1. Check Sheet
Also called: defect concentration
diagram
Description:
A check sheet is a structured, prepared
form for collecting and analyzing data. This is a generic tool that can be
adapted for a wide variety of purposes.
When to Use a Check Sheet:
•
When data can be observed and collected repeatedly by the same person or at the
same location.
•
When collecting data on the frequency or patterns of events, problems, defects,
defect location, defect causes, etc.
•
When collecting data from a production process.
Check Sheet Procedure:
•
Decide what event or problem will be observed. Develop operational definitions.
•
Decide when data will be collected and for how long.
•
Design the form. Set it up so that data can be recorded simply by making check
marks or Xs or similar symbols and so that data do not have to be recopied for
analysis.
•
Label all spaces on the form.
•
Test the check sheet for a short trial period to be sure it collects the
appropriate data and is easy to use.
•
Each time the targeted event or problem occurs, record data on the check sheet.
Check Sheet Example:
The figure below shows a check sheet
used to collect data on telephone interruptions. The tick marks were added as
data was collected over several weeks.
2. Fishbone Diagram
Also Called: Cause-and-Effect Diagram, Ishikawa Diagram
Variations: cause enumeration diagram, process fishbone,
time-delay fishbone, CEDAC (cause-and-effect diagram with the addition of cards),
desired-result fishbone, reverse fishbone diagram
Description
The fishbone diagram identifies many possible causes for an effect
or problem. It can be used to structure a brainstorming session. It immediately
sorts ideas into useful categories.
When to Use a Fishbone Diagram
• When identifying
possible causes for a problem.
• Especially when a
team’s thinking tends to fall into ruts.
Fishbone Diagram Procedure
Materials needed: flipchart or whiteboard, marking pens
• Agree on a
problem statement (effect). Write it at the centre right of the flipchart or
whiteboard. Draw a box around it and draw a horizontal arrow running to it.
• Brainstorm the
major categories of causes of the problem. If this is difficult use generic
headings:
o Methods
o Machines
(equipment)
o People
(manpower)
o
Materials
o Measurement
o
Environment
• Write the
categories of causes as branches from the main arrow.
• Brainstorm all
the possible causes of the problem. Ask: “Why does this happen?” As each idea
is given, the facilitator writes it as a branch from the appropriate category.
Causes can be written in several places if they relate to several categories.
• Again ask “why
does this happen?” about each cause. Write sub causes branching off the causes.
Continue to ask “Why?” and generate deeper levels of causes. Layers of branches
indicate causal relationships.
• When the group
runs out of ideas, focus attention to places on the chart where ideas are few.
Fishbone Diagram Example
This fishbone diagram was drawn by a manufacturing team to try to understand
the source of periodic iron contamination. The team used the six generic headings
to prompt ideas. Layers of branches show thorough thinking about the causes of
the problem. For example, under the heading “Machines,” the idea “materials of construction”
shows four kinds of equipment and then several specific machine numbers.
Note that some ideas appear
in two different places. “Calibration” shows up under “Methods” as a factor in
the analytical procedure, and also under “Measurement” as a cause of lab error.
“Iron tools” can be considered a “Methods” problem when taking samples or a
“Manpower” problem with maintenance personnel.
3. Control Chart
Description
The control chart is a graph used to study how a process changes
over time. Data are plotted in time order. A control chart always has a central
line for the average, an upper line for the upper control limit and a lower
line for the lower control limit. These lines are determined from historical
data. By comparing current data to these lines, you can draw conclusions about
whether the process variation is consistent (in control) or is unpredictable
(out of control, affected by special causes of variation).
Control charts for variable data are used in pairs. The top chart monitors
the average, or the centring of the distribution of data from the process. The
bottom chart monitors the range, or the width of the distribution. If your data
were shots in target practice, the average is where the shots are clustering,
and the range is how tightly they are clustered. Control charts for attribute
data are used singly.
When to Use a Control Chart
• When controlling
ongoing processes by finding and correcting problems as they occur.
• When predicting
the expected range of outcomes from a process.
• When determining
whether a process is stable (in statistical control).
• When analyzing
patterns of process variation from special causes (non routine events) or
common causes (built into the process).
• When determining
whether your quality improvement project should aim to prevent specific
problems or to make fundamental changes to the process.
Control Chart Basic Procedure
• Choose the
appropriate control chart for your data.
• Determine the
appropriate time period for collecting and plotting data.
• Collect data,
construct your chart and analyze the data.
• Look for
“out-of-control signals” on the control chart. When one is identified, mark it
on the chart and investigate the cause. Document how you investigated, what you
learned, the cause and how it was corrected.
Out-of-control signals
A single point
outside the control limits. In Figure 1, point sixteen is above the UCL (upper
control limit).
Two out of three
successive points are on the same side of the centreline and farther than 2 σ from
it. In Figure 1, point 4 sends that signal.
Four out of five
successive points are on the same side of the centreline and farther than 1 σ from
it. In Figure 1, point 11 sends that signal.
