Cream of the Crop 1/Cream of the Crop 1.iso/BUSINESS/SPC11.ARJ/SPCPAPER.PGH

Text File | 1992-01-20 | 61KB | 1,514 lines

@
paper
APPLICATION OF MACHINE LEARNING AND EXPERT SYSTEMS TO STATISTICAL
         PROCESS CONTROL (SPC) CHART INTERPRETATION

                  #mMark Shewhart#m

This paper consists  of the following sections :

        #m(-)#m ABSTRACT
        #m(0)#m INTRODUCTION
        #m(1)#m CONTROL CHARTS
        #m(2)#m SOFTWARE FUNCTIONALITY
        #m(3)#m SOFTWARE DESIGN
        #m(4)#m MACHINE LEARNING
        #m(5)#m EXPERT SYSTEM
        #m(6)#m CONCLUSION
        #mREFERENCES#m
        #mAttachment A#m
        #mAttachment B#m


        Abstract.  Statistical Process Control (SPC) Charts are one
        of several tools used in Quality Control.  Other tools
        include flow charts, histograms, cause-and-effect diagrams,
        check sheets, Pareto diagrams, graphs, and scatter diagrams.
        A control chart is simply a graph which indicates process
        variation over time.  The purpose of drawing a control chart
        is to detect any changes in the process, signalled by
        abnormal points or patterns on the graph.  The Artificial
        Intelligence Support Center (AISC) of the Acquisition
        Logistics Division (ALD/JTI) has developed a hybrid machine-
        learning/expert-system prototype which automates the process
        of constructing and interpreting control charts.


INTRODUCTION

The Air Force Logistics Command (AFLC) has provided TQM and Quality
Control training to its employees for several years now.  In
particular, Statistical Process Control has been emphasized in this
effort.  While many data collection efforts have been undertaken
within AFLC, the SPC Quality Control tool has been under-utilized
due to the lack of experienced personnel to identify and interpret
patterns within the control charts.  The AISC has developed a
prototype software tool which draws control charts, identifies
various chart patterns, advises what each pattern means, and
suggests possible corrective actions.  The application is easily
modifiable for process specific applications through simple
modifications to the knowledge base portion using any word
processing software.

The remainder of this paper consists  of the following sections :

        #m(1)#m CONTROL CHARTS
        #m(2)#m SOFTWARE FUNCTIONALITY
        #m(3)#m SOFTWARE DESIGN
        #m(4)#m MACHINE LEARNING
        #m(5)#m EXPERT SYSTEM
        #m(6)#m CONCLUSION
        #mREFERENCES#m
        #mAttachment A#m
        #mAttachment B#m

Section (1) provides a more in-depth explanation of the purpose of
control charts.  Section (2) details the initial functional
requirements for the SPC software, and section (3) outlines the
design approach used to implement the system requirements.
Sections (4) and (5) examine in detail the roles of machine
learning and expert system techniques respectively.  Finally,
section (6) offers some basic conclusions resulting from this
effort.   Two attachments are included after the references.
ATTACHMENT A provides a list of the chart patterns of interest and
their methods of identification.  ATTACHMENT B enumerates and
explains the twenty statistical features used by the machine
learning tool.

CONTROL CHARTS

An example of a control chart is given below in FIGURE 1.  A run
chart is a plot of a process measurement (e.g. bore diameter or
time to process an insurance claim for example) on the vertical
axis (y-axis) against time on the horizontal axis (x-axis).  A
control chart is simply a run chart with statistically determined
upper (Upper Control Limit - UCL) and lower (Lower Control Limit -
 LCL) lines drawn on either side of the process average.  These
limits are calculated by running a process untouched, taking
samples of the process measurement, and applying the appropriate
statistical formulas (references [3-9]).

The random fluctuation of points within the limits results from
variation built into the process.  Such random variation is
natural, results from common causes within the system (e.g. design,
choice of machine, preventative maintenance, etc.), and can only
be affected by changing the system itself.  However, points which
fall outside of the control limits or which form "unnatural"
patterns indicate that some of the variation within the process may
be due assignable causes.  Assignable causes of variation (e.g.
measurement errors, unplanned events, freak occurrences, etc.) can
be identified and result from occurrences that are not part of the
process.

The purpose of drawing the control chart is to detect any unusual
causes of variation in the process, signalled by abnormal points
or patterns on the graph.  The AISC developed software tool
automatically identifies nine types of patterns which indicate the
presence of assignable causes of variation in a process.  Examples
of these patterns are given in FIGURES 2 - 10.  Each such pattern
is associated with generic advice about what may be happening at
that point in the process.  More detailed information about each
of the nine patterns is given in ATTACHMENT A.


SOFTWARE FUNCTIONALITY

An overview of the functionality of the application (referred to
as SPC) is given below :

        (1) SPC determines which type of control chart is
        appropriate by asking a series of questions about the nature
        of the user's process data.  The appropriate control chart
        is selected from the following types of charts (See
        References [3,4,5,6]) :

                  (a) X-Bar R Chart
                  (b) p Chart
                  (c) pn Chart
                  (d) u Chart
                  (e) c Chart

        (2) SPC graphically displays the chart(s) selected in (1).

        (3) SPC identifies the following patterns in the chart(s)
        which indicate the presence of assignable causes of
        variation :

                  (a) increasing trends
                  (b) decreasing trends
                  (c) shifts up
                  (d) shifts down
                  (e) cycles
                  (f) runs
                  (g) stratification
                  (h) freak patterns
                  (i) freak points

        (4) SPC graphically displays and highlights each chart
        pattern  identified in (3).

        (5) SPC displays text in a window-like fashion which
        provides generic advice on the meaning of each chart pattern
        identified in (3).


SOFTWARE DESIGN

The basic approach to developing SPC was to integrate machine
learning, expert systems, and conventional programming techniques.
The machine learning portion of SPC was developed using the
Abductory Induction Mechanism (AIM) by AbTECH Inc.  The expert
system portion of SPC was developed using an embedded application
of the forward chaining expert system tool CLIPS along with a
generic end-user interface also developed by the AISC.  Turbo C++
was used as the conventional language into which the machine
learning and expert system applications were embedded.

The task for the machine learning portion of SPC is to classify
every sub-sequence of the control chart according to the presence
or absence of five specific chart patterns : increasing trends,
decreasing trends, shifts up, shifts down, and cycles.  The
remaining four chart patterns are identified by conventional
methods.

The expert system is initially utilized to help the user select the
appropriate type of control chart.  This determination is based
upon the type of data being collected and the constancy of the
sample sizes.

