©The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin

Chapter 7

Quality Tools:From Process Performance to

Process Perfection

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Learning Objectives

• Explain the function of the general-purpose quality analysis tools.• Explain how each quality tool aids in the QI story and DMAIC processes.• Explain how statistical process control can be used to prevent defects• from occurring.• Calculate control limits for X-bar charts, R-charts, P-charts, and C-charts. • Construct and interpret X-bar Charts, R-Charts, P-charts, and C-charts.• Describe and make computations for process capability using Cp and Cpk

capability indices.• Describe how acceptance sampling works and the role of the operating

characteristics curve.• Explain how Six Sigma quality relates to process capability.• Describe how moment-of-truth analysis can be used to improve service quality.• Describe Taguchi’s quality loss function and its implications.• Explain how customer relationship management systems relate to customer

satisfaction• Describe how “recovery” applies to quality failures.

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Quality Analysis Tools

• Six Sigma’s DMAIC and TQM’s QI Story provide structure, but neither defines how activities are to be accomplished. That can be determined through the use of a broad set of analysis tools.

Insert exhibit 7.1 DMAIC and QI

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General-Purpose Quality Analysis Tools

– Process Maps

– Run Charts

– Cause & Effect Diagram

– Pareto Charts

– Histograms

– Check Sheets

– Scatter Diagrams

– Control Charts

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General-Purpose Quality Analysis Tools: Process Maps

• A visual representation of a process.

• A Process Map for an Internet Retailer

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General-Purpose Quality Analysis Tools: Run Charts

Run Charts: Plotting a variable against time.

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Effect

ManMachine

MaterialMethod

Environment

Possible causes: The results

or effect

• Can be used to systematically track backwards to find a possible cause of a quality problem (or effect)

General-Purpose Quality Analysis Tools:

Cause & Effect Diagram

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General-Purpose Quality Analysis Tools: Cause & Effect Diagram

Also known as:Ishikawa DiagramsFishbone DiagramsRoot Cause Analysis

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Data Analysis Example

Exhibit 7.6: SleepCheap Hotel Survey Data

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• Can be used to identify the frequency of quality defect occurrence and display quality performance

General-Purpose Quality Analysis Tools: Histogram

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General-Purpose Quality Analysis Tools: Pareto Analysis

• A Variant of histogram that helps rank order quality problems so that most important can be identified

50.5% of complaints are that something is dirty

63.5% of complaints are about the bathroom

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General-Purpose Quality Analysis Tools: Scatter Plots

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General-Purpose Quality Analysis Tools: Checksheet

• Can be used to keep track of defects or used to make sure people collect data in the correct manner

Billing Errors

Wrong Account

Wrong Amount

A/R Errors

Wrong Account

Wrong Amount

Monday

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• Can be used to monitor ongoing production process quality and quality conformance to stated standards of quality

General-Purpose Quality Analysis Tools:

Control Charts

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• Common cause variability versus assignable cause variability

• Common cause variability comes from random fluctuation inherent to the process.

• Assignable cause variability is avoidable and not part of the process.

• SPC takes advantage of our knowledge about the standardized distribution of these measures.

• Process Control– Identifies potential problems before defects are created by watching

the process unfold– It uses X-bar Charts, R-Charts, P-charts, and C-charts

Controlling Process Variability:Statistical Process Control (SPC)

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• Measure a sample of the process output– Four to five units of output for most applications

– Many (>25) samples

• Calculate sample means ( X-bar ), grand mean (X-double bar), & ranges (R)

• Compare the “X-bars” being plotted to the upper and lower control limits and look for “assignable cause” variability.

• Assignable cause variability means that the process has changed.

X-bar Chart Steps

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• Cp and Cpk tell us whether the process will produce defective output as part of its normal operation.– i.e., is it “capable”?

• Control charts are maintained on an ongoing basis so that operators can ensure that a process is not changing– i.e., drifting to a different level of performance

– i.e., is it “in control”

Process Control

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• Measure a sample of the process output– Four to five units of output for most applications– Many (>25) samples

• Calculate sample means ( X ), grand mean (X), & ranges (R)• Calculate “process capability”

– Can you deliver within tolerances defined by the customer• Traditional standard is “correct 99.74% of the time”

• Monitor “process control”– Is anything changing about the process?

• In terms of mean or variation

SPC Steps

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X-Bar and R-Chart Construction

Insert Exhibit 7.17

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• Steps:-Calculate Upper & Lower Control Limits (UCL & LCL).

•Use special charts based on sample size

-Plot X-bar value for each sample-Investigate “Nonrandom” patterns

Control Charts: X-bar

Exhibit 7.18 X-bar Chart for Example 7.2

• Distinguishing between random fluctuation and fluctuation due to an assignable cause. – X-bar chart tracks the trend in sample means to see if any disturbing

patterns emerge.

??

??

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Nonrandom Patterns on Control Charts

• Investigate the process if X-bar or R chart illustrates:

– One data point above +3 or below -3

– 9 points in a row, all above or all below the mean

– 6 points in a row, all increasing or all decreasing

– 14 points in a row alternating up and down

– 4 out of 5 points in a row in Zone B or beyond

– 15 points in a row in Zone 3, above or below the center line

– 8 points in a row in Zone B, A, or beyond, on either side of the center line with no points in Zone C

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R-charts

• R-charts monitor variation within each sample.• R-charts are always used with X-bar charts.

Exhibit 7.22 R-Chart for Example 7.4

• Steps• Calculate Upper & Lower

Control Limits (UCL & LCL).• Use special tables based on

sample size.

• Plot the R value for each sample

• Investigate “Nonrandom” patterns

??

??

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Process Capability

• Capability Index: Quantifies the relationship between control limits and customer specifications.

