                  ========================
                  Tutorial for 'Variation'
                  ========================

This is a tutorial to use in conjunction with "Variation". 
It has been written assuming that the user has no previous experience
of Control Charts. This tutorial does, however, assume that you are 
familiar enough with the Windows environment to use menus, command 
buttons and dialogue boxes.  There is guidance on using the windows 
environment in the file INSTRUCT.TXT.
 
If you want to read this document on-screen and carry out the
instructions at the same time, make the Notepad or word processor
screen displaying this document wide enough to see whole lines of 
text, and adjust the height of the screen so that it is just enough
to see a few lines of text.  When 'Variation' is running, change the
size and positions of the main windows so that most of this document
remains visible.  If you have a very small screen, it might be easier 
to print this document and work from a paper copy.

To print this document, open it in Windows Write, or another word
processing application, select the entire document and format the
text in 10 point Courier before printing.

Throughout this document, indented texts are step-by-step instructions 
which you should carry out on your computer.  Run 'Variation' now:  

     double click on the icon in the Program Manager or double
     click on VARI.EXE in the File Manager

     read the message on the opening screen then press the
     Enter key or mouse click on the Start button

BEFORE YOU START THE TUTORIAL: 
If you have not already done so, read the first 4 pages of the on-line
instructions carefully.  This will take about 5 minutes. Read pages 
5 - 7 later:  

     select Instructions on the menu bar or press F1.

     Use the Next button or press Alt-n to change pages.

     When you have read page 4, click on the Close button 
     or press Esc. 


NEXT, RUN THE FUNNEL EXPERIMENT: 
This will take about 7 minutes.  In Funnel Experiment mode, the 
scales are changed to have zero in the centre.

     choose 'New' from the 'File' menu 

     click on 'Funnel Experiment Simulation' in the dialogue box 

     press o.k. 

     now follow the on-screen instructions 
 
One of the lessons to be learnt from the funnel experiment is that 
tinkering with a stable system (in our case, moving the launcher) will 
create more variation on the output than just leaving it alone. 
 
Now you are ready to learn how to control a process using statistical 
methods. During the following exercise, if you want explanations of
various section of the programme, you may press the 'Explain' buttons
as they appear in windows or dialogue boxes.  This will slow you down
so you may prefer to leave the explanations until after you have
completed the tutorial.   
 
This programme automatically creates charts and calculates control
lines for these charts from the results of the bouncing ball 'process'.  
The calculations for the control lines involve the use of published 
tables, but they are not complex.  So for real processes, it is not 
difficult to draw these charts on paper. It is very important for the 
process operator to be actively involved with the charts.  He or she 
should plot results without too much delay. Also, notes should be
written on the chart when anything occurs which might affect the 
process (e.g. changes of operators / sources of raw materials / 
machinery maintenance etc.). These notes may be needed later to track 
down the source of a special cause of variation.  
 
 
                       START OF TUTORIAL 
                       ----------------- 

The tutorial will take about 20 minutes.


With 'Variation' running, do the following: 

     choose 'Open' from the 'File' menu 

     Select "TUT1.VAR' in the dialogue box and press o.k. 

     (if there are any previous results visible on the screen, 
     remove them by choosing 'New' from the 'File' menu, click 
     on 'New File, retain settings' then press O.K.) 

Imagine that you are the operator of a machine - the launcher. Your 
job is to fire balls at the target and get them to land as close as 
possible to the ideal value of 500 (we are no longer using centre
zero scales).  First we need to 'centre' the process. We will fire a
number of balls, find the average, then move the launcher. 
       
Fire off 50 shots WITHOUT MOVING THE LAUNCHER 
 
     click on '50' in the 'Shots' frame in the main window 
     
     press 'Start' 
 
When all the balls have been fired, calculate the mean or average 
landing position 
 
     choose Mean from the Calculate menu 
     
     use all the results in the calculations (i.e. accept the 
     default values in the From and To boxes)

     click on Calculate.  

     note the Mean value - integer part only, ignore what comes 
     after the decimal point 

     press Cancel or Close
      
Now move the launcher so that the spread of future shots will centre 
on the 500 mark. 
 
     subtract the Mean value (average) from 500.  You have to do this 
     manually
     
     move the launcher by this amount (click on the Help button in
     the Launcher Position frame if you do not know how to do this) 
 
The process should now be centred (do not worry if you got the
calculations wrong, it is not important for the rest of the exercise). 

