S61

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Operations ManagementStatistical Process
ControlSupplement 6
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Outline

• Statistical Process Control (SPC).
• Mean charts or X-Charts.
• Range chart or R-Charts.
• Control charts for attributes.
• Managerial issues and control charts.
• Acceptance Sampling.

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Statistical Process Control (SPC)

• Statistical technique to identify when non-random
  variation is present in a process.
• All processes are subject to variability.
• Natural causes Random variations.
• Assignable causes Correctable problems.
• Machine wear, unskilled workers, poor materials.
• Uses process control charts.

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Statistical Process Control Steps
Start
Take Sample
Produce Good
Inspect Sample
Provide Service
Take Samples
No
Is process in control?
Create
Stop Process
Control Chart
Yes
Find Out Why
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Process Control Charts
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Control Charts

• Process is not in control if
• Sample is not between upper and lower control
  limits.
• A non-random pattern is present, even when
  between upper and lower control limits.
• Based on sample being normally distributed.

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Distribution of Sample Means
Standard deviation of the sample means
(mean)
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Central Limit Theorem
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Control Chart Types
Control
Categorical or Discrete Numerical Data
Charts
Continuous Numerical Data
Variables
Attributes
Charts
Charts
R
P
C
X
Chart
Chart
Chart
Chart
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Quality Characteristics
Attributes
Variables

• Characteristics for which you focus on defects.
• Categorical or discrete values.
• Good or Bad.
• of defects.

• Characteristics that you measure, e.g., weight,
  length.
• Continuous values.

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?X Chart

• Shows sample means over time.
• Monitors process average.
• Example Weigh samples of coffee.
• Collect many samples, each of n bags.
• Sample size n.
• Compute mean and range for each sample.
• Compute upper and lower control limits (UCL,
  LCL).
• Plot sample means and control limits.

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?X Chart Control Limits - std. deviation of
process is known
sample mean at time i
? known process standard deviation
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?X Chart - Example 1

• Each sample is 4 measurements.
• Process mean is 5 lbs.
• Process standard deviation is 0.1 lbs.
• Determine 3? control limits.

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?X Chart Control Limits - std. deviation of
process not known
A2 is from Table S6.1
sample range at time i
sample mean at time i
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Factors for Computing Control Chart Limits
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?X Chart - Example 2

• Each sample is 4 measurements.
• Determine 3? control limits.
• sample mean range
• 1 5.02 .12 4.96,
  5.03, 5.01, 5.08
• 2 4.99 .08
• 3 4.97 .13
• 4 5.03 .18
• 5 4.99 .14

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?X Chart - Example 2
5.1
Upper control limit
5.0
Sample Mean
Lower control limit
4.9
Time
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R Chart

• Shows sample ranges over time.
• Sample range largest - smallest value in
  sample.
• Monitors process variability.
• Example Weigh samples of coffee.
• Collect many samples, each of n bags.
• Sample size n.
• Compute range for each sample average range.
• Compute upper and lower control limits (UCL,
  LCL).
• Plot sample ranges and control limits.

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R Chart Control Limits
From Table S6.1
sample range at time i
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R Chart - Example 2

• Each sample is 4 measurements.
• Determine 3? control limits.
• sample mean range
• 1 5.02 .12
• 2 4.99 .08
• 3 4.97 .13
• 4 5.03 .18
• 5 4.99 .14

4.96, 5.03, 5.01, 5.08
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R Chart - Example 2
0.3
Upper control limit
Sample Range
0.2
0.1
Lower control limit
0
Time
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Control Chart Steps

• Collect 20 to 25 samples of n4 or n5 from a
  stable process compute the mean and range.
• Compute the overall mean and average range.
• Calculate upper and lower control limits.
• Graph the sample means and ranges on their
  respective control charts, and determine whether
  they fall outside the acceptable limits.

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Control Chart Steps - continued

• Investigate points or patterns that indicate the
  process is out of control. Assign causes for the
  variations.
• Collect additional samples and revalidate the
  control limits.

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Control Chart Patterns
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p Chart

• Attributes control chart.
• Shows of nonconforming items.
• Example Count defective chairs divide by
  total chairs inspected.
• Chair is either defective or not defective.

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c Chart

• Attributes control chart.
• Shows number of 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.

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Use of Control Charts
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Acceptance Sampling

• Quality testing for incoming materials or
  finished goods.
• Purchased material components.
• Final products.
• Procedure
• Take one or more samples at random from a lot
  (shipment) of items.
• Inspect each of the items in the sample.
• Decide whether to reject the whole lot based on
  the inspection results.