Image forming apparatus provided with self-diagnosis system

In an image forming machine, an objective model storage device stores parameter data that represent elements of the machine and relationships among such parameters, and parameter membership functions, and fault diagnosis knowledge. A degradation storage device stores a fuzzy qualitative value for a parameter changed by degradation of an element of the machine. Preferably, degradation indicative data are converted into fuzzy qualitative values, and the value of the parameter changed by degradation is represented by a fuzzy qualitative value. The machine includes sensors for sensing functional states thereof, and providing state data representative of such states. The state data sensed by the sensors are converted into fuzzy qualitative values. Then, a fault judgement device determines whether or not a fault exists by comparing the obtained fuzzy qualitative values with the parameter data stored in the objective model storage device. If the fault judgement device determines that a fault exists, a fault diagnosis device performs fault diagnosis by utilizing, as an initial value, the value of the parameter changed by degradation. A specification device specifies fault causes by comparing the result of the diagnosis with the state data which was converted into the fuzzy qualitative values. Then, a repair device operates actuators of the machine to overcome the specified fault.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a self-diagnosis and/or self-repair 
system, and more particularly, to a system or self-repair system, and more 
particularly, to a system capable of making a self-diagnosis of a degraded 
state, the operating state and the like of an apparatus by utilizing 
artificial intelligence and knowledge engineering which have been studied 
extensively in recent years as well as adopting fuzzy inference and making 
self-repair thereof as required. 
2. Description of the Prior Art 
In the development field of precision instruments, industrial machines and 
the like, expert systems utilizing artificial intelligence (so-called AI) 
techniques have been studied extensively in recent years for the purpose 
of realizing labor saving in maintenance work and long-term automatic 
operation. The expert systems a device for a device for making 
self-diagnose to judge whether or not a fault is caused in an apparatus 
and making self-repair of the fault caused. 
In a fault diagnosis system by the conventional expert system, such 
limitations have been pointed out that, for example, (A) there is no 
versatility in knowledge, which makes it impossible to make fault 
diagnosis on a variety of objects, (B) diagnosis cannot be made on unknown 
faults, (C) the quantity of knowledge required for fault diagnosis is 
increased explosively as an object becomes complicated, thus making 
implementation difficult, and (D) it is difficult to acquire knowledge. 
More specifically, in a conventional automatic control system and fault 
diagnosis system, an actuator corresponding to a sensor is basically made 
to operate on the basis of an output of the sensor. That is, one type of 
automatic control and fault diagnosis has been made by a predetermined 
combination of a sensor and an actuator. Accordingly, a certain sensor 
basically corresponds to a particular actuator, and the relationship 
therebetween has been stationary. Therefore, the conventional system has 
the following disadvantages: (a) The relationship between parameters of 
the sensor and parameters of the actuator must be clearly expressed 
numerically. (b) From the reason mentioned in the above item (a), the 
relationship between parameters of the sensor and parameters of the 
actuator depends largely on an object. Accordingly, the conventional 
system is lacking in versatility, that is, cannot be utilized for a 
variety of objects. (c) The relationships between parameters of respective 
sensors and between parameters of respective actuators have no relation 
with control. Accordingly, only simple control based on the relationship 
between the parameters of the sensors and the parameters of the actuators 
which correspond to each other can be carried out, and faults which can be 
coped with are previously restricted and unknown faults cannot be handled. 
(d) From the reason mentioned in the above item (c), secondary effects 
exerted on parameters of other actuators which might be caused by the 
operation of parameters of an arbitrary actuator cannot be forecast. 
In the conventional automatic control system and fault diagnosis system, 
therefore, only fault diagnosis based on sets respectively including 
independent sensors and actuators and fault repair based on the fault 
diagnosis have been made in such a manner that forecasting fault A is made 
on the basis of a set A of a sensor A and an actuator A, forecasting fault 
B is made on the basis of a set B of a sensor B and an actuator B, and 
forecasting fault C is made on the basis of a set C of a sensor C and an 
actuator C. 
The applicant of the present application and the like have proposed as a 
technique associated with the present invention a new system for making 
self-diagnosis and/or self-repair by adopting an image forming apparatus 
as an objective machine so as to eliminate the disadvantages of the prior 
art (see U.S. patent application Ser. Nos. 07/588,191 and 07/588,177). 
Qualitative inference used in the above described self-diagnosis and/or 
self-repair system already proposed is complete as the approach of 
determining the qualitative transition from a group of equations and the 
initial state. On the other hand, the qualitative inference has such an 
inevitable destiny that an ambiguous expression is not admitted as the 
state representation of an objective system (machine) because inference in 
the form of a qualitative, that is, symbolic expression is drawn. The 
qualitative inference is insufficient as the approach of making fault 
diagnosis and repair by handling information such as "ambiguous 
information" often seen in the maintenance activity, for example, 
information "this may be normal or abnormal" as the state of the machine. 
