Statistical Process Control (SPC)

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Statistical Process Control (SPC)

• Chapter 6

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Course Overview
Operations and Operations Strategy
Products, Processes, Quality
Operations Planning Control
Facilities and Work Systems
Mathematical Tools for Operations
Product Design
Project Management
Process Design
Linear Programming
Just-in-Time
Quality Management
Statistical Process Control
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Assuring Customer-Based Quality
Product launch activities Revise periodically
Statistical Process Control Measure monitor
quality
Ongoing activity
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Statistical Process Control (SPC)
Basic SPC Concepts
SPC for Variables
Types of Measures
Variation
Attributes
Mean charts
Range charts
Objectives
Variables
? and ? known
First steps
? unknown, ? known
?, ? unknown
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Variation in a Transformation Process
Variation
Variation

• Inputs
• Facilities
• Equipment
• Materials
• Energy

Variation

• Variation in inputs create variation in outputs
• Variations in the transformation process
• create variation in outputs

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Variation in a Transformation Process
Customer requirements are not met

• Inputs
• Facilities
• Equipment
• Materials
• Energy

• Variation in inputs create variation in outputs
• Variations in the transformation process
• create variation in outputs

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Variation

• 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.
• Assignable cause variation shows that the process
  or the inputs have changed, at least temporarily.

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Objectives of Statistical Process Control (SPC)

• Find out how much common cause variation the
  process has
• Find out if there is assignable cause variation.
• A process is in control if it has no assignable
  cause variation
• Being in control means that the process is stable
  and behaving as it usually does.

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First Steps in Statistical Process Control (SPC)

• Measure characteristics of goods or services that
  are important to customers
• Make a control chart for each characteristic
• The chart is used to determine whether the
  process is in control

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Types of Measures (1)Variable Measures

• Continuous random variables
• Measure does not have to be a whole number.
• Examples time, weight, miles per gallon, length,
  diameter

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Types of Measures (2)Attribute Measures

• Discrete random variables finite number of
  possibilities
• Also called categorical variables
• The measure may depend on perception or judgment.
• Different types of control charts are used for
  variable and attribute measures

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Examples of Attribute Measures

• Good/bad evaluations
• Good or defective
• Correct or incorrect
• Number of defects per unit
• Number of scratches on a table
• Opinion surveys of quality
• Customer satisfaction surveys
• Teacher evaluations

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SPC for VariablesThe Normal Distribution

• ? the population mean
• the standard deviation
• for the population
• 99.74 of the area under the normal curve is
  between
• ? - 3? and ? 3?

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SPC for Variables The Central Limit Theorem

• Samples are taken from a distribution with mean ?
  and standard deviation ?.
• k the number of samples
• n the number of units in each sample
• The sample means are normally distributed
• with mean ? and standard deviation
• when k is large.

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Control Limits for the Sample Mean when ? and ?
are known

• x is a variable, and samples of size n are taken
  from the population containing x.
• Given ? 10, ? 1, n 4
• Then
• A 99.7 confidence interval for is

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Control Limits for the Sample Mean when ? and ?
are known (2)

• The lower control limit for is

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Control Limits for the Sample Mean when ? and ?
are known (3)

• The upper control limit for is

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Control Limits for the Sample Mean when ? is
unknown, ? is known

• Example 6.1, page 179
• Given 25 samples, 4 units in each sample,
• ? 0.14. ?? is not given.
• k 25, n 4
• For i 1,...,k, the observations in sample i are
  
• For the ith sample, the sample mean is

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Control Limits for the Sample Mean when ? is
unknown, ? is known (2)

• Compute the mean for each sample. For example,
  
• Compute

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Control Limits for the Sample Mean when ? is
unknown, ? is known (3)

• Use instead of ? in the formulas for LCL and
  UCL.