Another function of the expert system is to interpret the
classification results of the trained AIM Network.  A control chart
with 40 data points will generate over 600 classification results;
with nine types of patterns this amounts to over 5500 individual
pieces of classification information.  This interpretation function
represents an ideal expert system application.  What requires a few
hundred lines of difficult-to-comprehend C code can be implemented
using an expert system with only three simple rules (TABLE 9)!
This classification information is boiled down to about one to ten
patterns which are reported to the final expert system application.

The final role of the expert system is to provide advice based upon
the types of charts and the chart patterns present.  The advice
currently provided by SPC is of a generic nature.  For example,

        "A shift up in the R chart indicates that the process is
        becoming less consistent.  This may be due to some sudden
        change in the process."

However, the knowledge base is designed to allow for quick
modifications to provide process specific advice.  For example,

        "A shift up in the R chart has historically been associated
        (90%) with a loose bearing in the preprocessing machine."


Conventional software is used to graphically display the control
charts, utilize the AIM Networks, provide an end-user interface,
and integrate the entire application.


MACHINE LEARNING

Role Of Machine Learning

The task of chart interpretation can be summarized as follows.  A
control chart is simply a sequence or array of floating point
numbers.  The art of chart interpretation is to determine whether
or not sub-sequences similar to several standard patterns are
present within the chart.  These patterns include trends, shifts,
and cycles.

The function of the machine learning tool is to generate code
(trained AIM Networks) which can effectively classify a specific
sub-sequence of a control chart (array) according to the presence
or absence of several standard patterns.  With this classification
function generated by machine learning techniques, all sub-
sequences of the control chart are exhaustively (conventionally)
classified by five AIM Networks.  The AIM Network classification
results are asserted into the fact-list of the CLIPS expert system
application.

Justification For The Use Of Machine Learning Techniques

Machine learning techniques are used to classify five types of
chart patterns - increasing trends, decreasing trends, shifts up,
shifts down, and cycles.  We could find no references which provide
an algorithm for determining whether or not a sequence of real
numbers is representative of one of these patterns.  In fact, most
references on control charts define these patterns by example!  The
most mathematical approaches to this problem are found in
references [1,2] on time series analysis and forecasting.  Despite
being mathematical in nature, these references still do not
describe a deterministic decision procedure.  Rather, they provide
mathematical heuristics.  A sampling of these rules-of-thumb for
a times series of length N are given below :

        (1) The number of increasing steps in an increasing trend
        may be significantly larger than (N-1)/2.

        (2) The number of discordances in a decreasing trend is
        usually larger than the expected number of discordances in
        a random sequence which is N*(N-1)/4.

        (3) The autocorrelation coefficient sequence of a cycle is
        usually cyclic.

        (4) The average of the first half of a shift down is always
        greater than the average of the second half.

Notice that most of these heuristics are in the form of rules with
confidence factors.  This would seem to suggest the possibility of
using a production system for the classification procedure.
However, it is almost always the case that the pattern-type (the
attribute for which we wish to determine a value) is on the left-
hand side of the rule.

This is very similar to some medical diagnosis problems whose
domain knowledge is in the form "Disorder A usually causes symptoms
1, 3, & 4 and may cause symptom 2."  In cases such as these, the
best knowledge-based approach is to use some form of a Hypothesize-
and-Test (HT) model.  Although the HT approach appears to model the
domain very well, we did not pursue this option for the following
reasons :

        (1) We do not have a Hypothesize-and-Test knowledge-based
        development tool available for use.

        (2) To my knowledge, there are no HT systems which can be
        embedded into an application in a manner similar to CLIPS.

        (3) The HT knowledge-based system approach involves the
        solution of a minimal covering problem.  This would
        probability cause the classification process to be
        unacceptably slow.

Attempting to implement such applications using a rule-based system
with confidence factors ultimately boils down to an iterative
process of re-adjusting confidence factors and re-testing the rule
base on a set of examples.  This iterative process, however, is
quite analogous to the process of training a neural network or a
machine learning tool on a set of examples.  Given this analysis
and the fact that most references on control charts define these
patterns by example, we elected to implement a portion of the
classification process using a machine learning tool.

Representation Of Control Chart Sub-sequence

The function of the machine learning tool is to classify a specific
sub-sequence of a control chart according to the presence or
absence of several standard patterns.  A key question relating to
the use of machine learning tools, is how do we represent an
arbitrary length sub-sequence of an arbitrary length sequence of
numbers as a fixed length vector of real numbers.  The approach is
to represent a sub-sequence of a control chart as a fixed length
vector of statistical features.

Twenty (20) statistical features are extracted from each sub-
sequence X[1..N] under consideration.  Features 1 - 10 are raw
statistical features while features 11 - 20 are Boolean type
indicator variables.  The features and their definitions are listed
in ATTACHMENT B.


Training And Test Sets For Machine Learning Tool

Over 70,000 sample chart sub-sequences were generated to train and
test the AIM Networks.  Most of these sub-sequences were generated
by adding random noise to existing control charts with existing
patterns.  Each chart sub-sequence generated a training/test vector
of dimension 25  -  20 real-valued Network inputs (statistical
features) and 5 bi-polar (-1 or 1) outputs.  One AIM Network was
trained for each of the 5 outputs.  Each AIM Network required from
two to six hours to train on a 386 machine with math co-processor.



EXPERT SYSTEM

Role Of Expert System

The role of the expert system in SPC is three-fold.  One knowledge
base helps the user select the type of control chart to be used,
another interprets the AIM Networks' classification results, and
the third knowledge base provides expert advice on the meaning of
any identified patterns.

Selecting Appropriate Control Chart Type

The knowledge base for this portion of the expert system
application in SPC is given below in TABLE 7. In short, the type
of control chart is selected based upon (1) whether the data is
attribute data or measurement data, (2) whether the logical group
size is constant or variable, and (3) whether the (attribute) data
is measuring defectives or defects.

(defrule data_type
   (initial-fact)
=>
   (ask_question "question.idx" "get_type" "data_type") )*

(defrule XBAR_R_Chart
   (data_type value)
=>
   (assert (chart_type XBAR_R)) )

(defrule group_size
   (data_type attribute)
=>
   (ask_question "question.idx" "get_size" "group_size")*
   (ask_question "question.idx" "get_att_type" "attribute") )*

(defrule PN_Chart
   (group_size constant)
   (attribute defectives)
=>
   (assert (chart_type PN_Chart)) )

(defrule C_Chart
   (group_size constant)
   (attribute defects)
=>
   (assert (chart_type C_Chart)) )

(defrule P_Chart
   (group_size variable)
   (attribute defectives)
=>
   (assert (chart_type P_Chart)) )

(defrule _Chart
   (group_size variable)
   (attribute defects)
=>
   (assert (chart_type U_Chart)) )

*The function ask_question is provided by the CLIPS Application
User Interface (AUI) also developed by the AISC at Wright-
Patterson AFB, Ohio.


