Statistical Process Contol (SPC)

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Statistical Process Contol (SPC)

• Lec-1

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Quality and SPC

• The concept of quality has been with us since the
  beginning of time.
• Typically the quality of products was described
  by some attribute such as strength, beauty or
  finish.
• However, the mass production of products that the
  reproducibility of the size or shape of a product
  became a quality issue.

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Quality and SPC

• Quality was obtained by inspecting each part and
  passing only those that met specifications.
• With SPC, the process is monitored through
  sampling.
• Considering the results of the sample,
  adjustments are made to the process before the
  process is able to produce defective parts.

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Process Variability

• The concept of process variability forms the
  heart of SPC.
• For example, if a basketball player shot free
  throws in practice, and the player shot 100 free
  throws every day, the player would not get
  exactly the same number of baskets each day.
• Some days the player would get 84 of 100, some
  days 67 of 100, and so on.
• All processes have this kind of variation or
  variability.

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Process Variability

• The variation can be partitioned into 2
  components.
• Natural process variation (common cause) or
  system variation.
• In the case of the basketball player, this
  variation would fluctuate around the player's
  long-run percentage of free throws made.
• Special cause variation is typically caused by
  some problem or extraordinary occurrence in the
  system.
• In the case of the player, a hand injury might
  cause the player to miss a larger than usual
  number of free throws on a particular day.

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Statistical Process Control (SPC)

• SPC is a methodology for charting the process and
  quickly determining when a process is "out of
  control.
• (e.g., a special cause variation is present
  because something unusual is occurring in the
  process).
• The process is then investigated to determine the
  root cause of the "out of control" condition.
• When the root cause of the problem is determined,
  a strategy is identified to correct it.

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Statistical Process Control (SPC)

• The management responsible to reduce common cause
  or system variation as well as special cause
  variation.
• This is done through process improvement
  techniques, investing in new technology, or
  reengineering the process to have fewer steps and
  therefore less variation.
• Reduced variation makes the process more
  predictable with process output closer to the
  desired or nominal value.

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Statistical Process Control (SPC)

• The process above is in apparent statistical
  control.
• Notice that all points lie within the upper
  control limits (UCL) and the lower control limits
  (LCL). CL-centerline
• This process exhibits only common cause variation.

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• The process above is out of statistical control.
• Notice that a single point can be found outside
  the control limits (above them).
• This means that a source of special cause
  variation is present.
• Having a point outside the control limits is the
  most easily detectable out-of-control condition.

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• The graphic above illustrates the typical cycle
  in SPC.
• First, the process is highly variable and out of
  statistical control.
• Second, as special causes of variation are found,
  the process comes into statistical control.
• Finally, through process improvement, variation
  is reduced.
• This is seen from the narrowing of the control
  limits.
• Eliminating special cause variation keeps the
  process in control process improvement reduces
  the process variation and moves the control
  limits in toward the centerline of the process.

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Out-of-Control Conditions

• Several types of conditions exist that indicate
  that a process is out of control
• Extreme Point Condition
• This process is out of control because a point is
  either above the UCL or below the LCL.

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Out-of-Control Conditions

• Control Chart Zones
• Control charts can be broken into 3 zones, a, b,
  c on each side of the process center line.
• A series of rules exist that are used to detect
  conditions in which the process is behaving
  abnormally to the extent that an out of control
  condition is declared.

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Out-of-Control Conditions

• The probability of having 2 out of 3 consecutive
  points either in or beyond zone A is an extremely
  unlikely occurrence when the process mean follows
  the normal distribution.
• This criteria applies only to X-bar charts for
  examining the process mean.

X, Y, and Z are all examples of this phenomena.
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Out-of-Control Conditions

• The probability of 4 out of 5 consecutive points
  either in or beyond zone B is also an extremely
  unlikely occurrence when the process mean follows
  the normal distribution.
• Applied to X-bar chart when analyzing a process
  mean.

X, Y, and Z are all examples of this phenomena.
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Out-of-Control Conditions

• Runs Above or Below the Centerline
• The probability of having long runs (8 or more
  consecutive points) either above or below the
  centerline is also an extremely unlikely
  occurrence when the process follows the normal
  distribution.
• Applied to both X-bar and r charts.

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Out-of-Control Conditions

• Linear Trends
• The probability of 6 or more consecutive points
  showing a continuous increase or decrease is also
  an extremely unlikely occurrence when the process
  follows the normal distribution.
• Applied to both X-bar and r charts.

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Out-of-Control Conditions

• Oscillatory Trend
• The probability of having 14 or more consecutive
  points oscillating back and forth is also an
  extremely unlikely occurrence when the process
  follows the normal distribution.
• Applied to both X-bar and r charts.

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Out-of-Control Conditions

• Avoidance of Zone C
• The probability of having 8 or more consecutive
  points occurring on either side of the center
  line and do not enter Zone C.
• This phenomena occurs when more than one process
  is being charted on the same chart, the use of
  improper sampling techniques, or perhaps the
  process is over controlled.

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Out-of-Control Conditions

• Run in Zone C
• The probability of having 15 or more consecutive
  points occurring the Zone C.
• This condition can arise from improper sampling,
  falsification of data, or a decrease in process
  variability that has not been accounted for when
  calculating control chart limits, UCL and LCL.

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The basics

• Dont inspect the product, inspect the process.
• You cant inspect it in, youve got to build it
  in.
• If you cant measure it, you cant manage it.