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Control Limits for the Sample Mean when ? and ?
are unknown

• Example 6.1 (continued), page 180
• Given 25 samples, 4 units in each sample
• ? and ? are not given
• k 25, n 4

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Control Limits for the Sample Mean when ? and ?
are unknown (2)

• Compute the mean for each sample. For example,
  
• Compute

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Control Limits for the Sample Mean when ? and ?
are unknown (3)

• For the ith sample, the sample range is
• Ri (largest value in sample i )
• - (smallest value in sample i )
• Compute Ri for every sample. For example,
• R1 16.02 15.83 0.19

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Control Limits for the Sample Mean when ? and
? are unknown (4)

• Compute , the average range
• We will approximate by , where
• A2 is a number that depends on the sample
• size n. We get A2 from Table 6.1, page 182

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Control Limits for the Sample Mean when ? and
? are unknown (5)

• n the number of units in each sample
• 4.
• From Table 6.1,
• A2 0.73.
• The same A2 is used
• for every problem
• with n 4.

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Control Limits for the Sample Mean when ? and
? are unknown (6)

• The formula for the lower control limit is
• The formula for the upper control limit is

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Control Chart for
The variation between LCL 15.74 and UCL
16.16 is the common cause variation.
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Common Cause andSpecial Cause Variation

• The range between the LCL and UCL, inclusive, is
  the common cause variation for the process. When
• is in this range, the process is in
  control.
• When a process is in control, it is predictable.
  Output from the process may or may not meet
  customer requirements.
• When is outside control limits, the process
  is out of control and has special cause
  variation. The cause of the variation should be
  identified and eliminated.

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Control Limits for R

• From the table,
• get D3 and D4
• for n 4.
• D3 0
• D4 2.28

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Control Limits for R (2)

• The formula for the lower control limit is
• The formula for the upper control limit is

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Statistical Process Control (SPC)
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Review of Specification Limits

• The target for a process 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.
• The allowable range is 15.8 16.2 ounces.
• Lower specification limit 15.8 ounces or LSL
  15.8 ounces
• Upper specification limit 16.2 ounces or USL
  16.2 ounces

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Control Limits vs. Specification Limits

• Control limits show the actual range of variation
  within a process
• What the process is doing
• Specification limits show the acceptable common
  cause variation that will meet customer
  requirements.

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Process is Capable Control Limits arewithin or
on Specification Limits
Upper specification limit
UCL
X
LCL
Lower specification limit
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Process is Not Capable One or BothControl
Limits are Outside Specification Limits
UCL
Upper specification limit
X
LCL
Lower specification limit
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Capability and Conformance Quality

• A process is capable if
• It is in control and
• It consistently produces outputs that meet
  specifications.
• This means that both control limits for the mean
  must be within the specification limits
• A capable process produces outputs that have
  conformance quality (outputs that meet
  specifications).

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Capable Transformation Process

• Inputs
• Facilities
• Equipment
• Materials
• Energy

Outputs Goods Services that meet specifications
Capable Transformation Process
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Process Capability Ratio

• Use to determine whether the process is
  capable when ? target.
• If , the process is capable,
• If , the process is not capable.

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Example

• Given Boffo Beverages produces 16-ounce bottles
  of soft drinks. The mean ounces of beverage in
  Boffo's bottle is 16. The allowable range is 15.8
  16.2. The standard deviation is 0.06. Find
  and determine whether the process is capable.

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Example (2)

• Given ? 16, ? 0.06, target 16
• LSL 15.8, USL 16.2
• The process is capable.

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Process Capability Index Cpk

• If Cpk gt 1, the process is capable.
• If Cpk lt 1, the process is not capable.
• We must use Cpk when ? does not equal the target.

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Cpk Example

• Given Boffo Beverages produces 16-ounce bottles
  of soft drinks. The mean ounces of beverage in
  Boffo's bottle is 15.9. The allowable range is
  15.8 16.2. The standard deviation is 0.06. Find
  and determine whether the process is
  capable.

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Cpk Example (2)

• Given ? 15.9, ? 0.06, target 16
• LSL 15.8, USL 16.2
• Cpk lt 1. Process is not capable.

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Statistical Process Control (SPC)