BA 301 Spring 2003

1
BA 301 Spring 2003

• Managing Quality
• and
• Statistical Process Control

2
Great Ideas in Quality Management The
Contributors

• Genechi Taguchi
• The Quality-Loss Function and Target Oriented
  Quality
• Walter Shewhart
• Statistical Quality/Process Control
• Process Capability
• W. Edwards Deming
• Total Quality Management
• Shigeo Shingo Taiichi Ohno
• Toyota Production System (aka Just-in-Time)

3
The Great Ideas in Quality Management Two
Stories

• Jon Ozmuns 1965 Ford Fairlane 500
• How to keep dust out of a new car.
• Watching Monday Night Football in the late 1980s
• San Francisco 49ers vs Detroit Lions
• A tale of two kicks

4
Great Contributors Genechi Taguchi Taguchi
Techniques

• Experimental methods (Called Design of
  Experiments) to improve product process design
• Identify key component process variables
  affecting product variation
• Taguchi Concepts
• Quality robustness
• Quality loss function
• Target specifications

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Quality Robustness Tacuchi Design the product

• so that it can be produced to specifications
  under adverse manufacturing conditions.
• so that it can perform under conditions more
  severe than it is expected to encounter.
• Coolant pump failure on 1983 Honda Accord

6
Quality Loss Function

• Shows social cost () of deviation from target
  value
• Assumptions
• Most measurable quality characteristics (e.g.,
  length, weight) have a target value
• Deviations from target value are undesirable
• Equation L D2C
• L Loss () D Deviation C Cost

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Quality Loss Function Graph
8
Target Specification Example
A study found U.S. consumers preferred Sony TVs
made in Japan to those made in the U.S. Both
factories used the same designs specifications.
The difference in quality goals made the
difference in consumer preferences.
Japanese factory (Target-oriented)
U.S. factory (Conformance-oriented)
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Quality Loss Function Distribution of Products
Produced
Quality Loss Function (a)
High loss
Unacceptable
Loss (to producing organization, customer, and
society)
Poor
Target-oriented quality yields more product in
the best category
Fair
Good
Best
Low loss
Target-oriented quality brings products toward
the target value
Conformance-oriented quality keeps product within
three standard deviations
Frequency
Distribution of specifications for product
produced (b)
Lower
Target
Upper
Specification
10
Japanese Target-Oriented Quality -Does it
really matter?

• In 1983, the Ozmuns bought a new Honda Accord.
  Based on their experience, they bought a new 1987
  Accord.
• The Ozmuns have purchased five new and four used
  vehicles since 1983. All have been either
  Honda/Acura or Toyota products.
• Their children and grandchildren have purchased
  one new Toyota and four used Hondas.

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Great Contributors Walter Shewhart Statistical
Quality Control

• In the early 1920s, the inspection group at
  Western Electric (a part of the Bell System) was
  given the task of developing new theories and
  methods of inspection for improving and
  maintaining product quality.
• Members of this group were W. Edwards Deming and
  Walter Shewhart.
• Shewhart is credited with the developing
  Statistical Quality Control (SQC).
• An earlier technique, called Acceptance
  Sampling had been the primary tool for quality
  control.

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What is/was Acceptance Sampling?

• A form of quality testing used for incoming
  materials or finished goods
• e.g., purchased material components
• The Procedure
• Take one or more samples at random from a lot
  (shipment) of items
• Inspect each of the items in the sample
• Decide whether to accept or reject the whole lot
  based on the inspection results
• This amounted to inspecting defects out after
  the product was made rather than building
  quality in while the product was being made.
• SPC was the foundation needed for building
  quality into the product.

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Statistical Quality Control (aka Statistical
Process Control - SPC)

• Shewhart determined that all processes are
  subject to variability. He separated the
  observed variability into common cause and
  special cause.
• Today, these are also called
• Natural causes Random variations
• Assignable causes Correctable problems
• Shewhart recognized that it was of utmost
  importance for management to know which type of
  variation was present in the process.
• If only natural cause variation was present, the
  process should be left alone.
• But, if assignable cause variation was present,
  it should be found and corrected.

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Statistical Process Control (SPC) continued

• Shewhart developed SPC to determine when a
  process is in control, or is out of control.
• A process is in statistical control when the only
  source of variation is common (natural) cause.
• SPC is grounded in statistical theory and
  involves collecting, organizing, interpreting
  data.
• The objective of SPC is to provide a statistical
  signal when assignable causes of variation are
  present.
• Today, SPC is used to control processes as
  products and services are created to insure
  that quality is built into the product.