Next, we need to find out if the process is "statistically stable".  
Fire off another 100 shots then create a control chart. 
 
     with 50 selected in the Shots frame, press Start twice 
     
     choose Control Charts from the Charts menu      
     
     accept the default chart type of X-bar and Range with subgroups
     of 5 so press O.K. 
 
The results will be arranged into subgroups of 5 shots. For each
subgroup, the average will be plotted (X-bar) along with the largest 
value in the subgroup minus the smallest value (Range).   
 
The point at which the launcher was moved is shown on the chart as a 
vertical line with the letter 'P' above.  This is the equivalent of 
writing a note on a paper chart and is the sort of information an 
operator should record somewhere on the chart.  Use the mouse to click 
on the vertical line to see the note.    

     mouse click on the vertical dotted line on the control chart. Hold
     down the mouse button to read the note
     
Next we calculate the control lines. The purpose of these lines is 
to show when we should suspect that something has changed which 
affects the process (in other words, a special cause of variation has 
occurred).  Of course we know that the launcher has been moved and 
moving the launcher is a special cause of variation, so we should 
calculate the lines with results which come after the launcher move. 
      
     press Calculate Lines above the X-bar chart 
     
     in the From box, enter 51, this shot number was just after 
     the launcher was moved (if you clicked on the note line on 
     the control chart before opening this dialogue box, you can 
     enter the number simply by clicking on the words under the 
     From box) 
     
     make sure that the last subgroup is in the To box (you can do
     this quickly by clicking on the words under the box) 
     
     press O.K. 
 
If all the results after moving the launcher are within the control 
lines, then the process is probably stable or "in statistical control".
This means that all the variation comes from common causes.  Common
cause variation is just the normal random variation which is inherent 
in the process.
 
If some of the results after moving the launcher are outside the lines, 
then this has probably been due to a special cause of variation. The 
process is described as "unstable" and because there is every reason to 
believe that this type of change will happen again, life is going to be 
pretty chaotic.  If we want to be in full control of a process we must 
use the charts to identify when special cause variation occurs, 
determine if things were better before or after the change, then make 
one of these situations permanent. 
 
So let us carry on producing.  Fire off another 100 shots 
 
     return to the main window, but do not close down the control
     chart. Minimise it or leave it in the background

     with 50 selected in the Shots frame, press Start twice 
 
Look at the control chart and do not recalculate the control lines.  
All we need to know now is whether there has been any change in the 
process since the lines were calculated.  Is the output stable?  
 
     bring the control chart to the foreground 

     look to see if any of the points are outside the control 
     lines (ignore the points before the control lines were 
     calculated)
 
It looks as if something unusual happened around shot 200.  Subgroup 
average drops below the control line so a special cause of variation 
has occurred.  As an operator, your job is to produce results as close 
as possible to 500 but the average landing position has suddenly 
changed.  You could, of course re-centre the process (move the 
launcher).  This might help, but you have no idea whether things 
might suddenly change back to normal. The only really satisfactory 
solution is to investigate and find the source of the special cause 
of variation, learn from what happened, and make sure that the change 
does not occur again. 
 
A word now about tolerance limits.  In most industrial processes, the 
operator is given conformance or tolerance limits as well as the target 
value.  However, these tolerance limits should always be looked on as 
representing the MINIMUM acceptable quality from the process.  World 
class quality does not come not from treating everything within the 
tolerance limits as equally acceptable. We must try to produce as close 
as we can to the target value.  This is what the customer really wants.

In our bouncing ball process, an unknown special cause of variation
made the subgroup average fall at around shot 200.  It might be that 
the individual results are still within the specified tolerance limits,
but our customer would prefer the results to be 500. So we must make 
efforts to produce with the average output at 500 and the minimum 
variation that our process is capable of. So we must investigate and 
remove special causes of variation even though we are still producing 
within tolerance limits.

At this point you should be at shot 250.  I can tell you that 
investigations show that that one batch of balls has slightly less 
bounce than normal.  We discard this batch and demand from our supplier 
that they supply us with statistically stable product (they can only be 
sure of doing this by using control charts).

I have removed this special cause of variation so things should return
to normal from shot 251. Fire off another 50 shots to see this. So this
time, there is no need to change the position of the launcher. 

     return to the main window but do not close the control chart
     window

     fire off another 50 shots 
 
The control chart should show clearly that a change occurred around 
shot 200 and things returned to normal around shot 250.  
 
     bring the control chart to the foreground 

     look at the plots on the X-bar chart

In this tutorial, the computer calculates and plots large quantities
of results at once. This means that we might not detect special causes
of variation for some time after they occur.  If an operator plots 
results manually, then he or she might know quickly that a change had 
occurred. 
 