Furthermore, when the fault diagnosis utilizing degradation and fault 
hysteresis information on respective components constituting the machine 
is synthesized, a fault diagnosis system and/or fault repair system having 
a higher degree of completion cannot be constructed unless an inference 
method having logic using any other method of representation added to the 
qualitative inference already proposed and the approach of handling 
ambiguous information added thereto is considered. 
The inventors of the present application have invented a self-diagnosis and 
self-repair system having a higher degree of completion by combining the 
fuzzy theory which is a theory mathematically handling ambiguity with the 
qualitative inference used in the above described self-diagnosis and/or 
self-repair system already proposed. 
SUMMARY OF THE INVENTION 
An object of the present invention is to provide an image forming apparatus 
having a system capable of developing inference admitting ambiguity from 
the point of view of maintenance, making self-diagnosis of the state of an 
apparatus using the inference and making self-repair thereof as required. 
The self-diagnosis and self-repair system according to the present 
invention calculates the amount of degradation relative to the time 
elapsed after the image forming apparatus starts to be used up to the 
present time on the basis of degradation data representing the 
relationship between the time elapsed after the image forming apparatus 
starts to be used and the amount of degradation. The value of a parameter 
changed by the amount of degradation calculated is converted into a fuzzy 
qualitative value using membership functions of the parameter, and is 
replaced with an expression used on qualitative data. In addition, data 
sensed by a plurality of sensor means is converted into a fuzzy 
qualitative value using the membership functions of the parameter, and it 
is judged on the basis of the fuzzy qualitative value whether or not a 
fault exists. If it is judged that a fault exists, fault diagnosis is made 
utilizing as an initial value the value of the parameter changed by the 
above described amount of degradation. The result of the diagnosis is 
outputted as an expression having ambiguity. 
Furthermore, the causes of the fault are specified by comparing the fuzzy 
qualitative value obtained by the conversion from the output of the sensor 
means with the result obtained by the fault diagnosis. More specifically, 
when a plurality of fault candidates are taken up as a result of the fault 
diagnosis, a fault candidate which best coincides with the actual state of 
the apparatus is examined. Consequently, the actual fault state is 
outputted more accurately. A predetermined one of a plurality of actuators 
is operated by repair means to repair the fault. 
In the self-diagnosis and self-repair system according to the present 
invention viewed at another angle, the amount of degradation of a 
component for each predetermined timing of fault diagnosis, for example, 
for each elapse of one month is estimated, and the change in the value of 
a parameter based on the estimated amount of degradation is stored by a 
fuzzy qualitative value. At the predetermined timing of fault diagnosis, 
data detected by a plurality of sensor means is converted into a fuzzy 
qualitative value using membership functions of the parameter, and it is 
judged whether or not a fault exists on the basis of the fuzzy qualitative 
value. In addition, if it is judged that a fault exists, the fuzzy 
qualitative value of the parameter at the timing of fault diagnosis is 
read out, and fault diagnosis is made utilizing the value as an initial 
value. The result of the diagnosis is outputted by an expression having 
ambiguity. 
Furthermore, the fuzzy qualitative value converted from a detection output 
of the sensor means is compared with the ID result obtained by the fault 
diagnosis, to specify the causes of the fault. More specifically, when a 
plurality of fault cause candidates are taken up as a result of the fault 
diagnosis, it is examined which fault cause candidate coincides with the 
actual state of the image forming apparatus more exactly. Consequently, 
the actual fault state is outputted more exactly. The repair means 
operates predetermined ones of a plurality of actuators, to repair the 
fault. 
Furthermore, the fuzzy qualitative value converted from a detection output 
of the sensor means is compared with the result obtained by the fault 
diagnosis, and the degree to which a fault phenomenon occurs at the timing 
of fault diagnosis is considered to specify the causes of the fault. More 
specifically, when a plurality of fault cause candidates are taken up as a 
result of the fault diagnosis, it is examined which fault cause candidate 
coincides with the actual state of the image forming apparatus more 
exactly on the basis of the degree of coincidence of the values of 
parameters and the degree to which a fault phenomenon occurs. 
Consequently, the actual fault state is acknowledged and outputted more 
exactly. The repair means operates predetermined ones of a plurality of 
actuators, to repair the fault. 
The foregoing and other objects, features, aspects and advantages of the 
present invention will become more apparent from the following detailed 
description of the present invention when taken in conjunction with the 
accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Fuzzy qualitative inference 
Description is now made of fuzzy qualitative inference which is a newly 
developed inference having ambiguity required for self-diagnosis. 
