Statistical Tools For Problem Solving_ Dr. A. Amsavel

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• STATISTICAL TOOLS FOR PROBLEM SOLVING
• Dr. A. Amsavel, M.Sc., B.Ed., Ph.D.

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Overview

• Problem Solving Steps
• Statistical Tools
• Run Chart
• Pareto Chart
• Cause and Effect diagram- Fishbone Diagram
• Brainstorming
• Histograms or Stem-and-Leaf Plot
• Control Chart
• Process Capability, etc

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Problem solving

• Problem solving is a strategy that employs the
  scientific method in searching for information,
  arriving at decisions based on facts, prior
  knowledge and reasoning.
• "Statistics is the branch of scientific method
  which deals with the data obtained by counting or
  measuring the properties of populations of
  natural phenomena.

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Want to solve the problem !Think Differently
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Problem Solving Methodology

• A systematic approach to defining the problem
  (uncertainty, perplexity or difficulty) and
  creating a vast number of possible solutions
  without judging these solutions.
• The act of narrowing down the possibilities,
  choosing a course of action, and determining the
  actions potential consequences.
• Problem solving is a cognitive processing
  directed at achieving a goal where no solution
  method is obvious to the problem solver.

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PDCA Wheel
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5 Step approach to Problem Solving

• Define the Problem clearly.
• Diagnose the situation, so that your focus is on
  the problem, not on its symptoms.
• Determine the Causes.
• Evaluate the Options for Solutions
• Generate Ideas / alternative solutions.
• Select the Best Solution.
• Take Action.
• Implement and follow up on the solution.

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5 Step approach to Problem Solving

1. Ask, "What is going on?.  Define the problem and
   Impact
2. Ask, "What is success?" . Define what the
   solution must do, what resources it needs, its
   scope, and the values it must uphold.
3. Ask, "What is the question?" . Generate a long
   list of questions that, when answered, will solve
   the problem
4. Forge the solution Evaluate the ideas with
   potential based on the criteria from step 2. Pick
   a solution.
5. Align resources Identify people and resources to
   execute the solution.

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How many Squares do you see.




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If you were to come up with a different number of
Squeres than another person, does this mean you
are wrong?!
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Being Open to Other Perspectives

• There is no Right or Wrong answer there are
  only individual perspectives.
• When you know that there are always more ways to
  see the same situation!, then every persons
  perspective is important to consider.

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Problem Solving Action Cycle
An Action cycle provide the method for
controlling the problem Solving process

MEASURE
No measurement without Recording
No action without measurement
RECORD
ACT
ANALYSE
No Analyssis without Record
No Anaysis without Action
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Statistical Process Control (SPC) Statistical
Quality Control (SQC)

• What causes defects?
• How are defectives made?
• Can we make okay?
• Are we making it okay?
• Is process consistent?
• Can we do right at first?
• Can we improve?
• Can we minimize the wastes?
• Use SPC SQC

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Why We Need Statistical Analysis?

• General causes of troubles/problems arises from
  wrong knowledge and or in-correct operation.
• To distinguish, start fact-finding process.
• How to eliminate the problem or Rejection?
• Identify
• Quantify
• Eliminate
• Prevent it re-occurrence

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Application

• The excessive consumption of energy or raw
  materials
• Problem in the process itself (low yield Quality
  defect)
• Problems arising, but not measured identified
  in the particular stage/step,
• Non-confirming of product/ rejection
• SPC/SQC used for
• Cost savings
• Higher productivity
• Better product quality
• Lower environmental impact.

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A Systematic Approach to Process Improvement

• What are wastes and its cost?
• Where is waste generating ?
• What are the possible causes?
• Is the process consistent
• Is there any drift or failure in the process?
• How can process be improved?
• How can be maintained and controlled?

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Type of Tools

• Run chart
• Pareto chart
• Flow chart
• Cause and Effect diagram- Fish bone
• Histograms or Stem-and-Leaf Plot
• Control Chart
• Scatter diagram
• Process capability, etc.