A run of eight in a
row are on the same side of the centreline. Or 10 out of 11, 12 out of 14 or 16
out of 20. In Figure 1, point 21 is eighth in a row above the centreline. Obvious
consistent or persistent patterns that suggest
something unusual about your data and
your process.
Continue to plot
data as they are generated. As each new data point is plotted, check for new
out-of-control signals.
o When you
start a new control chart, the process may be out of control. If so, the
control limits calculated from the first 20 points are conditional limits. When
you have at least 20 sequential points from a period when the process is
operating in control, recalculate control limits
4. Histogram
Description
A frequency distribution shows how often each different value in a
set of data occurs. A histogram is the most commonly used graph to show frequency
distributions. It looks very much like a bar chart, but there are important
differences between them.
When to Use a Histogram
• When the data are
numerical.
• When you want to
see the shape of the data’s distribution, especially when determining whether
the output of a process is distributed approximately normally.
• When analyzing
whether a process can meet the customer’s requirements.
• When analyzing
what the output from a supplier’s process looks like.
• When seeing
whether a process change has occurred from one time period to another.
• When determining
whether the outputs of two or more processes are different.
• When you wish to
communicate the distribution of data quickly and easily to others.
Histogram Construction
• Collect at least
50 consecutive data points from a process.
• Use the histogram
worksheet to set up the histogram. It will help you determine the number of
bars, the range of numbers that go into each bar and the labels for the bar
edges. After calculating W in step 2 of the worksheet, use your
judgment to adjust it to a convenient number. For example, you might decide to
round 0.9 to an even 1.0. The value for W must not have more decimal places
than the numbers you will be graphing.
• Draw x- and
y-axes on graph paper. Mark and label the y-axis for counting data values. Mark
and label the x-axis with the L values from the worksheet. The spaces between these numbers will
be the bars of the histogram. Do not allow for spaces between bars.
• For each data
point, mark off one count above the appropriate bar with an X or by shading
that portion of the bar.
Histogram Analysis
• Before drawing
any conclusions from your histogram, satisfy yourself that the process was
operating normally during the time period being studied. If any unusual events
affected the process during the time period of the histogram, your analysis of
the histogram shape probably cannot be generalized to all time periods.
Analyze the meaning of your histogram’s shape.
5. Pareto Chart
Also called: Pareto diagram, Pareto analysis
Variations: weighted Pareto chart, comparative Pareto charts
Description
A Pareto chart is a bar graph. The lengths of the bars represent frequency
or cost (time or money), and are arranged with longest bars on the left and the
shortest to the right. In this way the chart visually depicts which situations
are more significant.
When to Use a Pareto Chart
• When analyzing
data about the frequency of problems or
causes in a process.
• When there are
many problems or causes and you want to
focus on the most significant.
• When analyzing
broad causes by looking at their specific
components.
• When
communicating with others about your data.
• Pareto Chart
Procedure
• Decide what
categories you will use to group items.
• Decide what
measurement is appropriate. Common measurements are frequency, quantity, cost
and time.
• Decide what
period of time the Pareto chart will cover: One work cycle? One full day? A
week?
• Collect the data,
recording the category each time. (Or assemble data that already exist.)
• Subtotal the
measurements for each category.
• Determine the
appropriate scale for the measurements you have collected. The maximum value
will be the largest subtotal from step 5. (If you will do optional steps 8 and
9 below, the maximum value will be the sum of all subtotals from step 5.) Mark
the scale on the left side of the chart.
• Construct and
label bars for each category. Place the tallest at the far left, then the next
tallest to its right and so on. If there are many categories with small
measurements, they can be grouped as “other.”
• Steps 8 and 9 are
optional but are useful for analysis and communication.
• Calculate the
percentage for each category: the subtotal for that category divided by the
total for all categories. Draw a right vertical axis and label it with
percentages. Be sure the two scales match: For example, the left measurement
that corresponds to one-half should be exactly opposite 50% on the right scale.
• Calculate and
draw cumulative sums: Add the subtotals for the first and second categories,
and place a dot above the second bar indicating that sum. To that sum add the
subtotal for the third category, and place a dot above the third bar for that
new sum. Continue the process for all the bars. Connect the dots, starting at
the top of the first bar. The last dot should reach 100 percent on the right
scale.
Pareto Chart Examples
Example #1 shows how many customer complaints were received in each
of five categories.
Example #2 takes the largest category, “documents,” from Example #1,
breaks it down into six categories of document-related complaints, and shows cumulative
values.
If all complaints
cause equal distress to the customer, working on
eliminating document-related complaints would have the most
impact,
and of those, working on quality
certificates should be most fruitful.
6. Scatter Diagram
Also called: scatter plot, X–Y graph
Description
The scatter diagram graphs pairs of numerical data, with one
variable on each axis, to look for a relationship between them. If the
variables are correlated, the points will fall along a line or curve. The
better the correlation, the tighter the points will hug the line.
When to Use a Scatter Diagram
• When you have
paired numerical data.
• When your
dependent variable may have multiple values for each value of your independent
variable.