(1) Fuzzy qualitative value 
In qualitative inference used in a self-diagnosis and/or self-repair system 
according to the prior application of the applicant, the concepts of a 
quantity space and a qualitative value have been used as the approach of 
symbolically representing the value of a variable. The quantity space is a 
finite set obtained by symbolically representing a set of real numbers by 
a landmark which is a characteristic value having a physical meaning and a 
section enclosed by the landmark. Accordingly, either one of a boundary 
value or a section value is only taken as the qualitative value. 
Considering a self-diagnosis and/or self-repair system in an ideal 
objective machine taken as an example, it makes sense to judge whether a 
certain value is a landmark value or a section value. When a quantitative 
value obtained by measurements is converted into a qualitative expression 
and inference is drawn on the basis of the expression in the actual world, 
it may not be appropriate that the quantitative value obtained by 
measurements is only alternatively converted into a landmark value or a 
section value. The reason for this is that "ambiguous information" is seen 
in the maintenance activity, as described above, so that there can 
actually occur the situation where the quantitative value may be a 
landmark value or a section value. 
Therefore, the fuzzy theory is applied to the present invention. 
The fuzzy theory is a theory of mathematically handling ambiguity. The 
expression of a set in the fuzzy theory is characterized in that an 
intermediate state where it is not clear whether or not a certain element 
belongs to the set is indicated by decimal fractions from 0.0 to 1.0 as 
the degree to which the element belongs to the set. The intermediate state 
which cannot be represented by a conventional set can be represented by 
using this form of expression. In the fuzzy theory, a function for 
defining the degree to which a certain element belongs to a certain set 
(grade) is referred to as a "membership function". 
An expression having ambiguity added to a qualitative expression becomes 
possible by introducing the concept of a fuzzy set represented using this 
membership function. More specifically, in the present invention, the 
value of a variable is represented as a set of a conventional qualitative 
value and the degree to which it belongs to the qualitative value (grade). 
Such a form of expression will be referred to as a "fuzzy qualitative 
value". 
For example, when the value of a certain variable is represented by a fuzzy 
qualitative value in a quantity space shown in FIG. 1, the value is 
expressed, for example, as follows: 
EQU (Normal: 0.4, (Normal, nil): 0.6) 
It is possible to admit ambiguity by using this method of representation by 
a fuzzy qualitative value when sensor information is made use of for 
inference. More specifically, in a fault diagnosis system using the 
qualitative inference previously proposed, a certain constant range has 
been determined as a range of normal values. If a quantitative value 
obtained from a sensor is in the range, it is considered that the 
qualitative value is on a landmark of "normal values", to draw qualitative 
inference. 
On the other hand, in the present invention, membership functions are used 
for the operation of converting a quantitative value obtained from a 
sensor into a qualitative expression. When membership functions are used, 
membership functions such as "a normal value (Normal; hereinafter 
abbreviated as N)", "larger than a normal value (Normal, nil; hereinafter 
abbreviated as N, nil)", and "smaller than a normal value (0, Normal; 
hereinafter abbreviated as 0, N)" are previously determined on a space of 
real numbers of the sensor, as shown in FIG. 2. A quantitative value 
obtained from the sensor is mapped on the space shown in FIG. 2, to 
convert the quantitative value into a qualitative expression admitting 
ambiguity. 
(2) Operation rule of fuzzy qualitative value 
An algebraic operation of a fuzzy qualitative value comprises an algebraic 
operation rule of qualitative inference and the calculation of grades. 
Description is made while giving concrete examples. Following is a 
concrete example: 
Zf=Xf.times.Yf 
Xf=(N: 0.8, (N, nil): 0.2) 
Yf=((0, N)0.7, N: 0.3) 
and the relationship between landmarks is as follows: 
(Xf, Yf, Zf)=(N, N, N) 
All values which can be taken as the qualitative value of Zf are listed 
from the respective qualitative values of Xf and Yf (in this example, N 
and (N, nil) of Xf) and the relationship between the landmarks. The 
smaller one of the grades with respect to the qualitative values of Xf and 
Yf is adopted as a grade with respect to the qualitative value of Zf at 
that time. The foregoing will be described more specifically: 
______________________________________ 
Xf Yf Zf 
______________________________________ 
N .times. 
(0, N) = (0, N) : 0.8, 0.7 = 0.7 
N .times. 
N = N : 0.8, 0.3 = 0.3 
(N, nil) 
.times. 
(0, N) = (0, N) N (N, nil) 
: 0.2, 0.7 = 0.2 
(N, nil) 
.times. 
N = (N, nil) : 0.2, 0.3 = 0.2 
______________________________________ 
Furthermore, when not less than two types of grades are found with respect 
to the qualitative value of Zf, the maximum value thereof is adopted. In 
the foregoing example, since two types of grades, that is, 0.7 and 0.2 are 
found with respect to the qualitative value (0, N) of Zf in the first and 
third equations, the maximum value thereof, that is, 0.7 is adopted as the 
grade with respect to the qualitative value (0, n) of Zf. Similarly, since 
two types of grades, that is, 0.3 and 0.2 are found with respect to the 
qualitative value N of Zf in the second and third equations, the maximum 
value thereof, that is, 0.3 is selected. 
