                  =========================
                  Tutorial for 'SPC Tennis'
                  =========================

This is a tutorial to use in conjunction with "SPC Tennis". 
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 'SPC Tennis' now:  

     double click on the icon in the Program Manager or double
     click on TENNIS.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 TUTORIALS: 
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 OK 

     now follow the on-screen instructions 
 
One of the lessons to be learned 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. Whether the charts are drawn 
on paper or by a computerised system, it is very important for the 
process operator to be actively involved.  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
                       ----------------- 
This tutorial will take about 20 minutes.

With 'SPC Tennis' running, do the following: 

     choose 'Open' from the 'File' menu 

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

     (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 OK) 

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 Average 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 Average value - whole number 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 Average value 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 Xbar and Range with subgroups
     of 5 so press OK. 
 
The results will be arranged into subgroups of 5 shots. For each
subgroup, the average will be plotted (Xbar) 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.
     
Next we calculate 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 Add Lines above the Xbar 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 OK 
 
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 
 
     click the More Shots button above the charts

     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 specification or tolerance limits.  In most industrial 
processes, the operator is given specification or tolerance limits as 
well as the target value.  However, these specification 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 specification 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 (click More Shots above the charts)

     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 Xbar 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 and keeps an eye on the charts, then he or she should know 
quickly when a change occurs. 
 
I hope that you are beginning to understand how control charts are 
used and why. 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. We ask the questions:

   "what happened at that point to change the results?".

and

   "how can we stop this from happening again?

If no special causes are present and we are still getting unacceptable 
output, we ask different questions:

   "looking at all the results, is the average off-target?"

and

   "looking at all the results, why is there so much variation?"

To reduce common cause variation we might need better machinery, 
more frequent 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).

In the above exercise we used data from early results of a process to 
predict the limits of variation that can be expected from the process.  
The charts clearly indicate that with file TUT1.VAR, something 
unusual occurs at around shot 200 and things return to normal at 
around shot 250.

In that example, we had a process which was stable in the initial 
stages. The data from this period was used to calculate the control 
lines. In this next exercise we are going to investigate what happens 
if the process is unstable while producing data which will be used to 
calculate control lines. 
 
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 OK 
     (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 OK.) 
 
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 Xbar and Range with subgroups
     of 5 so press OK. 
 
Now calculate the lines.  We have not moved the launcher so we can use 
all results in the calculations. 
 
     press Add Lines above the Xbar chart 
     
     make sure that 1 is in the From box 
     
     make sure that the last subgroup is in the To box  
     
     press OK 
 
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 Average from the Calculate menu

     click the Calculate button 
          
     click on Show 3 x S. Dev. lines on Run Chart 
     
     click the Close & Apply button 
     
     note the warning and click OK
 
Lines at 3 times standard deviation from the average will now be drawn 
on the Run Chart on the main window.  Notice that this chart does NOT 
detect the special variation whereas the xbar chart does detect it 
(by 'detecting' we mean that there are points plotting outside the
control lines). You can spool back the Run Chart to see previous shots 
by clicking the scroll bar to the right of the chart.
 
The reason that the xbar chart detects special variation is because
the control lines are calculated using an estimate of standard 
deviation based on the subgroup range.  When using charts with real 
processes it is important to ensure that subgroups contain mostly 
common cause variation.  Normally this can be done by measuring a 
small number of consecutive products for each subgroup, and 
having a time gap between the subgroups.
    
Sometimes it is not possible to ensure that the subgroups will contain 
mostly common cause variation.  For example, it may not be possible to 
sample consecutive products. In this case, we will have to use a 
Moving Range chart. In this type of chart we plot the individual 
measurements on one graph and the differences between the consecutive 
measurements on the other graph (this is called the Moving Range). 
The distance of the control lines from the average is calculated 
from the average Moving Range.

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 short-term 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.

You have now come to the end of the tutorial.

                        ===============
                        END OF TUTORIAL
                        ===============

WHAT TO DO NEXT 

Return to the default settings:

     choose New in the FILE menu,

     select New File, Default Settings

     click OK. 

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 Taguchi Loss from the 
Calculate menu and press the Explain button).
 
The VPROGx .VAR files
---------------------
As well as the tutorial files, some other variation files have been
provided. Use the files with the name 'VPROG .VAR' to try to detect 
the 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 Xbar 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 Xbar 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 OK 
     
     click on Game Instructions on the menu bar or press F1
 
Good luck! 
 
Histograms and the Normal Distribution
--------------------------------------
SPC Tennis can draw histograms from the database of landing positions.
(choose Histogram from the Charts menu).  If you fire 1000 or more 
shots using the default settings, you will get a histogram which 
shows approximately a normal distribution.  

If you click the 'Colours' button above the histogram chart, it shows 
zones which are between 1, 2 and 3 standard deviations from Average. 

To see explanations of the coloured zones click on the Indices button
above the histogram, accept the default subgroup size of 5, then mouse 
click on 'S Dev' in the Indices box.


Non-conformity and Process Capability
-------------------------------------
When Specification or Tolerance Limits have been set for a product, it
is important to know if our processes are capable of producing 
products which will be consistently within the limits.  Capability 
indices like Cp, Cpk Ppk etc are designed to help us with this.  You 
can use SPC Tennis to learn about these indices.

Click the 'Spec Limits' button to superimpose Specification limit 
lines on the histogram.  Click on the Indices button to display the 
Indices box.

Now use the mouse to click on the titles and indices in the Indices 
box.  This will give you an explanation of how the indices are 
calculated.  Use the mouse to drag the specification limits and see 
how the various indices change.  Try this with both stable processes 
and unstable processes. With a stable process, notice that the 
Estimated Standard Deviation is close to the true Standard Deviation. 
Click the Colours button once to see coloured bands based on true 
standard deviation, then click it again to see coloured bands based 
on estimated standard deviation.

You can create an unstable process by moving the launcher a little 
between each batch of 50 shots fired.


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 'SPC Tennis'.  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

11 January 1996