Interpreting AIM Network Classification Results

A major issue during the development of SPC was how to interpret
the AIM Networks' classification results.  An example of a portion
of the results of the AIM Networks' classification during the
exhaustive conventional search is given in TABLE 6. The
classification results of the AIM Networks are asserted into the
CLIPS fact-list in the format :

        (chart-type pattern-type begin-index end-index network-
score).


( X cycle 1 13 0.743 )
( X inc_trend 5 17 0.098 )
( X shift_up 6 18 0.282 )
( X inc_trend 6 17 0.819 )
( X inc_trend 6 16 1.000 )
( X inc_trend 7 17 0.829 )
( X inc_trend 6 15 1.000 )
( X inc_trend 7 16 0.874 )
( X inc_trend 6 14 0.991 )
( X inc_trend 7 15 1.000 )
( X inc_trend 6 13 0.951 )
( X inc_trend 7 14 1.000 )
( X inc_trend 8 15 0.973 )
( X inc_trend 6 12 0.807 )
( X inc_trend 7 13 0.997 )
( X inc_trend 8 14 0.961 )
( X inc_trend 9 15 0.841 )
( X inc_trend 7 12 0.904 )
( X inc_trend 10 15 0.917 )
( X inc_trend 10 14 0.895 )


Notice in TABLE 6 that from points 6 to 17 there are 17 sub-
sequences which the AIM increasing trend Network gave high scores
to!  Clearly we cannot report to the user all 17 patterns.  The
expert system application which interprets the AIM Networks'
classification results is composed of three rules :

        (1) The first rule eliminates from consideration any pattern
        whose AIM Network score is below a certain threshold.  The
        sensitivity of the pattern recognition can be adjusted by
        altering these thresholds in the deffacts statement.

        (2) The second rule eliminates from consideration any
        pattern which is contained entirely within another existing
        pattern of the same type.  It is assumed that the first
        rule has previously been applied.  For example, the fact (X
        inc_trend 8 14 0.961) would be retracted due to the presence
        of the fact (X inc_trend 6 16 1.0).

        (3) The third rule eliminates from consideration any pattern
        which overlaps another existing pattern of the same type but
        with a higher AIM Network score.  It is assumed that the
        first two rules have previously been applied.  For example,
        this rule would retract the fact  (X inc_trend 8 14 0.961)
        due to the presence of the fact  (X inc_trend 7 13 0.997).

(deffacts thresholds
   (threshold run 0.99)
   (threshold inc_trend 0.95)
   (threshold dec_trend 0.95)
   (threshold shift_up 0.95)
   (threshold shift_down 0.95)
   (threshold stratification 0.99)
   (threshold freak_point 0.99)
   (threshold freak_pattern 0.99)
   (threshold cycle 0.95) )


(defrule simple_threshold
   (resolve thresholds)
   ?pattern <- (?chart ?type ?a ?b ?score)
   (threshold ?type ?thresh)
   (test (< ?score ?thresh))
=>
   (retract ?pattern) )


(defrule subset
   (resolve subsets)
   (?chart ?type ?a1 ?b1 ?score1)
   ?subset_pattern <- (?chart ?type ?a2 ?b2 ?score2)
   (test (not (and (= ?a1 ?a2) (= ?b1 ?b2))))
   (test (and (<= ?a1 ?a2) (<= ?b2 ?b1) ))
=>
   (retract ?subset_pattern) )


(defrule overlap
   (resolve overlap)
   (?chart ?type ?a1 ?b1 ?score1)
   ?pattern2 <- (?chart ?type ?a2 ?b2 ?score2)
   (test (not (and (= ?a1 ?a2) (= ?b1 ?b2))))
   (test (>= ?score1 ?score2))
   (test (or (and (<= ?a1 ?a2 ?b1) (< ?b1 ?b2) )
             (and (<= ?a2 ?a1 ?b2) (< ?b2 ?b1) ) ))
=>
   (retract ?pattern2) )


Expert Advice On Meaning Of Chart Patterns

The majority of the expert system interaction that the user will
see involves explanations and advice regarding any patterns that
the AIM Networks have identified as indicators of assignable causes
of variation.  At the most basic level, this expert knowledge
simply consists of triples of the form <chart-type, pattern-type,
advice-text>.  The current AISC SPC software consists of knowledge
at this level of complexity only.  A sample of the CLIPS
implementation of such knowledge is illustrated in TABLE 8.

However, the rule-based representation is justified for the
following reasons :

   (1) The interpretation of control charts with multiple patterns
   is more complex than simple chart-pattern-advice triples.  The
   representation scheme must be powerful enough to accommodate
   future enhancements to the system.

   (2) One requirement for the SPC software is that it be easily
   modifiable to process specific applications.  Without knowing
   what type of reasoning process might be required for such
   customized applications, we selected the more flexible
   representation scheme provided by a production system.


(defrule R_shift_up
   (R shift_up ?a ?b ?score)
=>
   (write_paragraph "advice.idx" "R_shift_up") )*

*The function write_paragraph is provided by the CLIPS Application
User Interface (AUI) also developed by the AISC at Wright-Patterson
AFB, Ohio.



CONCLUSION

SPC is a good example of a hybrid system which integrates machine
learning, expert system, and conventional programming techniques.
It is a classic example of pattern recognition and is an excellent
demonstration of problem representation techniques necessary when
using machine learning or neural network tools.



Two features distinguish SPC from most other control chart software
:

        (1) SPC automatically identifies and highlights unusual
        chart patterns.  Most related commercial software simply
        draws the chart and explains to the user what unusual
        patterns to look for.  We found no commercial software which
        automatically identified trends, shifts, or cycles.

        (2) SPC provides expert advice on the meaning of all
        identified unusual chart patterns.  Over 50% of available
        commercial software only construct the control chart for the
        user and go no further.

The first version of SPC is scheduled to be available by September
1991 and will be distributed with an AFLC sponsored course on
Statistical Process Control.  The AISC plans to provide software
enhancements to SPC based upon future customer feedback and demand.
Also, the AISC hopes to provide some customers with customized
versions of SPC for process specific applications.  Copies of SPC
and reprints of this paper are available to government agencies
upon request.


REFERENCES

[1] Spyros Makridakis and Stephen C. Wheelwright, "Forecasting:
Methods and Applications",Wiley/Hamilton, 1978.

[2] Sir Maurice Kendall and J Keith Ord, "Time Series", Oxford
University Press, 1990.

[3] SPC Course Materials, Decision Dynamics Inc., 1990

[4] Kaoru Ishikawa, "Guide to Quality Control", Asian Productivity
Organization, 1982.

[5] Perry Johnson Inc., "SPC Chart Interpretation", Perry Johnson,
Inc., 1987.