From the foregoing calculations, the fuzzy qualitative value of Zf is as 
follows: 
Zf=((0, N): 0.7, N: 0.3, (N, nil): 0.2) 
Furthermore, standardization is so achieved that the sum of the grades is 
1. The standardization is achieved by dividing the grade with respect to 
each of the qualitative values by 1.2 (where 1.2=0.7+0.3+0.2). As a result 
of the standardization, the qualitative value of Zf becomes as follows: 
Zf=((0, N): 0.58, N: 0.25, (N, nil): 0.17) 
(3) Inference 
Inference basically uses the propagation method. This propagation method is 
an algorithm for sequentially propagating the value of a parameter whose 
value is already determined to the other parameters using the relationship 
between the parameters to determine parameters in the entire system. 
The propagation procedure uses a method of determining an unfixed parameter 
out of parameters in the binomial relation or the trinomial relation using 
the parameters already determined and the relationship therebetween from 
the above described fuzzy operation rule. The specific inference method 
will be made clear from the concrete examples as described later. 
System composition 
FIG. 3 is a block diagram showing the construction of a system according to 
one embodiment of the present invention. This system comprises a plurality 
of sensors 1a, 1b and 1c installed on an objective machine (more 
concretely, a small-sized electrophotographic copying machine or the like) 
and a plurality of actuators 6a, 6b and 6c for changing the operating 
state or the like of the objective machine. 
The plurality of sensors 1a, 1b and 1c are respectively used for sensing 
the change of elements of the objective machine or relevant states among 
the machine elements which occur by the operation of the objective 
machine. Information which are taken in from the plurality of sensors 1a, 
1b and 1c, respectively, are amplified by an amplification circuit 2, are 
converted from analog signals to digital signals by an A/D conversion 
circuit 3, and are applied to a digital signal/FQ value (fuzzy qualitative 
value) conversion portion 11. The digital signal/FQ value conversion 
portion 11 is a portion for converting the digital signal applied from the 
A/D conversion circuit 3 into a fuzzy qualitative value, that is, has the 
converting function for representing the digital signal by a qualitative 
value (any one of four symbols, for example, "nothing (0)", small (0, N)", 
"normal (N)", and "large (N,nil)") and a grade (a numerical value of 0.0 
to 1.0). The signals applied from the sensors 1a, 1b and 1c are 
respectively converted into qualitative information represented by fuzzy 
qualitative values, thereby to make it possible to evaluate function of a 
machine accurately as described later. 
Furthermore, there are provided a degradation data calculation portion 12, 
a timer 19 for applying data on the time elapsed after the objective 
machine starts to be used to the degradation data calculation portion 12, 
a short-term simulation portion 13, a fault diagnosis portion 14, an 
objective model storage portion 15, and a fault simulation portion 16. The 
degradation data calculation portion 12 is a portion for calculating the 
amount of degradation with age of each of the components constituting the 
objective machine. The method of calculation will be described in detail 
later. The short-term simulation portion 13 is a portion for simulating 
the present state of the objective machine. The fault diagnosis portion 14 
is a portion for performing function evaluation using fuzzy qualitative 
values applied from the digital signal/FQ conversion portion 11 to specify 
the fault symptom as well as deriving the causes of the fault from the 
fault symptom. A processing step (fault diagnosis step) for deriving the 
causes of the fault from the fault symptom specified in the fault 
diagnosis portion 14 is carried out on the basis of inference (non-fuzzy 
inference using no fuzzy inference) in the self-diagnosis and/or 
self-repair system disclosed in the above described prior specification of 
the applicant. 
The objective model storage portion 15 previously stores a "substance 
model" in which an objective machine is grasped from a physical point of 
view and is represented by parameters as a combination of a plurality of 
elements in a substance level (see Table 2 as described later), a 
"parameter model" in which the objective machine is represented as a 
combined tree of the respective parameters (see FIG. 11 as described 
later), initial values of the respective parameters, membership functions 
of a function parameter (as shown in FIG. 2), the relationship between the 
time elapsed after the objective machine starts to be used and the 
degraded state of a component paid attention to (see FIG. 4 as described 
later), the relationship between the degraded state and membership 
functions of a parameter (see FIG. 5 as described later), the relationship 
between the degraded state and the degree to which a fault phenomenon 
occurs (see FIG. 6 as described later), a reference value for fault 
judgment, fault candidate knowledge, and the like. The types of knowledge 
stored in the objective model storage portion 15 are made use of when the 
digital signal/FQ value conversion portion 11, the degradation data 
calculation portion 12, the short-term simulation portion 13, or the fault 
diagnosis portion 14 performs processing. In addition, the fault 
simulation portion 16 is a portion for simulating a fault in cooperation 
with the short-term simulation portion 13 and the fault diagnosis portion 
14. 