– A process is “capable” when all of the common cause variability

occurs within the customer’s specification limits.

– Cp is used to determine “capability” when the process is centered.

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Cp CalculationFor Centered Processes

• Cp compares the range of the customer’s expectations to the range of the process to make sure that all common cause variability is inside of the customer’s specifications.

• Cp = UCS - LCS 6σ

• UCS - Upper control specification• LCS - Lower control specification - Standard deviation of process performance

• If Cp > 1.000 the process is considered capable.

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Example 7.4: Cp Calculation

• Customer specification– Mean of .375 inches– + or - .002 inches

– Therefore, customer specification limits at .373 and .377

• Process performance– Actual mean is .375– Standard deviation is 0.0024

Cp = 0.377 – 0.373 6(0.0024)= 0.27778

The process is not capable.

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Process Capability for Uncentered Processes

• Some processes are intentionally allowed to “shift.”

• In these cases, the range of process variability moves toward one of the customer specifications as the process shifts.

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Process Capability for Uncentered Processes

• As soon as one of the “tails” of the process distribution crosses the customer specifications, the process is no longer capable

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Process Capability for Uncentered Processes

• The process capability index for uncentered processes checks both ends of the distribution to ensure that the process has not shifted beyond the customer specifications.

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Cpk Calculation

• LCS - Lower control specification• UCS - Upper control specification• X - “Grand” mean of process performance - Standard deviation of process performance

,

3σ

XUCS,

3σ

LCSXminC pk

• If Cpk is > 1.000 then the process is “Capable”– Translation, we will produce good parts at least 99.74% of the time

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Example 7.3: Cpk Calculation

• Customer specification– Mean of .375 inches– + or - .002 inches

– Therefore, customer specification limits at .373 and .377

• Process performance– Actual mean is .376– Standard deviation is 0.0003

Cpk = min[ 0.376 – 0.373 , 0.377 – 0.376 ] 0.0009 0.0009

= min [3.333, 1.111]= 1.111

The process is capable.

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Process Control Charts for Attributes

• P-charts– Used to monitor the proportion or percentage of items defective in a

given sample.

UCL=

LCL=

n = the sample size

= the long-run average and center line

Z is the number of normal standard deviations for the desired confidence

pp z

pp z

(1 ) /p p p n

p

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Process Control Charts for Attributes

• C-charts– Used to monitor the counts of

noncomformities per unit.

UCL =

LCL =

2 c c

3( )c

3( )c

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Acceptance Sampling

• Purposes– Sampling to accept or reject the immediate lot of product at hand– Ensure quality is within predetermined level

Advantages Disadvantages

-Economy-Less handling damage-Fewer inspectors-Upgrading of the inspection job-Applicability to destructive testing-Entire lot rejection (motivation for improvement)

-Risks of accepting “bad” lots and rejecting “good” lots

-Added planning and documentation

-Sample provides less information than 100-percent inspection

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Acceptance Sampling

• Acceptable Quality Level (AQL)– Is the max. acceptable percentage of

defectives that defines a “good” lot

– Producer’s risk is the probability of rejecting a good lot

• Lot tolerance percent defective (LTPD)– Is the percentage of defectives that defines

consumer’s rejection point

– Consumer’s risk is the probability of accepting a bad lot

• The sampling plan is developed based on risk tolerance to determine size of sample and number in sample that can be defective

Exhibit 7.26 Operating Characteristics Curve

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Six Sigma Quality

Exhibit 7.28 Process Capability for Six Sigma Quality

• “Six sigma” refers to the variation that exists within plus or minus six standard deviations of the process outputs

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Six Sigma Quality

• In “process capability” terms, Six Sigma means that control limits set at plus or minus 6 σ will be inside of the customer’s specifications.

• This greatly reduces the likelihood of a defect occurring from common cause variability.

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Six Sigma Quality – Role of interdependencies

• 6 is often needed when products are complex.• At 3 quality, for example, the probability that

an assembly of interdependent parts works, given “n” parts and the need for all parts to work:– 1 part = .99741 = 99.74%– 10 parts = .997410 = 97.43%– 50 parts = .997450 = 87.79%– 100 parts = .9974100 = 77.08%– 267 parts = .9974267 = 49.90% – 1000 parts = .99741000 = 7.40%

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"Sigma" Level

Percent Error Free Output

Error Free/Million

Defects/Million (DPMO)

1 31% 310,000 690,000 2 69% 690,000 310,000 3 93.30% 933,000 67,000 4 99.40% 994,000 6,000 5 99.98% 999,800 200 6 99.9997% 999,997 3

• The odds of common cause variability creating a result that is 6 from the mean are 2 in 1 billion– 99.9999998% confident of a good outcome

• In practice, process mean is allowed to shift ±1.5

Six Sigma and Failure Rates

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Taguchi Method

• As deviation from the target increases, customers get increasingly dissatisfied and costs increase.

• Traditional views define deviation in terms of being “good” or “defective.” Taguchi views deviation in terms of costs that occur even if the deviation is slight, and increasing costs as deviation increases.

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• Moment-of-Truth Analysis: The identification of the critical

instances when a customer judges service quality and

determines the experience enhancers, standard expectations, and experience detractors.

• Experience enhancers: Experiences that make the customer feel good about the interaction and make the interaction better.

• Standard expectations: Experiences that are expected and taken for granted.

• Experience detractors: Experiences viewed by the customer as reducing the quality of service.

Moment-of-Truth Analysis

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Recovery

• There will always be times when customers do not get what they want.

• Failure to meet customers’ expectations does not have to mean lost customers.

• Recovery plans: Policies for how employees are to deal with quality failures so that customers will return.

• Example: A recovery for a customer who has had a bad meal at a restaurant might include eliminating the charges for the meal, apologizing, and offering gift certificates for future meals.