# Statistical Process Control SPC Attributes Charts Outline Attributes Charts

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```					       Statistical Process Control (SPC)                                          Outline
Attributes Charts
Attributes Charts
Managerial Decisions for SPC
MGNT 3430                                    Process Capability

Acceptance Sampling

Homework

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Control Chart Types                                                          Control Chart Types
Continuous                    Control           Categorical or Discrete                             Control           Categorical or Discrete
Numerical Data                Charts            Numerical Data                                      Charts            Numerical Data

Variables                             Attributes                                                            Attributes
Charts                                Charts                                                                Charts

R                    X                 P                   C                                                 p                   c
Chart               Chart             Chart                Chart                                            Chart                Chart

3                                                                             4
p Chart (p: percent or proportion)                              Calculating p Chart Control Limits

Type of attributes control chart                                z=2             95.45% limits; z = 3   99.73% limits
Categorize as defective or nondefective
=    p + zσ
–
Mean of sample
UCL          p                 p
proportions
Measures % of nonconforming items
–    Example: Count # defective chairs & divide by total       LCL          p   =    p − zσ   p
chairs inspected; Plot
Chair is either defective or not defective
p (1 − p )
Relies on Binomial distribution (or normal)                    σ   p    =
n
Like x-bar chart approach
–    Based on Central Limit Theorem                            n = sample size
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Example: p Chart                                                See excel file: SPC p c charts

Audit of order accuracy at Pea Bar & Grill                      Tabs
–   Enter hundreds of orders each week into the                   –   p chart fill-in
computerized point-of sale (POS) system
–   p chart data
–   Randomly choose 10 wait staff (# of samples)
–   p chart
–   Randomly choose 50 orders entered by each
–   Determines # of incorrect orders by each
Tool to track variation in the ordering process
–   Compare each server against the average server
–   Use a z = 3 or 99.73% control limits

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c Chart
c Chart                                                             Control Limits

Type of attributes control chart                                    UCL     c       = c + 3   c
–       Discrete quantitative data                                                                Use 3 for 99.7%
Shows number of nonconformities (defects) in                                                       limits
a unit                                                              LCL     c       = c − 3   c
–       Unit may be chair, steel sheet, car, fabric, etc.
–       Size of unit must be constant
# Defects in
Example: Count # defects (scratches, chips etc.) in                    k
–                                                                                                 Unit i
each chair of a sample of 100 chairs; Plot                          ∑ c        i

Relies on Poisson distribution
c =      i= 1
# Units Sampled
k
9     Mean = Variance                                               10

Example: c Chart                                                    See excel file: SPC p c charts

Out of control sports program                                       Tabs
–    A sports reporter is trying to evaluate the                 –   c chart fill-in
criminality of five targeted teams                          –   c chart data
–    Takes random sample of players                              –   c chart
–    # of recorded criminal offenses per team
Tool to track variation in criminal records
–    A single player sampled may have > 1 offense
–    Use a z = 3 or 99.73% control limits

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Outline                              SPC Decisions

Attributes Charts                    Which parts are critical to success?

Managerial Decisions for SPC         Which process steps tend to become OC?
Process Capability
Which control chart is appropriate?
Acceptance Sampling
When do we decide to stop the process?
Homework
–   Run test: rules for check for nonrandom variation

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Signals in Control Charts            Outline

Attributes Charts

Managerial Decisions for SPC

Process Capability
Acceptance Sampling

Homework

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Process Capability                                                     Process Capability Ratio, Cp

SPC                                                                  Capable process has Cp >= 1.0
–   Keep a process in control
–   Natural process variation narrow enough to meet quality         Relates spread of process output to tolerance
standards
(x-bar + or – 3σ)
Design specifications
–   Upper (USL) and Lower (LSL) limits)                             Six sigma initiatives           Cp = 2.0
–   From engineers or customers
Is a process capable of meeting specs
Upper Specificat ion − Lower Specificat ion
–
Process capability measures                                         Cp =
–
–
Process Capability Ratio (Cp)
Process Capability Index (Cpk)
6σ

17                                                                     18   σ = standard deviation of the process

Process Capability Index, Cpk                                          Example of Cp and Cpk

Proportion of natural variation between                              Honda wants us to machine an engine part
centerline and nearest spec. limit (USL,LSL)                          –   Our process produces this part with an average
diameter of 15.01 cm and σ = .01 cm
Cpk=Cp: Process is centered in USL & LSL                              –   They specify a USL=15.03 cm and LCL=14.97 cm
⎡ Upper Specificat ion Limit − x                        –   Is our current process capable of meeting
C pk = minimum of ⎢                                 , or                       Honda’s specification requirements?
⎣              3σ                                             Cp = USL – LSL / 6σ       .06 / .06 = 1.0
x − Lower Specificat ion Limit ⎤                           Cpk = min [USL – x_bar / 3σ , x_bar – LSL / 3σ]

3σ                ⎥                                = min [.02 / .03 , .04 / .03 ]
⎦                                = .67
where x = process mean
19        σ = standard deviation of the process population             20
Outline                              Acceptance Sampling

Attributes Charts                   Form of quality statistical testing used for
incoming materials or finished goods
Managerial Decisions for SPC         –   e.g., purchased material & components
Process Capability                  Procedure
–   Take one or more samples at random from a lot
(shipment) of items
Acceptance Sampling                  –   Inspect each of the items in the sample
–   Decide whether to reject the whole lot based on
Homework                                 the inspection results

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Outline                              Homework

Attributes Charts                    Supplement to Ch. 6
Managerial Decisions for SPC
Discussion Questions: 9, 11
Process Capability

Acceptance Sampling                  Problems: s6.15, s6.24, s6.27, s6.30

Homework
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