One of the features of the present embodiment and the present invention is 
that a system is provided with two constituent elements, that is, the 
degradation data calculation portion 12 and the short-term simulation 
portion 13. The two constituent elements will be described in more detail. 
(1) Degradation data calculation portion 
The degradation data calculation portion 12 takes up components associated 
with fault diagnosis out of the components constituting the objective 
machine, to calculate the degraded state with time for each component, the 
effects of the degraded state on the value of a parameter, and the degree 
to which a fault phenomenon occurs. 
Degradation data representing the relationship between the time T elapsed 
after the objective machine starts to be used and the amount of 
degradation X is previously set for each component associated with fault 
diagnosis or a group of relevant components. For example, data as shown in 
FIG. 4 is set. This degradation data is stored in the objective model 
storage portion 15. The degradation data calculation portion 12, for 
example, adds up time data applied from the timer 19 to find the total 
time elapsed after the machine starts to be used up to the present time 
and applies the time to FIG. 4, thereby to calculate the degraded state of 
a component paid attention to. 
Meanwhile, the degraded state calculated in this case is not for estimating 
the physical quantities on the parameter model of the objective machine on 
the basis of frequency of fault or the like. For example, it is assumed 
that the component paid attention to is a particular gear. Even if the 
degraded state of the gear (the amount of wear of the gear) is found, it 
is not found how change occurs on the parameter model of the objective 
machine. 
The effects of the degradation on the objective machine are then found from 
the relationship between the degraded state and the value of the parameter 
on the parameter model as shown in FIG. 5. The relationship between the 
degraded state and the value of the parameter as shown in FIG. 5 is 
previously set using the membership functions of the parameter and is 
stored in the objective model storage portion 15. The degradation data 
calculation portion 12 reads out the graph of the membership functions of 
the parameter against the degraded state as shown in FIG. 5 from the 
objective model storage portion 15 and maps the degraded state on this 
graph, thereby to calculate the effects of the degradation on the value of 
the parameter. 
Furthermore, the degradation data calculation portion 12 determines the 
degree to which a fault phenomenon occurs with respect to the degraded 
state calculated from the graph of the degree P to which a fault 
phenomenon occurs against the degraded X state as shown in FIG. 6 which is 
previously stored in the objective model storage portion 15. 
Meanwhile, the degraded state calculated on the basis of FIG. 4 is a value 
determined, if the time elapsed after the objective machine starts to be 
used is determined, corresponding to the time and is calculated as a 
quantitative value. 0n the other hand, the value of the parameter obtained 
on the basis of FIG. 5 is a value having ambiguity which is represented by 
a fuzzy qualitative value and is expressed, for example, as follows from a 
qualitative value and a grade: 
((0, N): 0.9, N: 0.1) 
Furthermore, the degree to which a fault phenomenon occurs which is 
calculated on the basis of FIG. 6 is a quantitative value determined 
depending on the degraded state. 
In place of the above described construction, a fuzzy qualitative value of 
a parameter and the degree to which a fault phenomenon occurs (see Table 1 
as described later) which are changed depending on the amount of 
degradation for each predetermined timing of fault diagnosis may be stored 
in the objective model storage portion 15 to calculate the change with age 
of the objective machine by the degradation data calculation portion 12. 
More specifically, a fuzzy qualitative value of a parameter and the degree 
to which a fault phenomenon occurs for each timing of fault diagnosis may 
be estimated and set for each component associated with the fault 
diagnosis or for each group of relevant components. For example, a 
degradation data shown in Table 1 is set. This degradation data is stored 
in the objective model storage portion 15. The degradation data 
calculation portion 12, for example, adds up time data applied from the 
timer 19 to find the time elapsed after the objective machine starts to be 
used up to the present time and applies the time to the table 1, thereby 
to calculate degradation data (a fuzzy qualitative value of a parameter 
and the degree to which a fault phenomenon occurs) of a component paid 
attention to. 
TABLE 1 
______________________________________ 
degree to which 
elapsed time 
FQ value of parameter Z 
phenomenon occurs 
______________________________________ 
T1 Z1 = (N : X1) P1 
T2 Z2 = P2 
((0,N) : X2, N : Y2) 
: : : 
: : : 
: : : 
Tn Zn = Pn 
((0,N) : Xn,N : Yn) 
: : : 
: : : 
: : : 
______________________________________ 
(2) Short-term simulation portion 
A short-term simulation (hereinafter referred to as SSIM) is a simulation 
for determining the state of the present objective machine. 