• When trying to
determine whether the two variables are related,
such as…
o When
trying to identify potential root causes of problems.
o After
brainstorming causes and effects using a fishbone diagram, to determine
objectively whether a particular cause and effect are related.
o When
determining whether two effects that appear to be related both occur with the
same cause.
o When
testing for autocorrelation before constructing a control chart.
Scatter Diagram Procedure
• Collect pairs of
data where a relationship is suspected.
• Draw a graph with
the independent variable on the horizontal axis and the dependent variable on
the vertical axis. For each pair of data, put a dot or a symbol where the
x-axis value intersects the y-axis value. (If two dots fall together, put them side
by side, touching, so that you can see both.)
• Look at the
pattern of points to see if a relationship is obvious. If the data clearly form
a line or a curve, you may stop. The variables are correlated. You may wish to
use regression or correlation analysis now. Otherwise, complete steps 4 through
7.
• Divide points on
the graph into four quadrants. If there are X points on the graph,
o Count
X/2 points from top to bottom and draw a horizontal line.
o Count
X/2 points from left to right and draw a vertical line.
o If
number of points is odd, draw the line through the middle point.
• Count the points
in each quadrant. Do not count points on a line.
• Add the
diagonally opposite quadrants. Find the smaller sum and the total of points in
all quadrants.
A = points in upper left + points in lower right B = points in
upper right + points in lower left Q = the smaller of A and B N = A + B
• Look up the limit
for N on the trend test table.
o If Q is
less than the limit, the two variables are related.
o If Q is
greater than or equal to the limit, the pattern could have occurred from random
chance.
Scatter Diagram Considerations
• Here are some
examples of situations in which might you use a scatter diagram:
o Variable
A is the temperature of a reaction after 15 minutes. Variable B measures the colour
of the product. You suspect higher temperature makes the product darker. Plot temperature
and colour on a scatter diagram.
o Variable
A is the number of employees trained on new software, and variable B is the
number of calls to the computer help line. You suspect that more training
reduces the number of calls. Plot number of people trained versus
number of calls.
o To test
for autocorrelation of a measurement being monitored on a control chart, plot
this pair of variables:
Variable A is the measurement at a given time. Variable B is the
same measurement, but at the previous time. If the scatter diagram shows correlation,
do another diagram where variable B is the measurement two times previously.
Keep increasing the separation between the two times until the
scatter diagram shows no correlation.
• Even if the
scatter diagram shows a relationship, do not assume that one variable caused
the other. Both may be influenced by a third variable.
• When the data are
plotted, the more the diagram resembles a straight line, the stronger the
relationship.
• If a line is not
clear, statistics (N and Q) determine whether there is reasonable certainty
that a relationship exists. If the statistics say that no relationship exists,
the pattern could have occurred by random chance.
• If the scatter
diagram shows no relationship between the variables, consider whether the data
might be stratified.
• If the diagram
shows no relationship, consider whether the independent (x-axis) variable has
been varied widely. Sometimes a relationship is not apparent because the data
don’t cover a wide enough range.
• Think creatively
about how to use scatter diagrams to discover a root cause.
o Drawing
a scatter diagram is the first step in looking for a relationship between
variables.
7. Stratification
Description
Stratification is a technique used in combination with other data analysis
tools. When data from a variety of sources or categories have been lumped
together, the meaning of the data can be impossible to see. This technique
separates the data so that patterns can be seen.
When to Use Stratification
• Before collecting
data.
• When data come
from several sources or conditions, such as shifts, days of the week, suppliers
or population groups.
• When data
analysis may require separating different sources or conditions.
Stratification Procedure
• Before collecting
data, consider which information about the sources of the data might have an
effect on the results. Set up the data collection so that you collect that
information as well.
• When plotting or
graphing the collected data on a scatter diagram, control chart, histogram or
other analysis tool, use different marks or colours to distinguish data from
various sources. Data that are distinguished in this way are said to be “stratified.”
• Analyze the
subsets of stratified data separately. For example, on a scatter diagram where
data are stratified into data from source 1 and data from source 2, draw
quadrants, count points and determine the critical value only for the data from
source 1, then only for the data from source 2.
Stratification Example
The ZZ-400 manufacturing team drew a scatter diagram to test whether
product purity and iron contamination were related, but the plot did not
demonstrate a relationship. Then a team member realized that the data came from
three different reactors. The team member redr
ew the diagram, using a different symbol for each reactor’s data:
Now patterns can be seen. The data from reactor 2 and reactor 3
are circled. Even without doing any calculations, it is clear that for those two
reactors, purity decreases as iron increases. However, the data from reactor 1,
the solid dots that are not circled, do not show that relationship. Something
is different about reactor 1.
Stratification Considerations
• Here are examples
of different sources that might require data to be stratified:
o
Equipment
o Shifts
o
Departments
o
Materials
o
Suppliers
o Day of
the week
o Time of
day
o Products
• Survey data
usually benefit from stratification.
• Always consider
before collecting data whether stratification might be needed during analysis.
Plan to collect stratification information. After the data are collected it
might be too late.
o On your
graph or chart, include a legend that identifies the marks or colours used.
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