?

When a process is not centered between the upper and lower tolerances.

The purpose of control charts is to

distinguish between random variation and assignable variation in the process

The decision about where to use control charts should focus on aspects of the process that _______.

have a tendency to go out of control, and affect product or service characteristics

Inspection

appraisal activity that compares goods/services toa standard. Vital but often unappreciated aspect of quality control. - LEAN orgs place an emphasis on quality and workers are responsible for quality, so they may not need lots of inspection. - Can occur at 3 points: 1. Before production: make sure inputs are acceptable (involves acceptance sampling procedures) 2. During production: make sure the conversion of inputs into outputs is proceeding in an acceptable manner (involves as process control) 3. After production: make a final verification of conformance b4 passing goods onto customers. (involves acceptance sampling procedures)

A process results in a few defects occurring in each unit of output. Long-run, these defects should be monitored with

c-charts

Approximately 99.7 percent of sample means will fall within plus or minus two standard deviations of the process mean if the process is under control.

false

Control limits are based on multiples of the process standard deviation

false

Control limits used on process control charts are specifications established by design or customers.

false

Run tests give managers an alternative to control charts; they are quicker and cost less

false

The Taguchi loss function suggests that the capability ratio can be improved by extending the spread between LCL and UCL

false

The number of defective parts in a sample is an example of variable data because it will "vary" from one sample to another.

false

A mean control chart is used to check ______.

for central tendency of a variable

Given a stable process, we must ask the question whether the ______ of process output is within an acceptable range.

inherent variability

The implication for Taguchi is that reducing the variation inherent in a process will result ______.

lowering the cost of poor quality lowering the loss to society

Process Capability

once the stability of a process has been established, its necessary to determine if the process is capable of producing output that is within an acceptable range. - SPECIFICATIONS/TOLERANCES are established by engineering design or customer requirements. They indicate a range of values in which individual units of output must fall in order to be acceptable - CONTROL LIMITS are statistical limits that reflect the extent to which sample statistics such as means and ranges can vary due to randomness alone. PROCESS VARIABILITY reflects the natural or inherent (random) variability in a process. Its measured in terms of the process std dev - control limits and process variability are directly related. - PROCESS CAPABILITY refers to the inherent variability of process output relative to the variation allowed by the design specs.

Quality Control

process that measures output relative to a standard and takes corrective action when output does NOT need standards

Which of the following quality control sample statistics indicates a quality characteristic that is an attribute?

proportion

Statistical Process Control

quality control efforts that occur during production

Statistical process control is ______.

quality control efforts that occur during production

A point which is outside of the lower control limit on an R-chart

should be investigated because an assignable cause of variation might be present

Random variation in a process indicates __________; whereas non-random variation indicates process __________.

stability/instability

The amount of inspection needed depends on _____ and _____.

the costs of inspection; the costs of passing on defective items

A range control chart is used to check ______.

the dispersion of a variable

For attribute data a c-chart is used to monitor ______.

the number of defects per unit

For attribute data a p-chart is used to monitor ______.

the proportion of defective items generated by a process

Attribute data are counted, variable data are measured

true

Concluding that a process is out of control when it is not is known as a Type I error.

true

High-cost, low-volume items often require careful inspection since we may have large costs associated with passing defectives.

true

The sampling distribution can be assumed to be approximately normal even when the underlying process distribution is not normally distributed.

true

True or false: Sometimes non-random variation can indicate excellent quality.

True Reason: If a p-chart or c-chart has points below the lower control limit, quality has improved (the result was not by random chance).

True or false: In the control process, only those characteristics that can be counted or measured are candidates for control.

True Reason: In quality control, if it cannot be counted or measured, it is not possible to perform a statistical analysis for comparison.

Statistical Process Control

- QUALITY OF CONFORMANCE: does the output of a process conform to the intent of the design? - STATISTICAL PROCESS CONTROL (SPC): used to evaluate process output to decide of a process is "in control" or if corrective action is needed. > Process Variability: 1. Are the variations random? If nonrandom variations are present, the process is unstable. Corrective action will need to be taken to improve the process by eliminating the causes of nonrandomness to achieve a stable process. 2. Given a stable process, is the inherent variability of process output within a range that conforms to performance criteria? Involves an assessment of a process's capability to meet standards, IF a process is not capable, it will need to be addressed. - RANDOM VARIATIONS: the natural or inherent process variations in process output that are due to the combined influences of countless minor factors. (Deming refers to this as COMMON VARIABILITY). - ASSIGNABLE VARIATION (non-random/special variation): main sources can usually be identified and eliminated. Typical sources are tool wear, defective materials, and human factors.

