Quality%20Control

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Quality Control

• Ross L. Fink

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Quality Control

• Quality control involves controlling the delivery
  processes to adhere to the specifications (or
  product design).

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Quality Control Approaches

• 100 Inspection
• Acceptance Sampling
• Statistical Process Control (SPC) or
  Control-Chart Method

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Acceptance Sampling
Accept or Reject Entire Lot Based Upon Quality of
Sample
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Statistical Process Control

• Basic Approach
• Take one sample of size 5 each hour
• Measure quality characteristic
• Plot measurement over time (sample number)

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Run Chart
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Distribution of Measurement on Control Chart

• Since we are taking a mean, the Central Limit
  Theorem of the Sample Mean applies
• Therefore, mean follows a normal distribution.
• Three Sigma Limits

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Plot of Mean
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Theory of Control Charts

• Purpose of control charts is to separate natural
  variability (common cause) from nonrandom
  variability (assignable cause).
• In-control (common cause) versus out-of-control
  (assignable cause).

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Types of Variability
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X-bar Chart
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Control Chart Rules

• Simple Rules
• One point above UCL
• One point below LCL
• Most organizations use more complex rules
• e.g., seven consecutive points increasing

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Constructing a Control Chart

• Obs. 1 2 3
  4 5
• Sample
• 1 11.63 14.44 14.52 17.58 12.71
• 2 13.30 16.21 15.04 16.09 14.19
• 3 12.60 11.49 14.73 15.58 17.41
• 4 13.68 13.49 13.24 16.98 16.23
• 5 15.12 15.21 11.69 14.91 16.36
• 6 15.70 16.09 16.78 15.48 14.56
• 7 13.46 14.28 17.09 13.84 15.85
• 8 14.22 13.90 14.47 15.18 19.31
• 9 12.44 15.12 16.00 14.62 16.05
• 10 14.04 14.88 19.26 14.37 16.35
• 11 12.42 13.25 15.56 15.18 14.13
• 12 15.65 12.94 16.16 15.98 18.67
• 13 15.71 13.78 14.19 16.02 13.78
• 14 14.80 12.17 16.00 12.93 12.34
• 15 15.63 12.14 14.98 16.61 14.21
• 16 10.13 15.43 17.09 17.72 18.72
• 17 13.73 15.26 13.53 14.43 15.22

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Find Sample Means and Ranges

• Obs. 1 2 3
  4 5 Mean Range
• Sample
• 1 11.63 14.44 14.52 17.58 12.71 14.18 5.95
• 2 13.30 16.21 15.04 16.09 14.19 14.96 2.93
• 3 12.60 11.49 14.73 15.58 17.41 14.36 5.92
• 4 13.68 13.49 13.24 16.98 16.23 14.72 3.75
• 5 15.12 15.21 11.69 14.91 16.36 14.66 4.67
• 6 15.70 16.09 16.78 15.48 14.56 15.72 2.22
• 7 13.46 14.28 17.09 13.84 15.85 14.90 3.63
• 8 14.22 13.90 14.47 15.18 19.31 15.42 5.39
• 9 12.44 15.12 16.00 14.62 16.05 14.85 3.62
• 10 14.04 14.88 19.26 14.37 16.35 15.78 5.22
• 11 12.42 13.25 15.56 15.18 14.13 14.11 3.14
• 12 15.65 12.94 16.16 15.98 18.67 15.88 5.72
• 13 15.71 13.78 14.19 16.02 13.78 14.70 2.23
• 14 14.80 12.17 16.00 12.93 12.34 13.65 3.83
• 15 15.63 12.14 14.98 16.61 14.21 14.71 4.47
• 16 10.13 15.43 17.09 17.72 18.72 15.82 8.59
• 17 13.73 15.26 13.53 14.43 15.22 14.43 1.73

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Calculate Grand Mean and Grand Range
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Control Limits
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Table

• Factors for Computing Control Chart Limits
• Sample Size Mean Factor Upper Range Lower Range
• N A2 D4 D3
• 2 1.880 3.268 0
• 3 1.023 2.574 0
• 4 .729 2.282 0
• 5 .577 2.115 0
• 6 .483 2.004 0
• 7 .419 1.924 0.076
• 8 .373 1.864 0.136
• 9 .337 1.816 0.184
• 10 .308 1.777 0.223

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Control Limits
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X-bar Chart
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R Chart
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In-Control v. Out-Of-Control

• What are the implications of being in-control?
• What are the implications of being
  out-of-control?