The state of the objective machine is represented by a set of physical 
quantities indicating attributes of the respective components constituting 
the objective machine. The SSIM is made on the parameter model in which 
the physical quantities are related to each other by a qualitative 
equation. The SSIM inference method uses the above described fuzzy 
qualitative inference. In addition, the propagation method is used as an 
algorithm for the fuzzy qualitative inference. Description is now made of 
this propagation method. 
Inference begins in a state where the respective values of constant 
parameters, parameters determined by values obtained from the sensors, and 
parameters determined by the degradation data calculation portion 12 are 
determined. 
In the case of the propagation, the following procedure is carried out: 
(1) If two parameters have been already determined out of parameters in the 
trinomial relation (+, -, x and the like), the remaining one parameter is 
determined. 
(2) If either one of parameters in the binomial relation (=) is determined, 
the other parameter is determined. 
The foregoing propagation procedure is repeated until the values of all the 
parameters are determined. 
As a result, the state of the entire objective machine, that is, the values 
of all the parameters are determined by the SSIM. 
Description is now made of the inference procedure for fault diagnosis 
which is made in the degradation data calculation portion 12, the 
short-term simulation portion 13, the fault diagnosis portion 14, and the 
fault simulation portion 16. 
Fault diagnosis in fuzzy qualitative inference utilizing degradation 
information 
Inference for fault diagnosis is drawn in the following procedure with 
reference to FIGS. 7, 8 and 9. 
The state of the objective machine at the time point is previously sensed 
by the sensors 1a, 1b and 1c provided for the objective machine (step S1), 
and the value of each of parameters obtained by the sensing is converted 
into a fuzzy qualitative value (step S2). The sensing of the value of the 
parameter in the step S1 is achieved by, if there is provided a sensor, 
the sensor (for example, the quantity of light H1 of a halogen lamp is 
measured by an AE sensor, as described later). If there is provided no 
sensor, however, the sensing may be achieved by using a method in which a 
service man or the like manually measures the objective machine and inputs 
a value obtained by the measurement into a system. In addition, the 
conversion of the value of the parameter into a fuzzy qualitative value in 
the step S2 is achieved by mapping a quantitative value obtained by the 
measurement on membership functions of each of the parameters previously 
stored in the objective model storage portion 15 (as shown in FIG. 2). 
(1) Calculation of degraded state 
The degraded state up to the present time point is then calculated (step 
S3). The degraded state is found by adding up time data applied from the 
timer 19 in the degradation data calculation portion 12 and applying a 
value obtained by the addition to the graph shown in FIG. 4 which is read 
out of the objective model storage portion 15, as described above. 
Meanwhile, the timer 19 itself may be one of such a time adding type that 
its output value can be directly utilized, or a service man or the like 
may manually input the time elapsed after the objective machine starts to 
be used without providing the timer 19. 
(2) Conversion of degraded state into effects on objective model 
The degraded state obtained from the graph shown in FIG. 4 is converted 
into the effects exerted on the parameters on the objective model (step 
S4). 
The conversion comprises the following types of processing: 
(i) processing for obtaining the change in the value of the parameter oil 
the parameter model by applying the degraded state calculated in the step 
S3 to the graph shown in FIG. S, and 
(ii) processing for obtaining the change in the degree to which a 
phenomenon occurs by applying the degraded state to the graph shown in 
FIG. 6. 
Although description was made of a case where the above described two 
changes are found as the effects of the degradation on the objective 
model, only (i) the change in the value of the parameter on the parameter 
model, for example, may be found. 
Description is now made of procedure of calculation of degraded state using 
the table 1 . 
(1+2) Calculation of degraded state (using the table 1) 
When the above described table 1 is used, the calculation of the degraded 
state is performed as follows: The calculation of the degraded state is 
performed by adding up time data applied from the timer 19 in the 
degradation data calculation portion 12 and applying a value obtained by 
the addition, when it reaches predetermined elapsed time T1, T2, . . . , 
to the table 1, to read out the value of the parameter and the degree to 
which a phenomenon occurs corresponding to the time T1, T2, . . . . 
Meanwhile, the timer 19 itself may be one of such a time adding type that 
its output value can be directly utilized, or a service man or the like 
may manually input the time elapsed after the objective machine starts to 
be used without providing the timer 19. 
The above described table 1 may be replaced with a simplified table showing 
only a fuzzy qualitative value of a parameter. In addition, only the fuzzy 
qualitative value of the parameter may be calculated as the degraded 
state. 
(3) SSIM 
The simulation is made utilizing as the initial conditions the change in 
value of parameters obtained as the effect exerted on-the component found 
in the foregoing item (2), to determine the values of parameters in the 
entire objective machine after an elapse of time. 
