2. 6. Graphs & Histograms
Graphs, either presentational or mathematical are
used to allow understanding and analysis of
collected data sets.
Tools for prioritizing and communicating
3. Graphs
BAR CHARTS
• This is the data set totalled up and shown graphically.
• It immediately identifies the major defects for all to
see.
Defects
0
2
4
6
8
10
12
14
16
Power
up
Boot
up
Sink
test
Case
damage
Keyboard
damage
Monitor
damaged
Bundled
s/w
included
Type
Quantity
4. Graphs
• The below graph shows a factory output for
February. This time it shows specific dates which
could be analysed.
0
10
20
30
40
50
60
70
80
90
100
01/02/03
02/02/03
03/02/03
04/02/03
05/02/03
06/02/03
07/02/03
08/02/03
09/02/03
10/02/03
11/02/03
12/02/03
13/02/03
14/02/03
15/02/03
16/02/03
17/02/03
18/02/03
19/02/03
20/02/03
21/02/03
22/02/03
23/02/03
24/02/03
25/02/03
26/02/03
27/02/03
28/02/03
Output %
Average
Feb production output
5. Graphs
• The graph below shows the major cause for
customer complaint, the use of the pie chart and the
colours enforce the message.
Customer complaints 2007
by qty
20
60
5
15
Product quality
Shipped Late
Shipped early
Shipped wrong goods
6. Rules for Graphing
• Use Clear titles an indicate when the data was
collected
• Ensure the scales are clear, understandable
and represent the data accurately.
• When possible use symbols for extra data.
• Always keep in mind the reason why the graph
is being used.
7. Exercise Graphs
• You are the marketing director of XZY automotive, a new
Scottish company. You have organised a local survey to rate
your car against other small cars.
• 30 people were polled and the results are shown below.
• Xzy, ka, Clio, Clio, ka, fiesta, xzy, ka, 206, xzy, fiesta, fiesta, xzy,
polo, fiesta, 206, 206, polo, 206, fiesta, fiesta, fiesta, polo, xzy,
polo, fiesta, xzy, xzy, ka, xzy.
• You recognise the power that graphs produce. And you have
decided to Graph the results as part of you marketing drive.
Explain your choice of graph.
8. What is a Histogram?
• The Histogram is a graphical representation of
data that is a dimensional measurement of
one feature.
9. What is a Histogram?
• This is the computer defect data set totalled up and
shown graphically, but is it a histogram?
Defects
0
2
4
6
8
10
12
14
16
Power
up
Sink
test
Keyboard
damage
Bundled
s/w
included
Type
Quantity
Checks/only record failures Total
Power up 4
Boot up 15
Sink test 5
Case damage 4
Keyboard damage 0
Monitor damaged 3
Bundled s/w included 7
10. What is a Histogram?
• The answer to the previous question is NO
• The Histogram is a graphical representation of
data that, is a dimensional measurement
of one feature.
11. When is a Histogram Used?
• To look at one particular set of results
• To check for patterns in a process
• To examine large amounts of data
12. Histograms
• The following data was collected when measuring the bow
(warp) of a plastic component. The specification is 0 to 8 x10-3
mm.
• At a glance this tells you very little, but it can be plotted as a
histogram because we have quantities data with target limits.
Bow measurements
2 5 8 8 2
4 6 6 6 4
4 7 6 6 4
8 7 7 5 9
14. What is a Histogram?
Exercise
• Sort the following data into appropriate sets,
then plot them.
• The limits are 3 volts ± 0.1
• What can you deduce from this?
16. 7. Pareto Analysis
Arranging data acc to its defects and
causes
80% of defects from 20% of causes –
vital few
Remaining % of defects from various
causes – trivial many/useful many
17. Pareto
What is Pareto Analysis?
• Pareto analysis is a method for prioritising
data.
• It consists of a Bar Chart displayed either in
order of frequency or relative cost.
18. Pareto
Example:
The information to be represented on a Pareto diagram should already
have been collected in some sort of record.
Houshold repairs over the last 10 years
Problem frequency
Cost £ per
occurance
Total cost
£
Light bulb fails 100 0.6 60
Broken central heating
pump 1 190 190
Broken window 2 50 100
Leaking taps 16 2.5 40
Faulty central heating
boiler 1 3000 3000
Leaking radiators 3 15 45
19. Pareto
Pareto Chart
The data are then displayed graphically. Firstly in terms of
frequency.....
House repairs 1998-2008
0
20
40
60
80
100
120
Light
bulb
fails
Leaking
taps
Leakiung
radiators
Broken
window
Broken
central
heating
Faulty
central
heating
Fault
Occurance
frequency
Cum %
20. Pareto
... and then by cost.
House repairs 1998-2008 Total cost £
0
500
1000
1500
2000
2500
3000
3500
Faulty
central
heating
boiler
Broken
central
heating
pump
Broken
window
Light
bulb fails
Leakiung
radiators
Leaking
taps
Total cost £
Editor's Notes
The Histogram is a tool for looking at data in groups rather than representing individual measurements. Units of measurement would be minutes, kilograms, millimetres.
Although histograms show continuous data values, they can also be used in the same way for discreet values i.e. number of defective parts, absenteeism, defectiveness etc. Although, you may often see asymmetrical shapes (skewed distributions). Also look for Bi-model (two peaks) distributions and check stratification.
The purpose of a Histogram is to take the data that is collected from a process and graph it to show how the data is distributed. The histogram will show:
The centre of the data.
The spread of the data.
The skew of the data (slant, bias or run at an angle).
The occurrence of out of range conditions.
The presence of peaks within the data.
The table shows the data sorted and tallied up.
The graph is a Histogram, showing that the components are not all within the limits and they are not centred correctly.
If the symptoms or causes of a defect or some other “effect” are identified and recorded, it will be possible to determine what percentage can be attributed to any cause, and the probable results will be that the bulk (typically 80%) of the errors, waste or “effects”, derive from a few of the causes (typically 20%).
Without an analysis of this sort it is all too easy to devote resources to addressing one symptom only because its cause seems immediately apparent. As someone once said “If the only tool you have is a hammer it is surprising how everything starts looking like a nail.”
It is based on the assumption that a “vital few” sub-problems are the main contributors to an overall problem and that the “trivial many” sub-problems make only a minor contribution.
Pareto Analysis is used to ensure that the” vital few” are tackled first and the “trivial many” are left for future examination.
Check sheets are a logical point to start in most process control or common problem solving efforts. It is particularly useful for recording direct observations and helping to gather in facts rather than opinions about the process.
(The word faulty does not accurately describe the mode of failure and is open to opinion rather than being a fact.)
Looking at this analysis it would appear that the biggest problem faced by the company is oversized spacers since it is the most re-curing problem. This would indicate that this should be the crucial problem in need of solution.
However if we look at the following analysis...
Although oversize spacers is the most re-occurring problem it is useful to look at the method of correcting all these problems. In the case of oversize spacers these items are likely to be thrown away and replaced at minimal cost. All the other faults are likely to involve some sort of rework procedure - some more complicated than others.
If we know look at this analysis it becomes apparent that the cost to correct one poor body coating far outweighs the cost of replacing all oversize spacers. In essence this suggests that poor body coating is the true vital problem which needs to be addressed.