In this case, the process was stable in the initial stages.  The 
control charts clearly indicated that a change had occurred compared 
with the time when the lines were calculated.  What happens if the 
process is unstable while the control lines are being calculated? 
 
Open the file TUT2.VAR.  Now, there will be special causes of 
variation in the early stages. 
 
     choose 'Open' from the 'File' menu in the main window

     Select "TUT2.VAR' in the dialogue box and press o.k. 
     (if there are any results visible at this stage, remove them by 
     choosing 'New' from the 'File' menu, click on 'New File, retain 
     settings'  then press O.K.) 
 
Fire off 100 shots and then create a control chart.  We will not worry 
about centring the process: 
 
     with 50 selected in the Shots frame, press Start twice 
     
     choose Control Charts from the Charts menu      
     
     accept the default chart type of X-bar and Range with subgroups
     of 5 so press O.K. 
 
Now calculate the lines.  We have not moved the launcher so we can use 
all results in the calculations. 
 
     press Calculate Lines above the X-bar chart 
     
     make sure that 1 is in the From box 
     
     make sure that the last subgroup is in the To box  
     
     press O.K. 
 
You should now see that the process is indicating instability even 
though the data used to calculate the lines contains instability.   We 
will need to investigate the special causes of variation and remove 
them to bring the process under control. After that, we can be 
confident that when we centre the process by moving the launcher, the 
position will not need to be changed again (unless, of course, another 
special cause of variation comes along). 
 
This ability of Shewhart control charts to detect special causes of 
variation, even when these special causes of variation are present in 
the data used to calculate the control lines is very important. Most 
commercial processes are not naturally in a state of statistical 
control. 
 
The control lines are set at 3 times sigma from the average. Sigma is 
similar to standard deviation but uses calculations based on the 
spread of results within subgroups.  

It is a mistake to calculate the control lines from individual 
results. See for yourself:  
 
     in the main screen choose Mean from the Calculate menu 
          
     click on Show 3 x S. Dev. lines on Minichart 
     
     click the Close button 
     
     note the warning and click O.K.
 
Lines at 3 times standard deviation from the average will now be drawn 
on the minichart on the main window.  Notice that this chart does NOT 
detect the special variation whereas the x-bar chart does detect it 
(by 'detecting' we mean that there are points plotting outside the
control lines). You can spool back the minichart to see previous shots 
by clicking the scroll bar to the right of the chart.
 
You have now come to the end of the tutorial.

                        ===============
                        END OF TUTORIAL 
                        =============== 
 
I hope that you are beginning to understand how control charts are 
used. By distinguishing between special cause variation and common 
cause variation, control charts can help operators and managers to 
run processes which produce on-target with minimum variation. Note that 
process capability indexes (like Cpk) work on the assumption that the 
future will behave like the past.  This assumption is only valid if a 
process is stable.

If special cause variation is present, we must find the root cause and
stop this from occurring again in the future.  If no special causes are 
present and the average output is on target, then if we are still 
getting unacceptable output, we must take steps to reduce the common 
cause variation.  For example we might need better machinery, more 
maintenance or less common cause variation within raw materials.

The simulation used in this programme is based on an industrial process
where the output is measured on a continuous scale.  There are similar 
techniques using different types of charts for processes where the 
important features are counted (such as the number of flaws or errors).

Distinguishing between common cause variation and special cause 
variation is just as important in non-manufacturing processes. For 
example, if the latest quarter's sales figures in an area are up 
compared with the previous period, we need to know if this is simply 
part of the natural ups and downs inherent in the selling process 
(common cause variation), or due to something unusual which has 
significantly altered the success rate - such as an improved 
advertising campaign or some extra-special effort from a salesperson 
(special cause variation).  

Imagine what happens if we think that the advertising campaign or 
the extra efforts were responsible for the improved figures but,
in fact, they were simply due to the normal common cause variation. We 
will probably declare the campaign a success and adopt it across the 
country, and we might give the salesperson a prize.

Next quarter, we are astonished to find that some areas get reduced 
sales with the new advertising campaign and the 'top' salesperson is
well down the league of achievers.  We do not understand why we did so 
badly and disillusion sets in. In fact we did not do badly, this is 
simply common cause variation at work again.


                                 =======
                                 Summary
                                 =======

Let us go over the main points that you should now understand about 
processes, and the use of this type of control chart:

1. All processes contain variation.

2. World class quality comes from producing with the average on target 
and with the minimum of variation about the target.