More specifically, the value of a predetermined parameter obtained by the 
step S4 is placed on the parameter model (step S5), and is propagated to 
the other parameters on the parameter model by the propagation method so 
that the values of all the parameters in the objective machine are 
determined, to create a state model of the objective machine (step S6). 
(4) Fault judgment 
It is then judged by viewing the sensor value of a function parameter out 
of the sensor values previously converted into fuzzy qualitative values in 
the step S2 whether or not a fault occurs (step S7). 
The sensor value of the function parameter is evaluated by comparison with 
a reference value for fault judgment previously stored in the objective 
model storage portion 15. If it is judged that the sensor value of the 
function parameter is normal, the program proceeds to the step S8. In the 
step S8, the value of the parameter on the parameter model found in the 
step S6 and the fuzzy qualitative value which converted in the step S2 are 
compared with each other, to determine the degree of coincidence between 
the parameter model and the actual state of the objective machine. 
As a result of the evaluation of the degree of coincidence in the step S8, 
processing is terminated when both coincides with each other, while the 
objective machine continues to be operated by giving precedence to the 
judgment in the step S7 that the sensor value of the function parameter is 
normal. However, the value on the model and the sensor value does not 
coincide with each other so that there is a possibility that a fault 
occurs. Accordingly, a display device or the like is caused to display a 
message (step S9). The message is displayed in various forms. For example, 
when the sensor value of the function parameter is normal and the value on 
the parameter model and the sensor value does not coincide with each 
other, it is considered that the sensor lot measuring the function 
parameter fails, so that a message such as "there is a possibility that 
the sensor is abnormal" is displayed. 
(5) Fault diagnosis 
When it is judged in the above described item (4) that a fault occurs, a 
fault candidate is derived from the fault symptom (step S10). 
A plurality of fault candidates are previously stored in the objective 
model storage portion 15 (see FIG. 3). The value of the function parameter 
is traced on the parameter model, to select and derive the corresponding 
fault candidate from the plurality of fault candidates previously stored. 
Alternatively, the fault candidate may be determined by inference 
(non-fuzzy inference using no fuzzy theory) described in the above 
described prior application of the applicant. 
(6) SSIM 
The SSIM is made with respect to each of the fault candidates derived in 
the step S10, to create a fault model. 
More specifically, the fault conditions and the value of the parameter 
obtained as a result of the calculation of degraded state and the 
conversion into the effect exerted on the model are placed as initial 
conditions on the parameter model with respect to each of the fault 
candidates (step S11), and the value of the parameter is traced on the 
parameter model by the propagation method, to create a state model of the 
objective machine (step S12). 
In the above described manner, a fault model is created. 
(7) Specification of causes of fault 
The causes of the fault are assigned priority and are narrowed down from 
sensor information, the degree to which a phenomenon occurs found in the 
item (2) (ii), and the like. 
More specifically, the degree of coincidence between the model and the 
sensor is evaluated on the basis of the value of the parameter on the 
state model and fuzzy qualitative value converted in the step S2 (step 
S13), and the degree of coincidence is evaluated again by adding the 
degree to which a phenomenon occurs to the result of the evaluation of the 
degree of coincidence, to assign the causes of the fault priority (step 
S14). 
Meanwhile, a simple method of specifying the causes of the fault by only 
the degree of coincidence between the value of the parameter on the model 
and the actual sensor value of the parameter which is evaluated in the 
step SI3 by omitting the processing in the step S14 may be used. 
The fault diagnosis is completed in the foregoing inference procedure. In 
addition, at the time of the completion of the fault diagnosis, the work 
of adding and/or repairing fault hysteresis information may be performed. 
Thereafter, it is judged by the operation of parameters whether or not the 
fault can be repaired (step S15). The fault is repaired when it can be 
repaired by the operation of parameters (step S16), while the processing 
is terminated without any modification because the fault cannot be 
repaired when it cannot be repaired by the operation of parameters, for 
example, when a halogen lamp is cut off in an electrophotographic copying 
machine. The repair operation in the step S16 is performed in a repair 
plan portion 17 as described below. 
Returning to FIG. 3, the remaining composition blocks will be described. 
The repair plan portion 17 is a composition portion for inferring a repair 
plan for repairing, when a fault exists, the fault as well as deriving 
repair work. The inference of the repair plan and the derivation of the 
repair work make use of non-fuzzy qualitative inference using no fuzzy 
theory, similarly to the inference in the self-diagnosis and/or 
self-repair system already proposed. 
The repair work outputted from the repair plan portion 17 is converted into 
a digital signal in a symbol-to-digital signal conversion portion 18. The 
digital signal converted is converted into an analog signal in a D/A 
conversion circuit 4, is amplified in an amplification circuit 5, and is 
applied to a plurality of actuators 6a, 6b and 6c so that the actuators 
6a, 6b and 6c are selectively operated, thereby to perform the repair 
work. 