Control Charts

- a CONTROL CHART is a time-ordered plot of sample statistics used to monitor sample statistics to determine if the variability exhibited reflects random variation, developed by Walter Shewhart. - In control/stable: data points must fall between the upper and lower control limits. A point that falls on or outside of either limit would suggest the process output may be nonrandom and not in control, in which the process would be halted to find and correct the cause of the nonrandom variation. - CONTROL LIMITS: dividing lines between what will be designated as random deviations from the mean and what will be designated as nonrandom deviations from the mean. There's a small probability that a value will fall outside the limits even tho only random variations are present. - TYPE I ERROR (alpha risk): nonrandomness is present when only randomness is present. (probability is at the 2 ends of the tails (above the UCL or below the LCL)). Using wider limits reduces the probability of a Type I error bc it decreases the area in the tails, but wider limits make it more difficult to detect nonrandom variations if they're present. - TYPE II ERROR: indicates a process is in control when it's really out of control (concluding nonrandom variations are present when they're not).

Sampling and Sampling Distributions

- in statistical process control, periodic samples of process output are taken and sample statistics are determined. Sample statistics can be used to judge randomness of process variations. A SAMPLING DISTRIBUTION is a theoretical distribution that describes the random variability of sample statistics. Serves as a basis for distinguishing b/w random and nonrandom values of a sampling statistic. - a sampling distribution and a process distribution (1) have the same mean (2) variability of the sampling distribution is less than the variability of the process and (3) the sampling distrib is normal - in case of sample means, the CENTRAL LIMIT THEOREM states that as a sample size increases, the distribution of sample averages approaches a normal distribution regardless of the shape of the samples population. Tends to be the case even for fairly small sample sizes.

Capability Analysis

- performed on a process that is in control for the purpose of determining if the range of variation is within design specs that would make the output acceptable for its intended use. If its within the specs, the process is said to be "capable", if not, mngr must decide how to correct the situation. > C(p): capability index used to assess the ability of a process to meet specifications. Use when a process is centered between the upper and lower specifications. - SIX SIGMA: goal of achieving a process variability so small that the design specifications represent 6 std devs about AND below the process mean. - care must be taken when interpreting the C(p) index, bs its computation doesn't involve the process mean. Unless the target value is CENTERED b/w the upper and lower specification, the C(p) can be misleading. > C(pk): use if process is not centered. if larger than 1.33, the process is capable. Take the smaller of the two calculation values for Cpk. Calculate the distance from the mean to the upper tolerance then do the same to the lower. > Improving process capability: requires reducing the process variability thats inherent in a process, which might involve simplifying, standardizing, making the process mistake-proof, upgrading equipment, or automating. Methods: 1. Simplify: eliminate steps, reduce the # of parts, use modular design 2. Standardize: use standard parts, standard procedures 3. Make mistake-proof: design parts that can only be assembled the correct way; have simple checks to verify a procedure has been performed correctly 4. Upgrade equipment: replace worn-out equipment; take advantage of tech improvements 5. Automate: substitute automated processing for manual processing

Managerial Considerations Concerning Control Charts

- using control charts adds to the cost and time needed to obtain output. Goal is to have processes so good that the desired level of quantity could be achieved w/o the use of any control charts. Mngrs must make the following important decisions: 1. At what points in the process to use control charts 2. What size samples to take: greater the sample, greater cost to inspect and longer process hold-up. Change is more likely to take place WITHIN a large sample than BETWEEN small samples. One needs a much smaller sample size for a mean chart than a p-chart 3. What type of control chart to use (variable or attribute) 4. How often should samples be taken - the decision about where to use control charts should focus on those aspects of the process that (1) have a tendency to go out of control and (2) are critical to the successful operation of the prod/serv