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Run Charts

• A Run chart shows What happens over a time
  /period
• Visualize the unexpected SHIFT, TREND, PATTERN
• Construction of Run chart
• Plot of Variable Vs. Time or Sequence
• Choose Critical elements (key variable) in the
  process
• Collect the data
• Plot a graph Time or sequence in X axis and
  variable in Y axis.

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Typical Run Chart
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Run Charts- Purpose

• To monitor process performance.
• Process monitoring against Time or Sequence
• Reaction or Drying progress Vs Batche No
  (Temp/converton/Time
• Output /Yield Vs Batch No
• Quality parameters Vs Batch No.
• Quantity Vs Distillation Time
• In determining when a change to a process might
  have occurred.

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Run Charts

• Information /Recording
• What is being measured, when it was measured and
  other information
• Update the chart frequently
• To indicate quality and productivity of an
  important process
• Utilization of Run Chart
• To monitor the on-going performance
• To monitor the performance of process over time /
  sequence to detect trends, shift or cycle.
• Investigate the reason and eliminate the defect
  or cause.

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Pareto Principle

• The Pareto principle (also known as the 80-20
  rule) states that, for many events, 80 of the
  effects come from 20 of the causes.
• Business management thinker Joseph M Juran
  suggested the principle and named it after
  Italian economist Vilfredo Pareto , who observed
  that 80 of income in Italy went to 20 of the
  population.
• 80 of problems usually Stem from 20 of the
  causes.

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Pareto Chart

• This is a simple bar graph ranking in order of
  importance the causes, Sources, types or reasons
  for problems / opportunities.
• It helps to identity the problems that affect
  greatest potential for improvement.
• Choose the unit of measures and critical elements
• Collect data for the problems
• Compare relative cost of each problem category
• Arrange in descending order

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Typical Pareto Chart
Eg Controller failure Analysis Down time Vs
Failures Reasons
Attributes for longer down time will be consider
as priority
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Typical Pareto Chart
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Pareto Chart

• Utilize Setting Priorities for Action
• Pickup an Important areas of waste /
  opportunities and decide how to measure the
  various contributors.
• Complaint Nature Vs. Year
• Contribution Vs. Product
• Non-conformity Vs Year
• Cost of failure Vs product

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Cause and Effect /Fishbone Diagram

• It is also called as Ishikawa Diagram
• Dr. Kaoru Ishikawa-invented the fishbone diagram.
  
• The fishbone diagram is an analysis tool that
  provides a systematic way of looking at effects
  and the causes that create or contribute to those
  effects.
• The design of the diagram looks much like the
  skeleton of a fish.
• A team which possess knowledge on this

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Cause and Effect /Fishbone Diagram

• Constriction of FB
• Establish a team which possess knowledge on this
• Write the Problem Statement at Head of a Fish
  bone.
• 6M or 5ME As Main Branch Manpower, Machines,
  Materials, Methods, Measures, Milieu /
  Environment.
• Identify the main categories of possible causes
• Add the sub-branch/factors in the diagram until
  to get useful information.
• Place these at ends of branches emanating from
  the back bone.

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Cause and Effect /Fishbone Diagram

• Brainstorm all possible causes and place these in
  the suitable area of the diagram.
• Use checklist /questions to support brainstorming
  
• Do not discourage the members ideas
• Analyze the results of the fishbone after
  obtained adequate detail to identify most likely
  causes.
• List most likely causes in priority order. First
  item being the cause or most probable cause.
• Typical Fishbone diagram....

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Typical Fishbone Diagram
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Typical Fishbone Diagram
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Example of Fish Bone Questions

• Measurement
• Is process performed as per established
  parameters?
• Are all measurement /entries / data correct?
• Calculations correct and verified?
• Are measuring devices appropriate, qualified
  calibrated?
• Do previous inspection or maintenance results
  indicate potential problems?
• Is quantity of input and output correct. Is
  quality suitable
• Is there any previous atypical results or
  trending history ie OOT
• Recent documentation history?

