Implementation of Statistical Process Control

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Implementation of Statistical Process Control

• Yolanda Samaranayake

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Usefulness of Control Charts

• Control charts are a proven technique for
  improving productivity.
• Control charts are effective in defect
  prevention.
• Control charts prevent unnecessary process
  adjustments.
• Control charts provide information about process
  capability.

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Types of Control Charts
Individual Control Chart
Where d2 1.128 for a moving range of 2.
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Exponentially Weighted Moving Average Chart (EWMA)
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Outliers in the Measurements
(Quantile Box Plot and Outlier Box Plot)
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Distribution of the Measurements
Data from a normal distribution
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Data from a non-normal distribution
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Data from a bi-modal distribution
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Tests of Normality

• Shapiro-Wilk W Test
• Normal Quantile Plot
• Skewness and Kurtosis

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Transformations of Non Normal Measurements
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Example of Non Normal Data
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(No Transcript)
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Distribution of log (X)
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Process Capability
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Rules for Out of Control

• Point outside the control limit of the individual
  control chart
• Point outside the EWMA

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Standardized Measurements for Batch Processes

• Approach 1Use when the standard deviations of
  the different products are similar (approximately
  10).
• Approach 2Use when the standard deviations of
  the different products vary by more than 10.
• Approach 3Use when the standard deviation is
  proportional to the process average

X actual measurement - TA where TA is some
target value
X ((actual measurement TA)/TA)100
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Calculation of Control Limits

• Determine number of measurements needed to
  calculate control limits (at least 30)
• When number of measurements is less than 30,
  limits can be based on some historical data
• Fixing limits after knowing a stable process
• Check limits at regular intervals to determine if
  a re-calculation is necessary (i.e. a change in
  the mean or standard deviation due to raw
  materials)

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Examples
Non-Normal Data
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Distributions Particles
Normal(11.6815,9.92325)
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Distributions Particles
Normal(9.516,6.2067)
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Log Particles
Normal(2.01563,0.74043)
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CPK 3.03 USl 60
CPK 1.02 UCL 57.4 Xbar 7.5 LCL .98
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Examples
Bi-Modal Distribution
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Distributions Iron
Normal(0.05784,0.02222)
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Population 1
Population 2
Normal(0.08395,0.00828)
Normal(0.03711,0.00511)
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Population 1
Population 2