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Lecture 4

Analytical tools used in Six Sigma

Purpose of analytical tools

1) Identifying the problem

2) Defining the problem

3) Solving the problem

Common analytical tools used in Six Sigma

Run chart

Control chart

Pareto chart

Cause and effect diagram

Tree diagram

Why-Why diagram

Scatter diagram

Flow chart

Histogram

XY matrix

F

Run chart (time series plot)

  • A run chart permits the study of observed data for trend or pattern over time.
  • In this chart, the x-axis is time and the y-axis is the measured variable.
  • It can be used to compare the performance before and after a solution has been implemented.
  • Generally 20-25 points are needed to establish patterns and baselines.

Example of Run (Trend) chart

  • This analysis shows how things are changing over time.
  • The chart shows exceptional spikes & dips in the data trend and may provide the reason for six sigma projects.

Example of Run chart for customer inquiries

Common analytical tools used in Six Sigma

Run chart

Control chart

Pareto chart

Cause and effect diagram

Tree diagram

Why-Why diagram

Scatter diagram

Flow chart

Histogram

XY matrix

F

Control charts

  • Control charts provides a study of variation and its source.
  • It monitors and controls the process.
  • It can also provide the direction for improvement.
  • Control charts can separate special and common cause issues of a process.
  • This is important because the approach to solve the problem is very different for these two type of situations.

Example of control chart

  • A control chart shows the range of variation in the process.
  • It helps the Six Sigma team to determine whether the process is stable or it needs further investigation.

Example of “x-bar” and “R” control charts

  • These control charts are the most common statistical tools to check for process variability.
  • x-bar measures the process variability from the mean and “R” measures the process variability of the range (compared to mean range value)

Interpretation of control chart

A process is out of control & needs investigation if any of the following conditions exist:

a) Any one point is beyond “zone A”.

b) Any two out of three consecutive points are in the same “zone A” or beyond.

c) Any four out of five consecutive points are in the same “zone B” or beyond.

d) Any eight consecutive points are in the same “zone C” or beyond.

Common analytical tools used in Six Sigma

Run chart

Control chart

Pareto chart

Cause and effect diagram

Tree diagram

Why-Why diagram

Scatter diagram

Flow chart

Histogram

XY matrix

F

Pareto chart

  • Pareto charts are a tool that can be helpful in identifying the source of chronic problems and common causes in a manufacturing process.
  • The pareto principle states that a vital few of the manufacturing process characteristics cause most of the quality problems (like 80-20 rule).
  • While trivial many manufacturing process characteristics cause only a small portion of the quality problem.

Example of Pareto Charts

  • It is a specialized bar chart which breaks down the data by categories and compares them from largest to smallest.
  • This chart indicates which item has the most impact on the problem and where to focus attention during the Six Sigma project.

Steps to construct a generic Pareto chart

1) Define the problem and process characteristic to use in the diagram.

2) Define the x-axis for the diagram; for example, time, department etc.

3) Determine the total of the number of times each characteristics occurred.

4) Rank the characteristics according to the total in step 3.

5) Plot the number of occurrences of each characteristic in the descending order in the bar graph.

6) Also draw the cumulative plot of the magnitudes from the bars.

Example of Pareto chart for solder defects

Example of Pareto chart of opportunities for improvement in the service center

Example of 2-level Pareto analysis for customer complaints

Common analytical tools used in Six Sigma

Run chart

Control chart

Pareto chart

Cause and effect diagram

Tree diagram

Why-Why diagram

Scatter diagram

Flow chart

Histogram

XY matrix

F

Cause-and-effect diagram

  • This analytical tool is very effective to solve problems.
  • It is also known as Ishikawa diagram or fishbone diagram.
  • This technique is useful to trigger ideas and promote a balanced approach in group brainstorming sessions.
  • This is constructed by listing the source (cause) of a problem (effect) provided by individual team members.
  • The cause-and-effect diagram provides a means for the teams to focus on the creation of a list of key process input variables (KPIV) that could affect key process output variables (KPOV).

Example of Fishbone diagram

  • This is also called cause-and-effect diagram.
  • It helps to evaluate all possible causes in major categories.
  • It tells you where to focus measurement & conduct root cause analysis.

Example of cause-and-effect diagram

Example of cause-and-effect diagram

Common analytical tools used in Six Sigma

Run chart

Control chart

Pareto chart

Cause and effect diagram

Tree diagram

Why-Why diagram

Scatter diagram

Flow chart

Histogram

XY matrix

F

Tree diagram

  • Tree diagrams can help people uncover, describe, and communicate a logical relationship that is hierarchical between important events or goals.
  • A tree can describe the hierarchy that leads to a desirable or undesirable event.
  • With this approach a big idea or problem is partitioned into smaller components.
  • Ideas can then become easier to understand, while problems become easier to solve.
  • It can be useful for the construction of a flow diagram by using AND or OR gates to connect lower elements in the hierarchy to higher elements of hierarchy.