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Variation in Processes

• Natural Variation the variation that is found
  in every process to some degree and is to be
  expected and tolerated
• Natural variations behave like a constant system
  of chance causes.
• Although the individual values are all different,
  as a group they form a pattern that can be
  described as a distribution.
• Assignable Variation the variation that can be
  traced to a specific reason and can therefore be
  corrected, e.g. machine wear, misadjusted
  equipment, fatigued or untrained workers, or new
  batches of raw or semi-finished goods materials

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Control Charts The heart of SPC

• The only way to know with 100 certainty what a
  process is doing is by 100 inspection. But this
  is usually too expensive.
• Control Charts provide us with a much less
  expensive way to know about a process.
• Control Charts do not provide 100 certainty.
  They provide a level of confidence that is
  dependent upon the way they are constructed.

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Different Control Charts for Different Situations

• Variable Measurement (Characteristics that have
  continuous dimensions, e.g. weight, volume,
  thickness, conductivity, etc)
• Control Charts for Variables are the
• X-bar chart (central tendency)
• R-chart (range or dispersion)
• Attribute Measurement (characteristics that have
  only two values, e.g. defective vs
  non-defective, on-time vs late, etc)
• Control Charts for Attributes are the
• p-chart (proportion defectives)
• c-chart (number defective)

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Theoretical Basis of Control Charts
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Theoretical Basis of Control Charts
Central Limit Theorem
Standard deviation
Mean
20
Sampling Distribution of Means, and Process
Distribution
21
Theoretical Basis of Control Charts
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Process Control Process Capability

• The ideal situation is that a process is both
  in control and capable of meeting the customers
  requirements.
• Other situations are
• Process is in control but incapable.
• Process is out of control but capable.
• Process is both out of control and
  incapable.
• We can determine which of these situations exists
  through the use information derived from control
  charts.

23
Process Capability Cpk

• Assumes that the process is
• under control
• normally distributed

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Constructing Using X-bar and R Control Charts

• Collect 20-25 samples of n 4 or 5 from a stable
  process and compute the mean and range of each.
• Compute the overall means (x double bar and R
  bar) and set appropriate control limits (usually
  3 sigma each side).
• Graph the sample means and ranges on their
  respective control charts to determine whether
  they fall outside the acceptable limits.
• If the process is deemed to be in statistical
  control, then continue to take periodic random
  samples to insure that the process stays in
  control.
• If the process is deemed to be out of control,
  then determine the source of the assignable
  cause variation and correct it.

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If the process is in control, can it meet the
customers specifications?

• To meet the customers specifications, the
  process variability cannot exceed the customers
  upper or lower specification limits.
• We determine the process variability from the
  variability of the sampling distribution.
• We have to convert standard deviation information
  from the sampling distribution to standard
  deviation information for the process.
• With this information, we determine the Process
  Capability Index (Cpk).

26
Converting Sampling Distribution information to
Process Distribution information

• For the Sampling Distribution
• One standard deviation (sigma) is
  (A2R-bar)/3
• The Process Distribution standard deviation is
  calculated from the Sampling Distribution
• Sigma (process) Sigma(sample) X (sq.rt.n)

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Process Control Process Capability A Sample
Problem

• Rockys Peanut Butter Company and Safeway Stores
  of Arizona
• Rockys wants to determine if they can meet
  Safeways quality standards and become a supplier
  to Safeway.
• Rockys can learn if their process is capable
  by developing a SPC system.
• Go to Rockys Peanut Butter handout.

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Rockys Peanut Butter

• X double bar 12.00 R bar 0.24
• Sample Size n 4
• UCLX bar X double bar A2 R bar 12.175
• LCLX bar X double bar A2 R bar 11.825
• UCLR D4 R bar 2.282 (0.24) 0.548
• LCLR D3 R bar 0 (0.24) 0

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Rockys Peanut Butter

• Plot the ten (10) individual sample means and
  range values in the control charts.
• Is there evidence of assignable cause variation?
  (Do any of the sample data fall outside the
  control limits?)

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Rockys Peanut Butter

• Can Rockys meet Safeways Specifications?
• We need to estimate three standard deviations of
  the filling process at Rockys
• We will use what we know to get the estimate of
  the standard deviation of the filling process.
• Three standard deviations for the sample
  distribution is equal to A2 R bar.
• Three standard deviations for the filling process
  
• (3 std dev of the sample distribution)X(sq rt
  n)
• A2 R bar X sq rt 4 0.175 X 2 0.35
• So we know that 99.7 of Rockys jars weigh
  between 11.65 and 12.35 ounces.

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Rockys Process Capability

• CPK (USL X bar) / 3 sigma
• (12.25 12.00) / 0.35
• 0.25 / 0.35 0.71
• When the Cpk is less than 1.0, this means that
  Rockys process is incapable of meeting Safeways
  quality specifications.
• What options are open to Rockys?