Statistical Process Control Chapters 20. 12345678 A B C D E F G H.
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Transcript of Statistical Process Control Chapters 20. 12345678 A B C D E F G H.
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Statistical Process Control
Chapters 20
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1 2 3 4 5 6 7 8
A
B
C
D
E
F
G
H
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Some Common Problems in Planning
We plan in terms of actions (tasks) rather than objectives
Responsibilities are not clearWe plan in silos, out of contextWe underestimate the time and effort
required to implementWe don’t make reviews part of the plan.
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Six-Step Problem-Solving Process
Step 1: Identify and Select the problemStep 2: Analyze the problemStep 3: Generate Potential SolutionsStep 4: Select and Plan the SolutionStep 5: Implement the SolutionStep 6: Evaluate the Solution
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StatisticalQuality Control
ProcessControl
AcceptanceSampling
VariablesCharts
AttributesCharts
Variables Attributes
Types of Statistical Quality Control
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Measures performance of a processUses mathematics (i.e., statistics)Involves collecting, organizing, &
interpreting data Objective: Regulate qualityUsed to
Control the process as products are produced or service is performed
Statistical Quality Control (SPC) key tool for 6 Sigma
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ControlCharts
RChart
VariablesCharts
AttributesCharts
XChart
PChart
CChart
Continuous Numerical Data
Categorical or Discrete Numerical Data
Control Chart Types
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Characteristics for which you focus on defects
Classify products as either ‘good’ or ‘bad’, or count # defects e.g., radio works or not
Categorical or discrete random variables
AttributesAttributesVariablesVariables
Quality Characteristics
¨ Characteristics that you measure, e.g., weight, length
¨ May be in whole or in fractional numbers
¨ Continuous random variables
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Statistical Process Control
VariationsCommon cause: due
to process itselfSpecial cause
2 ways of investigating variationPlot data using
histogram, looking for a normal distribution.
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Standard Deviation
1 σ away from mean in either direction accounts for approx. 68% of readings in the group (red area)
2 σ away from mean in either direction accounts for approx. 95% of readings in the group (red and green area)
3 σ away from mean in either direction accounts for approx. 99% of readings in the group (red, green, and blue areas)
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Process Control Charts
Plot of Sample Data Over Time
010203040506070
1 5 9 13 17 21
Time
Sam
ple
Va
lue
SampleValueUCL
Average
LCL
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Show changes in data patterne.g., trends
Make corrections before process is out of control
Show causes of changes in dataAssignable causes
Data outside control limits or trend in data
Natural causesRandom variations around average
Control Chart Purposes
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Type of variables control chart Interval or ratio scaled numerical data
Shows sample means over timeMonitors process averageExample: Weigh samples of coffee &
compute means of samples; Plot
X Chart
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Type of variables control chart Interval or ratio scaled numerical data
Shows sample ranges over timeDifference between smallest & largest values
in inspection sample
Monitors variability in processExample: Weigh samples of coffee &
compute ranges of samples; Plot
R Chart
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Formulas
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Type of attributes control chartNominally scaled categorical data
e.g., good-bad
Shows % of nonconforming itemsExample: Count # defective chairs &
divide by total chairs inspected; PlotChair is either defective or not defective
p Chart
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# Defective Items in Sample i
Size of sample i
z = 2 for 95.5% limits; z = 3 for 99.7% limits
p Chart Control Limits
i
k
1i
i
k
1ii
k
i
p
p
n
xp and
k
nn
n)p(p
zpLCL
n)p(p
zpUCL
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Statistical Process Control Chart
Using SPC to Address On-Time Medication Delivery
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Type of attributes control chartDiscrete quantitative data
Shows number of nonconformities (defects) in a unit Unit may be chair, steel sheet, car etc.Size of unit must be constant
Example: Count # defects (scratches, chips etc.) in each chair of a sample of 100 chairs; Plot
c Chart
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# Defects in Unit i
# Units Sampled
Use 3 for 99.7% limits
c Chart Control Limits
k
c c
ccLCL
ccUCL
i
k
1i
c
c
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Process Capability Cpk
population process theof deviation standard
mean process x where
LimitionSpecificat Lower x ,
x Limit ionSpecificatUpper of minimumCpk
Assumes that the process is:•under control•normally distributed
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Form of quality testing used for incoming materials or finished goodse.g., purchased material & components
ProcedureTake one or more samples at random from a lot
(shipment) of items Inspect each of the items in the sampleDecide whether to reject the whole lot based on
the inspection results
What Is Acceptance Sampling?
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Set of procedures for inspecting incoming materials or finished goods
IdentifiesType of sampleSample size (n)Criteria (c) used to reject or accept a lot
Producer (supplier) & consumer (buyer) must negotiate
What Is an Acceptance Plan?
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Producer's risk ()Probability of rejecting a good lot Type 1 error – results in over adjustment
Consumer's risk (ß)Probability of accepting a bad lot Type II error – results in under adjustment
Producer’s & Consumer’s Risk
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ANY QUESTIONS?