Example of Tree Diagram

  • A Tree Diagram is used to show links or hierarchy of objectives & causes.
  • It shows how goals & possible solutions are connected.
  • It can be used to analyze major customer needs.

Example of a Tree diagram

Printed circuit board open

Missing component

Internal open

in board

Component

Insufficient solder

Placement macine failure

Assembly handling problem

Bent lead

Internal open

Paste too old

Hole in stencil is plugged

Too little paste in screen printer

Common analytical tools used in Six Sigma

Run chart

Control chart

Pareto chart

Cause and effect diagram

Tree diagram

Why-Why diagram

Scatter diagram

Flow chart

Histogram

XY matrix

F

Why-Why diagram

Risk Factor Why? Why? Why?
Leaning forward Reach > 30 in. Shield restricts leg room and access in front of machine Cutting fluid splashes off cutters and creates slip hazard on floor
Base plate size Multiple parts are worked on the lathe – all sizes
Gauge design – long tool hold in from of the body. Turret lathe moves, so it is hard to leave the gauges in place over the part.
Difficulty in reading small dials Number size is determined by dial size (<2.5 cm, 1 in.)
Twisting Stabilizing the gauge on the part No support for the gauge – muscle effort stabilizes it Tool weight is the limiting factor
Reading the dials Arm can block the view of the dials Location and orientation of dish on gauge

Example
of
why-why diagram

Common analytical tools used in Six Sigma

Run chart

Control chart

Pareto chart

Cause and effect diagram

Tree diagram

Why-Why diagram

Scatter diagram

Flow chart

Histogram

XY matrix

F

Scatter diagram (plot of two variables)

  • It provides a relationship between two variables.
  • It offers a follow-up procedure to assess relationship from a cause-and effect diagram.
  • When creating a scatter diagram, 50-100 pairs of samples should be plotted.
  • The independent variable should be on the x-axis and the dependent variable should be on the y-axis.
  • A word of caution, a scatter diagram relationship does not always predict the cause-and effect relationship but merely the strength of relationship between two variables.

Example of Scatter Plot (Correlation)

  • A scatter plot looks for direct relationships (correlation) between two factors in a process.
  • Scatter plot indicates whether there is any correlation between the two variables.

Example of Scatter plot correlation

Common analytical tools used in Six Sigma

Run chart

Control chart

Pareto chart

Cause and effect diagram

Tree diagram

Why-Why diagram

Scatter diagram

Flow chart

Histogram

XY matrix

F

Flow chart (Process Map)

  • A flow chart is used to show details of a process. It includes:
  • tasks and procedures
  • alternative paths
  • decision points
  • rework loop
  • A flow chart “as is” map shows a process as it currently works.
  • A flow chart “should be” shows a process as it ought to work.

Example of Process Map (Flowchart)

Process Map (Flowchart) shows a process as it currently works.

It uses four basic symbols:

  • circle = start & end of the process
  • rectangle = task or activity
  • diamond = decision point
  • arrow = direction of flow

Example of a Flow chart in a service center

Example of Flow chart for lab work order process

Common analytical tools used in Six Sigma

Run chart

Control chart

Pareto chart

Cause and effect diagram

Tree diagram

Why-Why diagram

Scatter diagram

Flow chart

Histogram

XY matrix

F

Histogram (Frequency Plot)

A histogram is a type of bar chart which shows the distribution or variation of data over a range such as:

1) size

2) age

3) cost

4) length of time

5) weight

A pareto chart , by contrast plots the data by category

Example of Histogram (Frequency Plot)

  • A histogram is a type of bar chart, which shows the distribution or variation of data over a range.
  • Histograms helps analyze the shape, width and range of the bars (curve) and identifies the items which are meeting or not meeting the objectives.

How to analyze Histograms

  • Look for the shape of the bars or the curve.
  • Look for the width of the spread or range from top to bottom.
  • Look for the number of “humps” in the bars.
  • If you plot the customer requirements on a histogram, (a straight line) you can quickly see how much of what you do is meeting or not meeting your customer needs.

Common analytical tools used in Six Sigma

Run chart

Control chart

Pareto chart

Cause and effect diagram

Tree diagram

Why-Why diagram

Scatter diagram

Flow chart

Histogram

XY matrix

F

Example of XY matrix

Example of Charts & Graphs

  • Charts & graphs are visual displays of data.
  • This tool is very useful for Six Sigma teams to define the problem & analyze the causes.
  • Six Sigma black belts use this extensively on their projects.

Statistical analysis tools for Six Sigma

  • Tests of statistical significance: These tools look for the difference in groups of data to see whether they are meaningful. These tests include Chi-square, t-test, and analysis of variance (ANOVA).
  • Correlation and regression: These tools test for the presence, strength, and nature of the links among variables in a process or a product, such as how would tire pressure, temperature, and speed would affect gas mileage.
  • Design of experiments (DOE): It is a method of developing and conducting controlled assessments of how a process or a product performs through testing two or more characteristics under different conditions. DOE is an excellent tool for optimization.