Statistical Quality Statistical Process Control (SQC/SPC)

1
Statistical Quality Statistical Process Control
(SQC/SPC)
Objectives Insure high quality production by
reducing and controlling process
variation. Identify types of process
variation. Common cause variation small, random
forces that continually act on a process Special
cause variation that may be assigned to
abnormal, unpredictable forces Take action
whenever a process is judged to have been
influenced by special causes.
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A General SPC Procedure

• Periodically select from the process a sample of
  items, inspect them, and note the result.
• Because of common or special causes, the results
  of every sample will vary. Determine whether the
  cause of the variation is common or special.
• Take action depending on what was determined in
  step 2.

This procedure is enacted through the use of
control charts
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Types of Control Charts

• Charts used to track the number of units
  defective P Chart - fraction of a sample that is
  defective given different sample sizes
• Charts used to track the number of defects in one
  or more units C Chart - defects in a fixed sized
  sample
• Charts used to track a continuous variable
  Xbar-R Chart tracks the mean and range of a
  variable calculated from a fixed sample

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The P Chart

• Collect sample data for each sample record the
  number inspected (n) and number defective (np)
• Compute fraction defective for each sample
  (np/n)
• Calculate average fraction percent defective
• Compute and draw control limits
• Plot p

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Example of a P Chart
Assume that we test quantities of light bulbs to
see if they function. In order to calibrate a
control chart, we estimate the normal behavior of
this test by collecting data that we believe have
not been influenced by abnormal variation. We
sample 5925 bulbs and find 610 defectives
(p610/5925.103)
Note control limits calculated assuming z3
For this example, the control limits reduce to
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Example of a P Chart (cont)
25
20
Percent Defective
15
UCL
p
10
LCL
5
Sub-group
7
We assume the process is in an in control state
when

• Points are within the control limits
• Consecutive groups of points do not take a
  particular form.
• Runs on one side of the central line (7 out of 7,
  10 out of 11, or 12 out of 14)
• Trends of a continued rise or fall of points (7
  out of 7)
• Periodicity or same pattern repeated over equal
  interval
• Hugging the central line (most points within the
  center half of the control zone)
• Hugging the control limits (2 out of 3, 3 out of
  7, or 4 out of 10 points within the outer 1/3
  zone)

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The C Chart

• Assumes constant sample size
• Calculation of the control limits must be
  performed only once

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Example of a C Chart
In this example, a data point represents the
number of rips found in 5 yards of nylon fabric
Note control limits calculated assuming z3
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Example of a C Chart
For this example, the control limits reduce to
UCL
10
Defectives
5
C
Sub-group
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The Xbar-R Chart

• Collect sample data by sub-group (normally
  containing 2 - 5 data points) record the
  continuous variable under study.
• Compute the mean and range for each sub-group
• Calculate average mean and average range
• Compute and draw control limits
• Plot mean and range for each subgroup.

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Example of an Xbar-R Chart
Each data point is the pulling force applied to a
glass strand before breaking
For 5 obs. D30 D42.114 A20.577
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Example (cont)
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Mean
For this example, the control limits reduce to
13
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Sub-group
3
Range
2
1
Sub-group
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Example control chart the following
Count of blemish defects by canoe serial number
Serial number Defects Xc102
7 Xc103 6 Xc121 6 Xc134
3 Xc145 22 Xc156 8 . ... total
from 25 canoes 141
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Control chart the following
Count of defective bolts
Day Inspected Defective Monday 2
385 47 Tuesday 1451 18 Wednesday 1935 74 Thur
sday 2450 42 Friday 1997 39 Monday 2168 52
. ... Total from 30 days
50,515 1035
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Control chart the following
Depth of thread
Subgroup x1 x2 x3 x4 1 35 40 32 33
2 46 37 36 41 3 34 40 34 36
4 69 64 68 59 5 38 34 44 40
6 42 41 33 34 7 44 41 41 46
Grand mean of 25 samples 40.06 Average range
of 25 samples 11.09
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Control Limits and Specification Limits

• Control limits of a quality characteristic
  represent natural variation in a process
• Specification limits indicate acceptable
  variation set by the customer
• The process capability index is useful in
  comparison
• The capability index may be adjusted to to
  consider how well the process is centered
  within the limits

K2 design target - process average /
specification range
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Process Capability Example
Assume we manufacture steel plate. A customer
with a thickness requirements provides the
following specification USL10, LSL9.5 We know
that the thickness variation within our process
is ? .02
Currently, the average thickness of our plate is
9.95
K2 9.75 - 9.95 / .5 .8
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PC Example (cont)
Assume we can adjust the thickness
USL10 LSL9.5 ? .02
K2 9.75 - 9.79 / .5 .16
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4 sigma
3 sigma
2 sigma
Customer Specification
Customer Specification
Process Variability
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Motorolas Six-Sigma Limits
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Acceptance Sampling

• For many products, quick and effective inspection
  techniques allow for 100 inspection of outgoing
  quality.
• There are also situations in which sampling is
  necessary
• 100 inspection is uneconomical
• Testing requires a destructive procedure
• Shipments of raw material
• An acceptance plan is a procedure for accepting
  or rejecting a lot based on sampling information.

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A Single Sample Plan
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Operating Characteristics Curve
n 50 (sample size) c 1 (max
defectives to accept lot) AQL lots with lt
1 defects LTPD lots with gt 8 defects
100
90
80
70
60
Probability of accepting lots
50
40
30
20
10
1
2
3
4
5
6
7
8
9
10
11
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Percent defectives in lots