STATISTICAL PROCESS CONTROL AND QUALITY MANAGEMENT

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STATISTICAL PROCESS CONTROL AND QUALITY MANAGEMENT
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Quality

• Fitness for use, acceptable standard
• Based on needs, expectations, perceptions and
  customer requests

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Types of Quality

• Quality of design
• Quality of conformance
• Quality of performance

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Quality of Design

• Differences in quality due to design differences,
  intentional differences

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Quality of Conformance

• Degree to which product meets or exceeds standards

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Quality of Performance

• Long term consistent functioning of the product,
  reliability, safety, serviceability,
  maintainability

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Quality and Productivity

• Improved quality leads to lower costs and
  increased profits

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Statistics and Quality Management

• Statistical analysis is used to assist with
  product design, monitor the production process,
  and check quality of the finished product

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Checking Finished Product Quality

• Random samples selected from batches of finished
  product can be used to check for product quality

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Assisting With Production Design

• A variety of experimental design techniques are
  available for improving the production process

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Monitoring the Process

• Control charts can be used to monitor the process
  as it unfolds
• Sampling from the production line to see if
  variation in product quality is consistent with
  expectations

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The Control Chart

• A special type of sequence plot which is used to
  monitor a process
• Throughout the process measurements are taken and
  plotted in a sequence plot
• Plot also contains upper and lower control limits
  indicating the expected range of the process when
  it is behaving properly

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Examples
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Examples
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Examples
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Examples
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Examples
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Two Types of Variability in Control Charts

• Chance or Common Causes
• Special or Assignable Causes

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Chance or Common Causes

• Numerous small causes which are inherent to the
  process and which occur at random
• Considered to be normal variation when process is
  under control

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Special or Assignable Causes

• Have large effects on the process
• Occur rarely or sporadically

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Statistical Control/Stable Process

• Variability only due to common or chance causes
• Variability natural, expected
• Variability managed

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Out of Control Process

• When special causes or assignable causes are
  present

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Types of Control Charts

• Control Chart For The Mean
• Control Chart For The Range
• Control Chart For A Proportion

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Control Chart For The Sample Mean

• Assuming that the sample mean is approximately
  normal with mean ? and standard deviation ?, a
  control chart for the mean usually consists of
  three horizontal lines
• The vertical axis is used to plot the magnitude
  of observed sample means while the horizontal
  axis represents time or the order of the sequence
  of observed means

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Control Chart For The Sample Mean

• The center line is at the mean, ? and upper and
  lower control limits are at
• 3 and -3
• Since ? is usually unknown the
• term is usually replaced by an
  estimator based on the sample range (see below)

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Control Chart For The Sample Mean

• The formula is given by
• where average value of the range
• k number of samples
• The values of A2 depend on the sample size

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Control Chart For The Sample Mean

• LCL
• UCL

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Control Chart For The Range

• Designed to monitor variability in the product
• Range easier to determine than standard deviation
• Distribution of sample range assumes product
  measurement is normally distributed

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Control Chart For The Range

• Upper and lower control limits and centre line
  obtained from and the values of D3, D4
• according to the formulae
• LCL
• UCL
• The values of D3, D4 are based on sample size and
  are given in a table below

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Examples
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Examples
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Control Chart For The Sample Proportion

• Population proportion ?
• The sample mean is now a mean proportion given by
  
• Where total number of objects in sample
  with characteristic divided by total sample size

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Control Chart For The Sample Proportion

• Using the central limit theorem the control
  limits are given by

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Control Chart For The Sample Proportion

• Since the true proportion ? is usually unknown we
  replace it by the average proportion
• If the sample size varies then the upper and
  lower limits will vary and the equations become
• where ni sample size in sample i

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Examples