[6] J.M. Juran, Dr. Frank M. Gryna, Jr., and R.S. Bingham, Jr.,
"Quality Control Handbook",Third Edition, McGraw-Hill, 1974.

[7] Western Electric Company, "Statistical Quality Control
Handbook", Western Ellectric Co., Inc., 1958.

[8] H. Besterfield, "Quality Control", Second Edition, Prentice-
Hall.

[9] Douglas C. Montogomery, "Introduction to Statistical Quality
Control".




ATTACHMENT A

Patterns To Be Identified And Methods Of Identification

(1) Freak Point  -  This is any point which falls outside of the
three sigma control limits.  This is conventionally identified.

(2) Freak Pattern  -  This is any sequence of points for which a
large percentage fall more than a given amount away from the mean.
This definition is vague since many experts and source materials
disagree on what conditions to use.  This is conventionally
identified.  The following criteria are used to identify a freak
pattern:

   (a) Two out of three points in a row outside of the 2 sigma
   limits.  Reference [3].
   (b) Four out of five points in a row outside of the 1 sigma
   limits.  Reference [3].

(3) Stratification  -  Sometimes referred to as "hugging the center
line."  This is any sequence of points for which a large percentage
fall less than a given amount away from the mean.  This definition
is vague since many experts and source materials disagree on what
conditions to use.  This is conventionally identified.  The
following criteria are used to identify a stratification pattern:

   (a) Ten or more points in a row which are within the 1 sigma
   limits.

(4) Runs -  This is any sequence of points for which a large
percentage fall on the same side of the mean.  This definition is
vague since many experts and source materials disagree on what
conditions to use.  This is conventionally identified.  The
following criteria are used to identify a freak pattern:

   (a) More than 5 (some say 7 and others say 8) points in a row on
   the same side of the mean.

   (b) Ten of 12 on the same side of the mean.


(5) Increasing Trends  -  This pattern is identified with C code
generated by the machine learning tool AIM.  *Current accuracy is
97.5% based upon a test set of 2662 patterns.

(6) Decreasing Trends  -  This pattern is identified with C code
generated by the machine learning tool AIM.  *Current accuracy is
97.3% based upon a test set of 2663 patterns.

(7) Shifts Up  -  This pattern is identified with C code generated
by the machine learning tool AIM.  *Current accuracy is 98.8% based
upon a test set of 1990 patterns.

(8) Shifts Down  -  This pattern is identified with C code
generated by the machine learning tool AIM.  *Current accuracy is
98.8% based upon a test set of 1990 patterns.

(9) Cycles  -  This pattern is identified with C code generated by
the machine learning tool AIM.  *Current accuracy is 92.0% based
upon a test set of 22492 patterns.



* For further details, see Machine Learning Results.




ATTACHMENT B

Statistical Features Used To Represent Chart Subsequences

   (1) RMS_SU  -  This is the root-mean-squared difference between
   X[1..N] and an "ideal" shift-up pattern.

   (2) RMS_SD  -  This is the root-mean-squared difference between
   X[1..N] and an "ideal" shift-down pattern.

   (3) A  -  This is the simple linear regression coefficient when
   trying to approximate the time series X[t] using X[t] = A + Bt.

   (4) B  -  This is the simple linear regression coefficient when
   trying to approximate the time series X[t] using X[t] = A + Bt.

   (5) SIGMA_1  -  This is the standard deviation of the first half
   X[1..N/2] of the sequence X[1..N].

   (6) SIGMA_2  -  This is the standard deviation of the second half
   X[N/2+1..N] of the sequence X[1..N].

   (7) R_root_N_r  -  The percentage of the first N/4+1
   autocorrelation coefficients r(k) for which abs(r(k)) >
   1.96/sqrt(N).

   (8) CHI_SQ_TEST  -  This is the Box-Pierce Q-statistic which is
   capable of determining whether several autocorrelation
   coefficients are significantly different from zero.  This is
   defined in reference [1,p 269]

   (9) CONCORD  -  This is the number of concordances Q in X[1..N]
   divided by the maximum possible number N(N-1)/2 of concordances.
   This is defined in reference [2,pp 21-23].

   (10) DISCORD  -  This is the number of discordances P in X[1..N]
   divided by the maximum possible number N(N-1)/2 of discordances.
   This is defined in reference [2,pp 21-23].


   (11) TEN_PLUS  -  An indicator variable used to indicate if
   X[1..N] has length less than ten.  This is important since many
   statistical significance tests are ineffective for small sample
   sizes.

   (12) CCRD_LOW  -  An indicator variable used to indicate whether
   CONCORD is less than 0.7.  The value of 0.7 was chosen since a
   database analysis indicated that a high percentage of increasing
   trends had CONCORD > 0.7.

   (13) DCRD_LOW  -  An indicator variable used to indicate whether
   DISCORD is less than 0.7.  The value of 0.7 was chosen since a
   database analysis indicated that a high percentage of decreasing
   trends had DISCORD > 0.7.

   (14) HIGH_ISD  -  An indicator variable used to indicate whether
   RMS_SD is greater than 1.8.  The value of 1.8 was chosen since
   a database analysis indicated that a high percentage of shifts-
   up had RMS_SD > 1.8.

   (15) HIGH_ISU  -  An indicator variable used to indicate whether
   RMS_SU is greater than 1.8.  The value of 1.8 was chosen since
   a database analysis indicated that a high percentage of shifts-
   down had RMS_SU > 1.8.

   (16) GOOD_INC_MM  -  An indicator variable used to indicate when
   the sequence minimum was early and the sequence maximum was late.
   The first 20% and last 20% was chosen since a database analysis
   indicated that a high percentage of increasing trends had their
   minimum and maximum within the first 20% and last 20%
   respectively of the sequence.

   (17) GOOD_DEC_MM  -  An indicator variable used to indicate when
   the sequence maximum was early and the sequence minimum was late.
   The first 20% and last 20% was chosen since a database analysis
   indicated that a high percentage of decreasing trends had their
   maximum and minimum within the first 20% and last 20%
   respectively of the sequence.

   (18) HIGH_R_root_N  -  An indicator variable used to indicate
   whether R_root_N_r is greater than 0.1.  The object of
   introducing this variable was to help draw a distinction between
   random sequences and cycles.  The value of 0.1 was chosen since
   a database analysis indicated that a high percentage of cycles
   and a low percentage of random sequences had R_root_N_r > 0.1.

   (19) SMALL_A  -  An indicator variable used to indicate whether
   the absolute value of A is less than 0.8.  The object of
   introducing this variable was to help draw a distinction between
   random sequences or cycles and the other chart patterns.  The
   value of 0.8 was chosen since a database analysis indicated that
   a high percentage of cycles and random sequences and a low
   percentage of other types of patterns had abs(A) < 0.8.