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Example of Fish Bone Questions

• Method / Process
• Is the process validated?
• Is the process operating within its validated
  parameters?
• Any deviations from standard operating
  procedures?
• Is the right procedure used?
• Is the procedure accurate / clear?
• Samples pulled at appropriate steps?
• Any sampling issues?
• Were processing steps properly verified?

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Example of Fish Bone Questions

• Machine/Equipment
• Has equipment been recently replaced or repaired?
  
• Is qualified and suitable assessed
• It is within calibration?
• Is preventative maintenance completed?
• Maintenance records reviewed?
• Are any equipment cleanliness issues?
• Equipment capacity or availability an issue?
• Is equipment being used for its intended purpose?
  

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Example of Fish Bone Questions

• Materials
• Are material / components tested approved ?
• Is properly released and issued ?
• Are materials charged correct quantity in
  sequence?
• Material properly stored temperature /
  humidity?
• Is within expiration dating?
• Is properly labeled segregated adequately?
• Is it from new source / vendor?
• Material sensitive/ protected

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Brainstorming

• Brainstorming is a technique to generate as many
  ideas with team /group.
• To identify problems, analyze causes, select
  alternative solutions, do strategic planning,
  generate ideas for change or Improvements

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Conducting Brainstorming

• Explain the objective, Problems, Causes,
  generate ideas.
• Explain the brainstorming technique
• The idea of brainstorming is to produce as many
  innovative ideas as possible.
• looking for a lot of ideas, thoughts to flow
  freely.
• There is no right or wrong answer.
• Silent reflection
• Participants to think about the proposed
  objective or topic for a few minutes.

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Dos and Dont in Brainstorming

• When we brainstorm, any idea is a good idea.
• Dont judge or criticize.
• Build off of each others ideas.
• A really good solution can come from a wild and
  crazy idea.
• Dont use this step as a time to become a bully,
  like taking control or pushing your solution.
• Be sincere, listen and take every idea seriously.

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Brainstorming

• Brainstorm in a team
• Call out their ideas
• Write them on a flip chart in the order
• Write down the ideas and get clarity if required
• Once the list is finished, discuss it with the
  group to
• Clarify the meaning of some ideas
• Combine similar ideas that are worded in
  different ways
• Eliminate those ideas which are not related
• Do all this by group consensus. At the end reduce
  the list to major ideas of the group

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Histogram

• A Histogram is a Graphical Display of tabulated
  Frequencies.
• It is a picture of the variation in a process or
  a product.
• It shows the capability of process and helps us
  to understand the below
• Analyze what is happening.
• Shows the spread of variation
• Average (center) and dispersion
• Range Lowest and highest

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Histogram

• Construction of Histograms
• First decide on the process to be measured
• Collect the data as required
• Make a check sheet
• Calculate the range and average
• Prepare frequency table (Measurement at interval
  frequency)
• Draw a bar chart (X-Class width Y Frequency)
• Connect the center point and draw line

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Typical Histogram
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Types of Histograms
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Histogram

• Interpretation of Histograms
• Check the shape (symmetrical, cliff like, either
  side, skewed)
• Check for normal distribution
• Compare the range with specification
• Check for improvement
• Prepare action plan with target
• Implement the planned action
• Verify the improvement in the process

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Control Chart

• Control Chart was developed by Dr. Walter A.
  Shewhart in 1920, it is widely used to monitor
  process control
• It graphically depicts the average value and the
  upper and lower control limits (UCL LCL) of a
  process.
• A control chart is a moving picture of the
  variation in a process. This can be used to
  identify the drift or variability and analyse,
  stabilize, control and improve the process.
• It provides the current status, capabilities,
  variation, etc.
• This can be used to reduce scrap and rework, then
  productivity increases, cost decreases, and
  production capacity

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Control Chart

• Preparing Control Charts
• Decide what factor to be studied
• Measure the value
• Calculate X or R and standard deviation.
• Use 25 or more points
• Plot immediately to discover the problems
• Compute a new average after making process change
• For any out of control point on the control
  chart, record the reason for it and the action
  taken.