3. To achieve the above, we must distinguish between special cause
variation and common cause variation.  We need to know this difference 
because the things we will have to do to remove or reduce the two types 
of variation are very different.

4. The way to distinguish between common cause variation and special 
cause variation is to use a control chart.

5. The calculations for the distance of the control lines from the 
average are based on an average dispersion measurement.

6. We must use our knowledge of the process when deciding how to 
sample results and arrange them into subgroups.  We should do this in
a way which we know will reduce the chances of special cause variation 
occurring within subgroups.  The range of each subgroup is a convenient
dispersion measurement. 

7. If we do not know much about the process and we cannot be confident 
that little special cause variation will be present within subgroups, 
then we should use a Moving Range chart where the dispersion measurement 
is based on the difference between subsequent individual results. 

8. Operators should understand the charts.  They should be involved in 
producing them and plotting the results.

9. Before we can consider a process to be "under control", efforts must 
be made to remove special causes of variation.  We must also learn from 
each incident of special variation and take action to make sure that 
these types of changes do not happen again - this may require close 
co-operation with suppliers (some companies are not capable of this type 
of management - they will always exist in a state of chaos even if they 
have control charts).

10. If the process is statistically stable, any adjustments that we 
make to the process average will create more variation on the output.


                      ===============
                      WHAT TO DO NEXT 
                      ===============

Return to the default settings:

     choose New in the FILE menu,

     select New File, Default Settings

     click O.K.. 

Fire off some shots, then create special causes of variation either 
by moving the launcher or by changing the variation settings (Choose 
Variation from the Control menu). Read all the messages available from 
the Explain buttons as you find them. Create control charts and 
experiment with control lines calculated from different sections of 
the data. Read about 'Taguchi Loss' (Choose Loss from the Calculate 
menu and press the Explain button).
 
The VPROGx .VAR files
---------------------
As well as the tutorial files, 9 other variation files have been
provided. Try to detect the unknown special variation created by these
files.  With this exercise, do not attempt to keep the balls landing 
close to 500.  The only purpose here is to give more experience in 
detecting special cause variation using control charts.

After Variation is running, open one of the files.

     choose OPEN in the FILE menu,

     select one of the VPROG files. 

Do not use the control menu to look at the pre-programmed variation.
Instead, use control charts to try to figure out what is happening 
to the centring and spread of the results.
 
Fire off one or two hundred shots before looking at the results 
(don't change the Launcher position, this will add another 
source of variation). You may want to calculate the control 
lines for the X-bar and Range chart after about 100 shots. Do 
not go beyond 500 shots, there will be no special causes of 
variation after that.

In most cases it should be possible to determine what sort of 
change has taken place by looking at the X-bar and Range charts 
with subgroups of 5; you should also be able to tell 
approximately when the change happened. (Note: It is not 
possible to determine from the charts if the changes were caused 
by the velocity of the ball or the bounce factor).

With some of the programmes, however, it may be difficult or even 
impossible. One of the programmes explores how little change the 
charts will detect (you will have look for 8 consecutive plots on 
one side of the centre line to find a signal with this file). One 
of the files has been deliberately produced to cause variation which 
gives misleading results with subgroup size 5.  (The lesson here is 
that it is vital to subgroup intelligently.  Using your knowledge of 
the process, you must choose a subgroup size where there is little 
chance of special variation being present.)  One of the files will 
cause no special variation at all.  This has been included so that 
you keep an open mind when interpreting the results.

When you think you have determined the special causes of variation, 
look to see if you are right, 

     select Variation from the Control menu in the main window

     look at the Programmed Variation Changes section.  This will 
     show the shot number where special variation occurred, and
     whether it affected the Centring (average) or Spread (range).

Game Mode
---------
When you are happy with the concept of what control charts are trying 
to achieve, try the game.  Read the game instructions carefully before 
you start, perhaps more than once.  It is important that you understand 
the process and all the factors which may influence it before you try to 
play the game.  
 
     choose New from the File menu

     click on New game

     click on O.K. 
     
     click on Game Instructions on the menu bar or press F1
 
Good luck! 
 
FINALLY
-------
I recommend that you read Donald J. Wheeler's book "Understanding 
Statistical Process Control" before applying SPC to real processes.  
See the final page of the on-line instructions in File mode for 
details of the book.

I hope that you enjoy using 'Variation'.  I would be very grateful 
for any feedback from users. 


Steve Horn,
21 Benjamin Drive, Bo'ness, West Lothian EH51 0QS, United Kingdom
CompuServe 100116,3151
Internet steve@horn.demon.co.uk

8 January 1995