   (20)  MAYBE_CYCLE  -  An indicator variable used to indicate when
   both R_root_N_r > 0.1 and ABS(A) < 0.8.  This is the logical AND
   of variables 18 and 19.
@
(1)
CONTROL CHARTS

An example of a control chart is given below in FIGURE 1.  A run
chart is a plot of a process measurement (e.g. bore diameter or
time to process an insurance claim for example) on the vertical
axis (y-axis) against time on the horizontal axis (x-axis).  A
control chart is simply a run chart with statistically determined
upper (Upper Control Limit - UCL) and lower (Lower Control Limit -
 LCL) lines drawn on either side of the process average.  These
limits are calculated by running a process untouched, taking
samples of the process measurement, and applying the appropriate
statistical formulas (references [3-9]).

The random fluctuation of points within the limits results from
variation built into the process.  Such random variation is
natural, results from common causes within the system (e.g. design,
choice of machine, preventative maintenance, etc.), and can only
be affected by changing the system itself.  However, points which
fall outside of the control limits or which form "unnatural"
patterns indicate that some of the variation within the process may
be due assignable causes.  Assignable causes of variation (e.g.
measurement errors, unplanned events, freak occurrences, etc.) can
be identified and result from occurrences that are not part of the
process.

The purpose of drawing the control chart is to detect any unusual
causes of variation in the process, signalled by abnormal points
or patterns on the graph.  The AISC developed software tool
automatically identifies nine types of patterns which indicate the
presence of assignable causes of variation in a process.  Examples
of these patterns are given in FIGURES 2 - 10.  Each such pattern
is associated with generic advice about what may be happening at
that point in the process.  More detailed information about each
of the nine patterns is given in ATTACHMENT A.
@
(2)
SOFTWARE FUNCTIONALITY

An overview of the functionality of the application (referred to
as SPC) is given below :

        (1) SPC determines which type of control chart is
        appropriate by asking a series of questions about the nature
        of the user's process data.  The appropriate control chart
        is selected from the following types of charts (See
        References [3,4,5,6]) :

                  (a) X-Bar R Chart
                  (b) p Chart
                  (c) pn Chart
                  (d) u Chart
                  (e) c Chart

        (2) SPC graphically displays the chart(s) selected in (1).

        (3) SPC identifies the following patterns in the chart(s)
        which indicate the presence of assignable causes of
        variation :

                  (a) increasing trends
                  (b) decreasing trends
                  (c) shifts up
                  (d) shifts down
                  (e) cycles
                  (f) runs
                  (g) stratification
                  (h) freak patterns
                  (i) freak points

        (4) SPC graphically displays and highlights each chart
        pattern  identified in (3).

        (5) SPC displays text in a window-like fashion which
        provides generic advice on the meaning of each chart pattern
        identified in (3).


@
(3)
SOFTWARE DESIGN

The basic approach to developing SPC was to integrate machine
learning, expert systems, and conventional programming techniques.
The machine learning portion of SPC was developed using the
Abductory Induction Mechanism (AIM) by AbTECH Inc.  The expert
system portion of SPC was developed using an embedded application
of the forward chaining expert system tool CLIPS along with a
generic end-user interface also developed by the AISC.  Turbo C++
was used as the conventional language into which the machine
learning and expert system applications were embedded.

The task for the machine learning portion of SPC is to classify
every sub-sequence of the control chart according to the presence
or absence of five specific chart patterns : increasing trends,
decreasing trends, shifts up, shifts down, and cycles.  The
remaining four chart patterns are identified by conventional
methods.

The expert system is initially utilized to help the user select the
appropriate type of control chart.  This determination is based
upon the type of data being collected and the constancy of the
sample sizes.

Another function of the expert system is to interpret the
classification results of the trained AIM Network.  A control chart
with 40 data points will generate over 600 classification results;
with nine types of patterns this amounts to over 5500 individual
pieces of classification information.  This interpretation function
represents an ideal expert system application.  What requires a few
hundred lines of difficult-to-comprehend C code can be implemented
using an expert system with only three simple rules (TABLE 9)!
This classification information is boiled down to about one to ten
patterns which are reported to the final expert system application.

The final role of the expert system is to provide advice based upon
the types of charts and the chart patterns present.  The advice
currently provided by SPC is of a generic nature.  For example,

        "A shift up in the R chart indicates that the process is
        becoming less consistent.  This may be due to some sudden
        change in the process."

However, the knowledge base is designed to allow for quick
modifications to provide process specific advice.  For example,

        "A shift up in the R chart has historically been associated
        (90%) with a loose bearing in the preprocessing machine."


Conventional software is used to graphically display the control
charts, utilize the AIM Networks, provide an end-user interface,
and integrate the entire application.


@
(4)
MACHINE LEARNING

Role Of Machine Learning

The task of chart interpretation can be summarized as follows.  A
control chart is simply a sequence or array of floating point
numbers.  The art of chart interpretation is to determine whether
or not sub-sequences similar to several standard patterns are
present within the chart.  These patterns include trends, shifts,
and cycles.

The function of the machine learning tool is to generate code
(trained AIM Networks) which can effectively classify a specific
sub-sequence of a control chart (array) according to the presence
or absence of several standard patterns.  With this classification
function generated by machine learning techniques, all sub-
sequences of the control chart are exhaustively (conventionally)
classified by five AIM Networks.  The AIM Network classification
results are asserted into the fact-list of the CLIPS expert system
application.

Justification For The Use Of Machine Learning Techniques

Machine learning techniques are used to classify five types of
chart patterns - increasing trends, decreasing trends, shifts up,
shifts down, and cycles.  We could find no references which provide
an algorithm for determining whether or not a sequence of real
numbers is representative of one of these patterns.  In fact, most
references on control charts define these patterns by example!  The
most mathematical approaches to this problem are found in
references [1,2] on time series analysis and forecasting.  Despite
being mathematical in nature, these references still do not
describe a deterministic decision procedure.  Rather, they provide
mathematical heuristics.  A sampling of these rules-of-thumb for
a times series of length N are given below :

        (1) The number of increasing steps in an increasing trend
        may be significantly larger than (N-1)/2.

        (2) The number of discordances in a decreasing trend is
        usually larger than the expected number of discordances in
        a random sequence which is N*(N-1)/4.

        (3) The autocorrelation coefficient sequence of a cycle is
        usually cyclic.

        (4) The average of the first half of a shift down is always
        greater than the average of the second half.

Notice that most of these heuristics are in the form of rules with
confidence factors.  This would seem to suggest the possibility of
using a production system for the classification procedure.
However, it is almost always the case that the pattern-type (the
attribute for which we wish to determine a value) is on the left-
hand side of the rule.