Using Control Charts and Run Tests Together

1. Compute control limits for the process output a. Determine which type of control chart is appropriate b. Compute control limits using the appropriate formulas. If no probability is given, use a value of z=2.0 to compute the control limits c. If any samples statistics fall outside of the control limits, the process is not in control. If all values are within the control limits, proceed to step 2 2. Conduct median and up-down run tests. Use z +-2.00 for comparing test scores. If either or both test scores are not within z=+-2.00, the output is probably not random. If both test scores are within z=+-2.00, proceed to Step 3 3. Plot the sample data and visually check for patterns. If you see a pattern, the output is probably not random. Otherwise, conclude the output is random and that the process is in control > What Happens When a Process Exhibits Possible Nonrandom Variation: nonrandom variation is indicated when a point is observed that is outside the control limits, or a run test produces a large z-value (greater than +-1.96), but it may be a false alarm (ex. Type I Error), or it may be a real indication of the presence of an assignable cause of variation. If it appears to be a false alarm, resume the process but monitor it for a while to confirm this. If an assignable cause can be found, it needs to be addressed. If its a good result (ex. an obs below the LCL of a p-chart, a c-chart, or a range chart would indicate unusually good quality), it may be possible to change the process to achieve similar results on an ongoing basis. Operators can be trained to handle simple problems, while teams may be needed to handle more complex problems

How Much to Inspect and How Often

1. Low-cost, high-volume items (ex. paper clips, nails, wooden pencils) often require little inspection because (a) the cost associated w/ passing defective items is quite low and (b) the processes that produce these items are usually highly reliable, so defects are rare. 2. High-cost, low-volume items (ex. planes, ships) that have large costs associated w/ passing defective products often require more intensive inspections. - operations w/ a high proportion of human involvement necessitate more inspection effort than mechanical operations - frequency of inspection depends on (1) the rate @ which a process may go out of control or on (2) the # of lots being inspected. Stable process will only require infrequent checks and an unstable one will need more frequent checks

When control charts and run tests are used together, rank the order in which actions should be taken to compute control limits for process output. (1 is first, 3 is last.)

1. determine appropriate control chart based upon data type 2. compute upper and lower control limits 3. if sample stats fall outside control limits, stop and look for cause. If all are inside, conduct run tests to check for randomness

Which of the following is not a step in the control process?

100% inspection

Off-Site vs On-Site Inspection

> On-Site Inspection: allows for quicker decisions and avoidance of introduction of extraneous factors. Can access specialized equipment and a more favorable test environment. Some companies rely on self-inspections by operators if errors can be traced back to specific operators. Places responsibility for errors at their source

Taguchi Loss Function

Genichi Taguchi holds a nontraditional view of the cost of poor quality. As long as output is within specifications, theres no cost. Believed any deviation away for the tgt value represents poor quality and costs are greater the further away. Reducing the variation inherent in a process will result in lowering the cost of poor quality, and the loss to society.

A plot below the lower control limit on the range chart (I) should be ignored since lower variation is desirable. (II) may be an indication that process variation has decreased. (III) should be investigated for assignable cause

I, II, and III

The probability of concluding that assignable variation exists when only random variation is present is (I) the probability of a Type I error. (II) known as the alpha risk. (III) highly unlikely. (IV) the sum of probabilities in the two tails of the normal distribution

I, II, and IV

What are some risks of using capability indexes?

If the process output is not normally distributed, statistical inferences are incorrect. If the process is not centered but Cp is used anyway, it gives misleading indications. If the process is not stable, Cp and Cpk are meaningless.

Which of the following statements is/are correct about Inspection?

Inspection involves checking for conformance against a quality standard. Inspection can occur before, during or after production.

Which is/are examples of acceptance sampling?

Inspection of final assembly lots after production Inspection of raw material batches before production

Which of the following is the best definition of statistical process control?

It is analysis of data from some point in the process to determine if the process is likely to be in or out of control.

Which of the following are examples of inspection points in service organizations?

Kitchen cleanliness at fast food restaurant at shift start Outgoing patient billing accuracy at medical clinic

Which product characteristics would prompt the most intensive inspection?

Low-volume, high-cost