Transcript Statistical Process Control (SPC)

Quality Control
Chapter 6
Transformation Process
Inputs
• Facilities
• Equipment
• Materials
• Energy
Transformation
Process
Outputs
Goods &
Services
•Variation in inputs create variation in outputs
• Variations in the transformation process
create variation in outputs
Variation
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All processes have variation.
Common cause variation is random variation
that is always present in a process.
Assignable cause variation results from
changes in the inputs or the process. The
cause can and should be identified.
A process is in control if it has no assignable
cause variation.
 The process is consistent
Statistical Process Control (SPC)
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Distinguishes between common cause and
assignable cause variation
Measure characteristics of goods or services
that are important to customers
Make a control chart for each characteristic
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The chart is used to determine whether the
process is in control
Capability and Conformance Quality (1)
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A process is capable if
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It is in control and
It consistently produces outputs that meet
specifications.
A capable process produces outputs that have
conformance quality (outputs that meet
specifications).
Capable Transformation Process
Inputs
• Facilities
• Equipment
• Materials
• Energy
Capable
Transformation
Process
Outputs
Goods &
Services
that meet
specifications
Capability and Conformance Quality (2)

If the process is capable and the product
specification is based on current customer
requirements, outputs will meet customer
expectations.
Customer Satisfaction
Capable
Transformation
Process
+
Product
specification
that meets
current
customer
requirements
= Customer satisfaction
Objectives of SPC
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To determine if the process is in control
(predictable)
To determine if the process is capable
(in control and meets specifications)
Variable Measures
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Continuous random variables
Measure does not have to be a whole
number.
Examples: time, weight, miles per gallon,
length, diameter
Attribute Measures
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Discrete random variables – finite number of
possibilities
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Also called categorical variables
Different types of control charts are used for
variable and attribute measures
Examples of Attribute Measures
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Good/bad evaluations
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Number of defects per unit
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Good or defective
Correct or incorrect
Number of scratches on a table
Opinion surveys of quality
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Customer satisfaction surveys
Teacher evaluations
Descriptive Statistics
Describe Results from a Random Sample
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The Mean- measure of
central tendency
n
x
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x
i 1
i
n
The Range- difference
between largest/smallest
observations in a set of data
 x
n
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Standard Deviation
measures the amount of
data dispersion around mean
σ
i 1
i
X
n 1

2
Distribution of Data
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Normal distributions
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Skewed distribution
Control chart for
the mean of a
product
characteristic
• Random samples are taken from process output
• A process characteristic is measured
• Sample means are plotted
• Control limits are based on a confidence interval for
the mean
• CL = center line (mean line)
• LCL = lower control limit UCL = upper control limit
Percentage of values
under normal curve
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m = population mean
s = population standard
deviation
95.4% of the population is
within 2s of the mean
99.74% of the population is
within 3s of the mean
99.74% of the population is
within the interval from
m  3s to m + 3s
We will compute 3s
confidence intervals for
sample means
X-bar Chart
R Chart
Interpreting Control Charts for Variables
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Use x-bar and R charts
together
x-bar chart monitors the
mean
R charts monitors
dispersion
Specification Limits
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The target is the ideal value
 Example: if the amount of beverage in a bottle should be 16
ounces, the target is 16 ounces
Specification limits are the acceptable range of values for a
variable
Example: the amount of beverage in a bottle must be at least
15.8 ounces and no more than 16.2 ounces.
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Range is 15.8 – 16.2 ounces.
Lower specification limit = 15.8 ounces or LSPEC = 15.8 ounces
Upper specification limit = 16.2 ounces or USPEC = 16.2 ounces
Test for Process Capability
(with respect to x )
The process is in control with respect to x
AND
 The control limits (LCL and UCL) for x are
within the specification limits
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Capability index, Cpk is used to determine
whether a process is capable
Process is Capable
Upper specification limit
UCL
X
LCL
Lower specification limit
Process is Not Capable
UCL outside specification limits  not capable
UCL
Upper specification limit
X
LCL
Lower specification limit
Cpk Index
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m = process mean (or estimated mean)
LSPEC = lower specification limit
USPEC = upper specification limit
Cpk = Smaller {(USPEC- m)/3s, m – LSPEC)/ 3s}
If Cpk >= 1, process meets customer requirements
99.74% of the time.
To allow for changes in the mean, many firms set a
requirement that Cpk >= 1.33.
3-Sigma Quality
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Uses 3s control limits for x.
Corresponds to 3 defects per 1,000 units.
 If a product has 250 parts and each has 3s
control limits, P[at least 1 bad part] = 0.528
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6-Sigma Quality
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Use 6-s control limits for x.
Control limits are (X- 2A2R, X + 2A2R).
Corresponds to 3.4 defects per million
 If a product has 250 parts and each has 6s
control limits, P[at least 1 bad part] <0.001
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