This is very similar to some medical diagnosis problems whose
domain knowledge is in the form "Disorder A usually causes symptoms
1, 3, & 4 and may cause symptom 2."  In cases such as these, the
best knowledge-based approach is to use some form of a Hypothesize-
and-Test (HT) model.  Although the HT approach appears to model the
domain very well, we did not pursue this option for the following
reasons :

        (1) We do not have a Hypothesize-and-Test knowledge-based
        development tool available for use.

        (2) To my knowledge, there are no HT systems which can be
        embedded into an application in a manner similar to CLIPS.

        (3) The HT knowledge-based system approach involves the
        solution of a minimal covering problem.  This would
        probability cause the classification process to be
        unacceptably slow.

Attempting to implement such applications using a rule-based system
with confidence factors ultimately boils down to an iterative
process of re-adjusting confidence factors and re-testing the rule
base on a set of examples.  This iterative process, however, is
quite analogous to the process of training a neural network or a
machine learning tool on a set of examples.  Given this analysis
and the fact that most references on control charts define these
patterns by example, we elected to implement a portion of the
classification process using a machine learning tool.

Representation Of Control Chart Sub-sequence

The function of the machine learning tool is to classify a specific
sub-sequence of a control chart according to the presence or
absence of several standard patterns.  A key question relating to
the use of machine learning tools, is how do we represent an
arbitrary length sub-sequence of an arbitrary length sequence of
numbers as a fixed length vector of real numbers.  The approach is
to represent a sub-sequence of a control chart as a fixed length
vector of statistical features.

Twenty (20) statistical features are extracted from each sub-
sequence X[1..N] under consideration.  Features 1 - 10 are raw
statistical features while features 11 - 20 are Boolean type
indicator variables.  The features and their definitions are listed
in ATTACHMENT B.


Training And Test Sets For Machine Learning Tool

Over 70,000 sample chart sub-sequences were generated to train and
test the AIM Networks.  Most of these sub-sequences were generated
by adding random noise to existing control charts with existing
patterns.  Each chart sub-sequence generated a training/test vector
of dimension 25  -  20 real-valued Network inputs (statistical
features) and 5 bi-polar (-1 or 1) outputs.  One AIM Network was
trained for each of the 5 outputs.  Each AIM Network required from
two to six hours to train on a 386 machine with math co-processor.

@
(5)
EXPERT SYSTEM

Role Of Expert System

The role of the expert system in SPC is three-fold.  One knowledge
base helps the user select the type of control chart to be used,
another interprets the AIM Networks' classification results, and
the third knowledge base provides expert advice on the meaning of
any identified patterns.

Selecting Appropriate Control Chart Type

The knowledge base for this portion of the expert system
application in SPC is given below in TABLE 7. In short, the type
of control chart is selected based upon (1) whether the data is
attribute data or measurement data, (2) whether the logical group
size is constant or variable, and (3) whether the (attribute) data
is measuring defectives or defects.

(defrule data_type
   (initial-fact)
=>
   (ask_question "question.idx" "get_type" "data_type") )*

(defrule XBAR_R_Chart
   (data_type value)
=>
   (assert (chart_type XBAR_R)) )

(defrule group_size
   (data_type attribute)
=>
   (ask_question "question.idx" "get_size" "group_size")*
   (ask_question "question.idx" "get_att_type" "attribute") )*

(defrule PN_Chart
   (group_size constant)
   (attribute defectives)
=>
   (assert (chart_type PN_Chart)) )

(defrule C_Chart
   (group_size constant)
   (attribute defects)
=>
   (assert (chart_type C_Chart)) )

(defrule P_Chart
   (group_size variable)
   (attribute defectives)
=>
   (assert (chart_type P_Chart)) )

(defrule _Chart
   (group_size variable)
   (attribute defects)
=>
   (assert (chart_type U_Chart)) )

*The function ask_question is provided by the CLIPS Application
User Interface (AUI) also developed by the AISC at Wright-
Patterson AFB, Ohio.


Interpreting AIM Network Classification Results

A major issue during the development of SPC was how to interpret
the AIM Networks' classification results.  An example of a portion
of the results of the AIM Networks' classification during the
exhaustive conventional search is given in TABLE 6. The
classification results of the AIM Networks are asserted into the
CLIPS fact-list in the format :

        (chart-type pattern-type begin-index end-index network-
score).


( X cycle 1 13 0.743 )
( X inc_trend 5 17 0.098 )
( X shift_up 6 18 0.282 )
( X inc_trend 6 17 0.819 )
( X inc_trend 6 16 1.000 )
( X inc_trend 7 17 0.829 )
( X inc_trend 6 15 1.000 )
( X inc_trend 7 16 0.874 )
( X inc_trend 6 14 0.991 )
( X inc_trend 7 15 1.000 )
( X inc_trend 6 13 0.951 )
( X inc_trend 7 14 1.000 )
( X inc_trend 8 15 0.973 )
( X inc_trend 6 12 0.807 )
( X inc_trend 7 13 0.997 )
( X inc_trend 8 14 0.961 )
( X inc_trend 9 15 0.841 )
( X inc_trend 7 12 0.904 )
( X inc_trend 10 15 0.917 )
( X inc_trend 10 14 0.895 )


Notice in TABLE 6 that from points 6 to 17 there are 17 sub-
sequences which the AIM increasing trend Network gave high scores
to!  Clearly we cannot report to the user all 17 patterns.  The
expert system application which interprets the AIM Networks'
classification results is composed of three rules :

        (1) The first rule eliminates from consideration any pattern
        whose AIM Network score is below a certain threshold.  The
        sensitivity of the pattern recognition can be adjusted by
        altering these thresholds in the deffacts statement.

        (2) The second rule eliminates from consideration any
        pattern which is contained entirely within another existing
        pattern of the same type.  It is assumed that the first
        rule has previously been applied.  For example, the fact (X
        inc_trend 8 14 0.961) would be retracted due to the presence
        of the fact (X inc_trend 6 16 1.0).

        (3) The third rule eliminates from consideration any pattern
        which overlaps another existing pattern of the same type but
        with a higher AIM Network score.  It is assumed that the
        first two rules have previously been applied.  For example,
        this rule would retract the fact  (X inc_trend 8 14 0.961)
        due to the presence of the fact  (X inc_trend 7 13 0.997).