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The SPC steps

• Basic approach
• Awareness that a problem exists.
• Determine the specific problem to be solved.
• Diagnose the causes of the problem.
• Determine and implement remedies.
• Implement controls to hold the gains achieved by
  solving the problem.

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SPC requires the use of statistics

• Quality improvement efforts have their foundation
  in statistics.
• SPC involves the
• collection
• tabulation
• analysis
• interpretation
• presentation of numerical data.

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SPC is comprised of 7 tools

• Pareto diagram
• Histogram
• Cause and Effect Diagram
• Check sheet
• Process flow diagram
• Scatter diagram
• Control chart

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Pareto Principle

• Alfredo Pareto (1848-1923) Italian Economist
• Conducted studies of the distribution of wealth
  in Europe.
• 20 of the population has 80 of the wealth
• Joseph Juran used the term vital few trivial
  many or useful many. He noted that 20 of the
  quality problems caused 80 of the dollar loss.

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Pareto diagram
(64)
A pareto diagram is a graph that ranks data
classifications in descending order from left to
right.
Percent from each cause
(13)
(10)
(6)
(3)
(2)
(2)
Poor Design
Defective parts
Operator errors
Machine calibrations
Defective materials
Surface abrasions
Wrong dimensions
Causes of poor quality
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Pareto diagram
Complaints
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Pareto diagram

• Sometimes a pareto diagram has a cumulative line.
• This line represents the sum of the data as they
  are added together from left to right.

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Pareto diagram

• Sometimes a pareto diagram has a cumulative line.
• This line represents the sum of the data as they
  are added together from left to right.

Above the bars, using the 2nd Y-axis representing
the cumulative data, plot the cumulative
percentage values in the form of a line.
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Pareto diagram

• The cumulative percentage can be computed (dotted
  line).
• On the right, add a vertical percent scale equal
  in length to the scale on the left.
• Label this from 0 to 100 .

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Pareto diagram
Table 1. Example of a Tabulation of Causes of
Ball Bond Lifting for use in a Pareto Chart
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Pareto diagram
Table 1. Example of a Tabulation of Causes of
Ball Bond Lifting for use in a Pareto Chart
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Histogram
The histogram, graphically shows the process
capability and, if desired, the relationship to
the specifications and the nominal. It also
suggests the shape of the population and
indicates if there are any gaps in the data.
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Histogram
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Histogram
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Cause-and-Effect Diagrams

• Show the relationships between a problem and its
  possible causes.
• Developed by Kaoru Ishikawa (1953)
• Also known as
• Fishbone diagrams
• Ishikawa diagrams

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Cause and Effect Skeleton
Materials
Procedures
Quality Problem
Equipment
People
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Fishbone Diagram

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Fishbone Diagram
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Cause-and-Effect Diagrams

• Advantages
• making the diagram is educational in itself
• diagram demonstrates knowledge of problem solving
  team
• diagram results in active searches for causes
• diagram is a guide for data collection

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Cause-and-Effect Diagrams

• To construct the skeleton, remember
• For manufacturing - the 4 Ms
• man, method, machine, material
• For service applications
• equipment, policies, procedures, people

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Check Sheet
Shifts
? ? ?
? ? ? ?
?
? ? ?
? ?
? ? ?
Defect Type
? ? ?
? ? ? ?
? ?
?
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Check Sheet
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Flowcharts

• Graphical description of how work is done.
• Used to describe processes that are to be
  improved.

• "Draw a flowchart for whatever you do. Until you
  do, you do not know what you are doing, you just
  have a job.
• Dr. W. Edwards Deming.

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Flowcharts
Activity
Decision
Yes
No
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Flowcharts
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Flow Diagrams
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Process Chart Symbols
Operations
Inspection
Transportation
Delay
Storage
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Flow Diagrams
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(No Transcript)
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Scatter Diagram
.
(a) Positive correlation
(b) No correlation
(c) Curvilinear relationship
The patterns described in (a) and (b) are easy to
understand however, those described in (c) are
more difficult.
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Run Charts

• Run Charts (time series plot)
• Examine the behavior of a variable over time.
• Basis for Control Charts

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Control Chart
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UCL 23.35
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c 12.67
18
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Number of defects
12
9
6
LCL 1.99
3
2
4
6
8
10
12
14
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Sample number
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Control Chart
7 Quality Tools
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SUMMARY

• SPC using statistical techniques to
• measure and analyze the variation in processes 
• to monitor product quality and
• maintain processes to fixed targets. 
• Statistical quality control using statistical
  techniques for
• measuring and improving the quality of processes,
  
• sampling plans,
• experimental design,
• variation reduction,
• process capability analysis,
• process improvement plans.

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SUMMARY

• A primary tool used for SPC is
• the control chart,
• a graphical representation of certain descriptive
  statistics for specific quantitative measurements
  of the process. 
• These descriptive statistics are displayed in the
  control chart in comparison to their "in-control"
  sampling distributions. 
• The comparison detects any unusual variation in
  the process, which could indicate a problem with
  the process. 

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SUMMARY - benefits

• Provides surveillance and feedback for keeping
  processes in control
• Signals when a problem with the process has
  occurred
• Detects assignable causes of variation
• Reduces need for inspection
• Monitors process quality
• Provides mechanism to make process changes and
  track effects of those changes
• Once a process is stable, provides process
  capability analysis with comparison to the
  product tolerance