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Control Chart
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Control Chart

• Interpretation from Control Chart
• A process must be stable before you can use a
  control chart effectively for improvement.
• Use control chart to help track reason for
  special cause and any significant change.
• Utilization of Control Chart
• Monitor the performance of process over time /
  sequence to detect trends, shift or cycle.
• Investigate the reason and eliminate by applying
  corrective action.
• Compare variables before and after improvement

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Control Chart

• In Control Process Process average and standard
  deviation are known and predictable, stable,
  consistent and unchanging
• Out of Control Process ( OOT or Alert level)
  Process average and standard deviation changing,
  unstable and inconsistent.
• Six points consecutive points upward or downward
  (Figure1)
• Two out of three points in a row in Zone A (µ s
  ) (Figure-2)
• Four out of five points in a row in Zone B (µ 2
  s) or beyond A (Figure-2)
• Nine points in a row on one side of the center
  line (Figure-3)
• Fourteen points in a row alternate up and down
  (Figure-3)

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Out of Trend
Figure-1
Figure-3
Figure-2
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Process Capability

• Normal Distribution
• µ s 68.26
• µ 2s 95.44
• µ 3s 99.73
• µ is mean value s is standard deviation
• The capability of the process to meet the
  specifications determined by stability of the
  process, the range of variation and the process
  aim point

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Normal distribution
Histogram follows NORMAL DISTRIBUTION Process
meets the Specification, consistent and capable
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Process Capability Index

• Process Capability Index Calculation
• Cpk (SU SL)/ 6 s (s- Standard deviation,
• If Specification is one sided
• Cpk (SU X)/ 3 s
• Cpk (X - SL)/ 3 s

SU- Upper spec limit SL- Lower spec limit X- Base
value of one side (s- Standard deviation,
CPk Value Process Capability
1 1.33 Cpk Satisfiable enough
2 1.00 Cpk lt 1.33 Adequate
3 Cpk lt 1.00 Inadequate
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Process Capability (Cpk)

• Assumption- Chemical process-A give Yield
  range100 -120kg, Standard deviation 3.4 and
  mean is 12kg. Calculate the process capability
• 20
• Cp -------
• 63.4
• Cp 0.98
• Process in not capable, there is inconstant

Assumption- Chemical process-A give Yield range
100 -120 kg Mean is 111kg and
standard deviation 2.2. Calculate the process
capability 20 Cp -------
62.2 Cp 1.52 Process is capable constant
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Statistical Tools and Application
METHODOLOGY TOOLS / TECHNIQUES
1. Search for opportunities decide what to work on. Identify the area for improvement Pareto charts Cause and effect diagrams, flow chart.
2. Clearly define the project Select the improvement team. Pareto charts Brainstorming.
3. Study the current process/ situation. Check sheet Run chart Flow chart Cause and effect diagram Histogram Pareto charts Control charts
4. Analyse causes plan the improvement. Cause and effect diagram Correlation chart Pareto charts Brainstorming Histogram.
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Statistical Tools and Application
METHODOLOGY TOOLS / TECHNIQUES
5. Carry out the improvement plan. Run chart Histogram flow chart.
6. Study the effect of the changes. Run chart Histogram Control chart.
7. Standardize the improved process. Flow chart Run chart Histogram
8. Assess progress and plan for the future. Cause and effect diagram Pareto charts Brain storming
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• What does not get Measured, Can not be Recorded
• What does not get Recorded, Can not be Monitored
• What does not get Monitored, Can not be
  Controlled
• What does not get Controlled, Can not be Improved

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Thank you