(deffacts thresholds
   (threshold run 0.99)
   (threshold inc_trend 0.95)
   (threshold dec_trend 0.95)
   (threshold shift_up 0.95)
   (threshold shift_down 0.95)
   (threshold stratification 0.99)
   (threshold freak_point 0.99)
   (threshold freak_pattern 0.99)
   (threshold cycle 0.95) )


(defrule simple_threshold
   (resolve thresholds)
   ?pattern <- (?chart ?type ?a ?b ?score)
   (threshold ?type ?thresh)
   (test (< ?score ?thresh))
=>
   (retract ?pattern) )


(defrule subset
   (resolve subsets)
   (?chart ?type ?a1 ?b1 ?score1)
   ?subset_pattern <- (?chart ?type ?a2 ?b2 ?score2)
   (test (not (and (= ?a1 ?a2) (= ?b1 ?b2))))
   (test (and (<= ?a1 ?a2) (<= ?b2 ?b1) ))
=>
   (retract ?subset_pattern) )


(defrule overlap
   (resolve overlap)
   (?chart ?type ?a1 ?b1 ?score1)
   ?pattern2 <- (?chart ?type ?a2 ?b2 ?score2)
   (test (not (and (= ?a1 ?a2) (= ?b1 ?b2))))
   (test (>= ?score1 ?score2))
   (test (or (and (<= ?a1 ?a2 ?b1) (< ?b1 ?b2) )
             (and (<= ?a2 ?a1 ?b2) (< ?b2 ?b1) ) ))
=>
   (retract ?pattern2) )


Expert Advice On Meaning Of Chart Patterns

The majority of the expert system interaction that the user will
see involves explanations and advice regarding any patterns that
the AIM Networks have identified as indicators of assignable causes
of variation.  At the most basic level, this expert knowledge
simply consists of triples of the form <chart-type, pattern-type,
advice-text>.  The current AISC SPC software consists of knowledge
at this level of complexity only.  A sample of the CLIPS
implementation of such knowledge is illustrated in TABLE 8.

However, the rule-based representation is justified for the
following reasons :

   (1) The interpretation of control charts with multiple patterns
   is more complex than simple chart-pattern-advice triples.  The
   representation scheme must be powerful enough to accommodate
   future enhancements to the system.

   (2) One requirement for the SPC software is that it be easily
   modifiable to process specific applications.  Without knowing
   what type of reasoning process might be required for such
   customized applications, we selected the more flexible
   representation scheme provided by a production system.


(defrule R_shift_up
   (R shift_up ?a ?b ?score)
=>
   (write_paragraph "advice.idx" "R_shift_up") )*

*The function write_paragraph is provided by the CLIPS Application
User Interface (AUI) also developed by the AISC at Wright-Patterson
AFB, Ohio.

@
(6)
CONCLUSION

SPC is a good example of a hybrid system which integrates machine
learning, expert system, and conventional programming techniques.
It is a classic example of pattern recognition and is an excellent
demonstration of problem representation techniques necessary when
using machine learning or neural network tools.



Two features distinguish SPC from most other control chart software
:

        (1) SPC automatically identifies and highlights unusual
        chart patterns.  Most related commercial software simply
        draws the chart and explains to the user what unusual
        patterns to look for.  We found no commercial software which
        automatically identified trends, shifts, or cycles.

        (2) SPC provides expert advice on the meaning of all
        identified unusual chart patterns.  Over 50% of available
        commercial software only construct the control chart for the
        user and go no further.

The first version of SPC is scheduled to be available by September
1991 and will be distributed with an AFLC sponsored course on
Statistical Process Control.  The AISC plans to provide software
enhancements to SPC based upon future customer feedback and demand.
Also, the AISC hopes to provide some customers with customized
versions of SPC for process specific applications.  Copies of SPC
and reprints of this paper are available to government agencies
upon request.

@
REFERENCES
REFERENCES

[1] Spyros Makridakis and Stephen C. Wheelwright, "Forecasting:
Methods and Applications",Wiley/Hamilton, 1978.

[2] Sir Maurice Kendall and J Keith Ord, "Time Series", Oxford
University Press, 1990.

[3] SPC Course Materials, Decision Dynamics Inc., 1990

[4] Kaoru Ishikawa, "Guide to Quality Control", Asian Productivity
Organization, 1982.

[5] Perry Johnson Inc., "SPC Chart Interpretation", Perry Johnson,
Inc., 1987.

[6] J.M. Juran, Dr. Frank M. Gryna, Jr., and R.S. Bingham, Jr.,
"Quality Control Handbook",Third Edition, McGraw-Hill, 1974.

[7] Western Electric Company, "Statistical Quality Control
Handbook", Western Ellectric Co., Inc., 1958.

[8] H. Besterfield, "Quality Control", Second Edition, Prentice-
Hall.

[9] Douglas C. Montogomery, "Introduction to Statistical Quality
Control".

@
Attachment A
ATTACHMENT A

Patterns To Be Identified And Methods Of Identification

(1) Freak Point  -  This is any point which falls outside of the
three sigma control limits.  This is conventionally identified.

(2) Freak Pattern  -  This is any sequence of points for which a
large percentage fall more than a given amount away from the mean.
This definition is vague since many experts and source materials
disagree on what conditions to use.  This is conventionally
identified.  The following criteria are used to identify a freak
pattern:

   (a) Two out of three points in a row outside of the 2 sigma
   limits.  Reference [3].
   (b) Four out of five points in a row outside of the 1 sigma
   limits.  Reference [3].

(3) Stratification  -  Sometimes referred to as "hugging the center
line."  This is any sequence of points for which a large percentage
fall less than a given amount away from the mean.  This definition
is vague since many experts and source materials disagree on what
conditions to use.  This is conventionally identified.  The
following criteria are used to identify a stratification pattern:

   (a) Ten or more points in a row which are within the 1 sigma
   limits.

(4) Runs -  This is any sequence of points for which a large
percentage fall on the same side of the mean.  This definition is
vague since many experts and source materials disagree on what
conditions to use.  This is conventionally identified.  The
following criteria are used to identify a freak pattern:

   (a) More than 5 (some say 7 and others say 8) points in a row on
   the same side of the mean.

   (b) Ten of 12 on the same side of the mean.


(5) Increasing Trends  -  This pattern is identified with C code
generated by the machine learning tool AIM.  *Current accuracy is
97.5% based upon a test set of 2662 patterns.

(6) Decreasing Trends  -  This pattern is identified with C code
generated by the machine learning tool AIM.  *Current accuracy is
97.3% based upon a test set of 2663 patterns.

(7) Shifts Up  -  This pattern is identified with C code generated
by the machine learning tool AIM.  *Current accuracy is 98.8% based
upon a test set of 1990 patterns.

(8) Shifts Down  -  This pattern is identified with C code
generated by the machine learning tool AIM.  *Current accuracy is
98.8% based upon a test set of 1990 patterns.

(9) Cycles  -  This pattern is identified with C code generated by
the machine learning tool AIM.  *Current accuracy is 92.0% based
upon a test set of 22492 patterns.



* For further details, see Machine Learning Results.

