Variation thinking

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Variation thinking

• 2WS02 Industrial Statistics
• A. Di Bucchianico

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SPC Philosophy

• Let the process do the talking
• Goal realize constant quality by controlling the
  process with quantitative information
• Constant quality means quality with controlled
  and known variation around a fixed target
• Operator should be able to do the routine
  controlling

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Variation I
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Variation II
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Variation III
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Example Dartec
disqualification when outside range
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Examples of variation patterns
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Metric for sample variation range
maximum
minimum
range

• easy to compute (pre-computer era!)
• rather accurate for sample size lt 10

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Metric for sample variation standard deviation

• 2nd formula easier to compute by hand
• 2nd formula less rounding errors
• correct dimension of units
• n-1 to ensure that average value equals
  population variance (unbiased estimator)

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Visualisation of sample variation

• Box-and Whisker plot

histogram
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all observations
first 60 observations
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Variation and stability

• Can variation be stable?
• yes, if we mean that observations
• follow fixed probability distribution
• do not influence each other (independence)
• stability -gt predictability
• How to handle a stable production process?

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Why stable processes?

• behaviour is predictable
• processes can be left on itself intervention may
  be expensive

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Demings funnel experiment
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Lessons from funnel experiment

• tampering a stable process may lead to increase
  of variation
• adjustments should be based on understanding of
  process (engineering knowledge)
• we need a tool to check for stability

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Attributive versus variable

• two main types of measurements
• attributive (yes/no, categories)
• variable (continuous data)
• hybrid type
• classes or bins
• use variable data whenever possible!

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Statistically in control

• Constant mean and spread
• Process-inherent variation only
• Do not intervene

Intervene?
Measurement
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Tijd
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Statistically versus technically in control

• Statistically in control
• stable over time /predictable
• Technically in control
• within specifications

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Statistically in control vs technically in control

• statistically controlled process
• inhibits only natural random fluctuations (common
  causes)
• is stable
• is predictable
• may yield products out of specification
• technically controlled process
• presently yields products within specification
• need not be stable nor predictable

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Priorities

• what is preferable
• statistical control or
• technically in control ??
• process must first be in statistical control

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Variation and production processes

• Shewhart distinguishes two forms of variation in
  production processes
• common causes
• inherent to process
• cannot be removed, but are harmless
• special causes
• external causes
• must be detected and eliminated

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Chance or noise

• How do we detect special causes ?
• use statistics to distinguish between chance and
  real cause

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Shewhart control chart

• graphical display of product characteristic which
  is important for product quality

Upper Control Limit
Centre Line
Lower Control Limit
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Control charts
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Why control charts?

• control charts are effective preventive device
• control charts avoid tampering of processes
• control charts yield diagnostic information

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Basic principles

• take samples and compute statistic
• if statistic falls above UCL or below LCL, then
  out-of-control signal e.g.,

how to choose control limits?
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Normal distribution

• often used in SPC
• justification by Central Limit Theorem
• accumulation of many small errors

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Meaning of control limits

• limits at 3 x standard deviation of plotted
  statistic
• basic example

UCL
LCL
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Example

• diameters of piston rings
• process mean 74 mm
• process standard deviation 0.01 mm
• measurements via repeated samples of 5 rings
  yields

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Specifications vs. natural tolerance limits

• never put specification limits on a control chart
• control chart displays inherent process variance
• during trial run charts (also called tolerance
  chart of tier chart) often yields useful
  graphical information