@
Attachment B
ATTACHMENT B

Statistical Features Used To Represent Chart Subsequences

   (1) RMS_SU  -  This is the root-mean-squared difference between
   X[1..N] and an "ideal" shift-up pattern.

   (2) RMS_SD  -  This is the root-mean-squared difference between
   X[1..N] and an "ideal" shift-down pattern.

   (3) A  -  This is the simple linear regression coefficient when
   trying to approximate the time series X[t] using X[t] = A + Bt.

   (4) B  -  This is the simple linear regression coefficient when
   trying to approximate the time series X[t] using X[t] = A + Bt.

   (5) SIGMA_1  -  This is the standard deviation of the first half
   X[1..N/2] of the sequence X[1..N].

   (6) SIGMA_2  -  This is the standard deviation of the second half
   X[N/2+1..N] of the sequence X[1..N].

   (7) R_root_N_r  -  The percentage of the first N/4+1
   autocorrelation coefficients r(k) for which abs(r(k)) >
   1.96/sqrt(N).

   (8) CHI_SQ_TEST  -  This is the Box-Pierce Q-statistic which is
   capable of determining whether several autocorrelation
   coefficients are significantly different from zero.  This is
   defined in reference [1,p 269]

   (9) CONCORD  -  This is the number of concordances Q in X[1..N]
   divided by the maximum possible number N(N-1)/2 of concordances.
   This is defined in reference [2,pp 21-23].

   (10) DISCORD  -  This is the number of discordances P in X[1..N]
   divided by the maximum possible number N(N-1)/2 of discordances.
   This is defined in reference [2,pp 21-23].


   (11) TEN_PLUS  -  An indicator variable used to indicate if
   X[1..N] has length less than ten.  This is important since many
   statistical significance tests are ineffective for small sample
   sizes.

   (12) CCRD_LOW  -  An indicator variable used to indicate whether
   CONCORD is less than 0.7.  The value of 0.7 was chosen since a
   database analysis indicated that a high percentage of increasing
   trends had CONCORD > 0.7.

   (13) DCRD_LOW  -  An indicator variable used to indicate whether
   DISCORD is less than 0.7.  The value of 0.7 was chosen since a
   database analysis indicated that a high percentage of decreasing
   trends had DISCORD > 0.7.

   (14) HIGH_ISD  -  An indicator variable used to indicate whether
   RMS_SD is greater than 1.8.  The value of 1.8 was chosen since
   a database analysis indicated that a high percentage of shifts-
   up had RMS_SD > 1.8.

   (15) HIGH_ISU  -  An indicator variable used to indicate whether
   RMS_SU is greater than 1.8.  The value of 1.8 was chosen since
   a database analysis indicated that a high percentage of shifts-
   down had RMS_SU > 1.8.

   (16) GOOD_INC_MM  -  An indicator variable used to indicate when
   the sequence minimum was early and the sequence maximum was late.
   The first 20% and last 20% was chosen since a database analysis
   indicated that a high percentage of increasing trends had their
   minimum and maximum within the first 20% and last 20%
   respectively of the sequence.

   (17) GOOD_DEC_MM  -  An indicator variable used to indicate when
   the sequence maximum was early and the sequence minimum was late.
   The first 20% and last 20% was chosen since a database analysis
   indicated that a high percentage of decreasing trends had their
   maximum and minimum within the first 20% and last 20%
   respectively of the sequence.

   (18) HIGH_R_root_N  -  An indicator variable used to indicate
   whether R_root_N_r is greater than 0.1.  The object of
   introducing this variable was to help draw a distinction between
   random sequences and cycles.  The value of 0.1 was chosen since
   a database analysis indicated that a high percentage of cycles
   and a low percentage of random sequences had R_root_N_r > 0.1.

   (19) SMALL_A  -  An indicator variable used to indicate whether
   the absolute value of A is less than 0.8.  The object of
   introducing this variable was to help draw a distinction between
   random sequences or cycles and the other chart patterns.  The
   value of 0.8 was chosen since a database analysis indicated that
   a high percentage of cycles and random sequences and a low
   percentage of other types of patterns had abs(A) < 0.8.

   (20)  MAYBE_CYCLE  -  An indicator variable used to indicate when
   both R_root_N_r > 0.1 and ABS(A) < 0.8.  This is the logical AND
   of variables 18 and 19.

@
Mark Shewhart
       About the Author

Mark Shewhart
Air Force Logistics Command (AFLC)
Acquisition Logistics Division
Joint Technology Application Office (ALD/JTI)
Artificial Intelligence Support Center (AISC)
Wright Patterson AFB, Ohio 45433
@
(-)
Abstract.  Statistical Process Control (SPC) Charts are one
of several tools used in Quality Control.  Other tools
include flow charts, histograms, cause-and-effect diagrams,
check sheets, Pareto diagrams, graphs, and scatter diagrams.
A control chart is simply a graph which indicates process
variation over time.  The purpose of drawing a control chart
is to detect any changes in the process, signalled by
abnormal points or patterns on the graph.  The Artificial
Intelligence Support Center (AISC) of the Acquisition
Logistics Division (ALD/JTI) has developed a hybrid machine-
learning/expert-system prototype which automates the process
of constructing and interpreting control charts.
@
(0)
INTRODUCTION

The Air Force Logistics Command (AFLC) has provided TQM and Quality
Control training to its employees for several years now.  In
particular, Statistical Process Control has been emphasized in this
effort.  While many data collection efforts have been undertaken
within AFLC, the SPC Quality Control tool has been under-utilized
due to the lack of experienced personnel to identify and interpret
patterns within the control charts.  The AISC has developed a
prototype software tool which draws control charts, identifies
various chart patterns, advises what each pattern means, and
suggests possible corrective actions.  The application is easily
modifiable for process specific applications through simple
modifications to the knowledge base portion using any word
processing software.

The remainder of this paper consists  of the following sections :

        #m(1)#m CONTROL CHARTS
        #m(2)#m SOFTWARE FUNCTIONALITY
        #m(3)#m SOFTWARE DESIGN
        #m(4)#m MACHINE LEARNING
        #m(5)#m EXPERT SYSTEM
        #m(6)#m CONCLUSION
        #mREFERENCES#m
        #mAttachment A#m
        #mAttachment B#m

Section (1) provides a more in-depth explanation of the purpose of
control charts.  Section (2) details the initial functional
requirements for the SPC software, and section (3) outlines the
design approach used to implement the system requirements.
Sections (4) and (5) examine in detail the roles of machine
learning and expert system techniques respectively.  Finally,
section (6) offers some basic conclusions resulting from this
effort.   Two attachments are included after the references.
ATTACHMENT A provides a list of the chart patterns of interest and
their methods of identification.  ATTACHMENT B enumerates and
explains the twenty statistical features used by the machine
learning tool.
@