Description by taking as example specific objective machine Construction 
and state of specific objective machine 
Description is now made by taking as an example a case where this system is 
applied to an image forming apparatus serving as a specific objective 
machine and more specifically, to a small-sized electrophotographic 
copying machine. 
FIG. 10 is an illustration showing a small-sized electrophotographic 
copying machine serving as a specific objective machine. In FIG. 10, 
reference numeral 21 designates a photosensitive drum, reference numeral 
22 designates a principal electro static charger, reference numeral 23 
designates a halogen lamp for copy illumination, reference numeral 24 
designates a developing device, and reference numeral 25 designates a 
transfer charger. 
This specific objective machine is provided with, for example, three 
sensors 1a, 1b and 1c. More specifically, the sensor 1a is an AE sensor 
for measuring the quantity of light incident on the photosensitive drum 
21, the sensor 1b is a surface potential sensor for measuring a surface 
potential of the photosensitive drum 21, and the sensor 1c is a 
densitometer for measuring the density of a picture image copied on paper. 
Furthermore, three types of actuators are provided. That is, three volumes, 
that is, a principal charge volume VR1 for changing a principal charge 
voltage of the photosensitive drum 21, a lamp volume AVR for controlling 
the quantity of light of the halogen lamp 23, and a transfer volume VR2 
for controlling a transfer voltage between the photosensitive drum 21 and 
copy paper are provided as the actuators. 
Meanwhile, when the electrophotographic copying machine shown in FIG. 10 is 
looked at from a physical point of view. the electrophotographic copying 
machine is expressed as a combination of a plurality of elements at a 
substance level, and behaviors and attributes of the respective elements 
as well as the combinational relationship among the respective elements 
are expressed qualitatively using parameters, as shown in Table 2. The 
form of expression will be referred to as a "substance model". 
TABLE 2 
______________________________________ 
Substance Model 
______________________________________ 
Exposure portion: X = H1 - D 
X : logarithm of original reflected quantity of light 
H1 : logarithm of halogen lamp output quantity of light 
D : optical density of copy 
Photosensitive portion: Vs = Vn - .beta. X 
Vs : surface potential after exposure 
Vn : surface potential after principal charge 
.beta. b : sensitivity of photosensitive substance 
Development portion: Ds = .gamma. c (Vs - Vb) 
Ds : toner density on drum 
.gamma. 0 : toner density 
Vb : bias voltage 
Output portion : Os = .zeta. f .multidot. Vt .multidot. Ds 
Os : toner density on output paper 
.zeta. : sensitivity of paper 
Vt : transfer voltage 
Separation portion: Sp = (Vt - Asp) .multidot. (Vs - Asp) 
Sp : adsorbing force between drum and paper 
Asp : amplitude of separating AC voltage 
______________________________________ 
Furthermore, the expression of FIG. 11 in which the substance model is 
abstracted and shown as a combined tree of the parameters will be referred 
to as a "parameter model". 
The "substance model" and the "parameter model" are referred to as an 
"objective model" collectively. The "objective model" is qualitative data 
common to image forming apparatuses which is also made use of for fault 
repair as described later. The respective contents of the substance model 
and the parameter model are stored in the objective model storage portion 
15 (see FIG. 3). 
In the substance model shown in the table 2 or the parameter model shogun 
in FIG. 11, the relationship between the time elapsed after the objective 
machine starts to be used and the degraded state is previously set with 
respect to each of parameters D1, D, Vn, .beta., Vb, .gamma.O, .zeta. and 
AsP basic to the construction of the objective machine, sensor parameters 
X, Vs and Os obtained from the sensors, and parameters which may be 
degraded, and is stored in the objective model storage portion 15. This 
relationship is a relationship as shown in FIG. 12 in the case of, for 
example, the parameter H1. When data on the time elapsed after the 
objective machine starts to be used, for example, data one month after the 
objective machine starts to be used, data two months after the objective 
machine starts to be used, . . . are applied from the relationship shown 
in FIG. 12, degraded states D1, D2, . . . of the parameter H1 are 
determined corresponding to the data. 
Furthermore, each of the parameters has a qualitative fuzzy quantity space 
as shown in FIG. 13. This qualitative fuzzy quantity space is created in 
accordance with membership functions determined for each parameter and is 
stored in the objective model storage portion 15. From the qualitative 
fuzzy quantity space shown in FIG. 13, it is possible to find the change 
in the value of the parameter H1 corresponding to the degraded state 
thereof. For example, the value of the parameter is (N: 1.0) when the 
degraded state is D1, while being ((0, N): 0.085, N: 0.915) when the 
degraded state is Dn. 
Additionally, the relationship between the degraded state and the degree to 
which a fault phenomenon occurs is previously set for each parameter and 
is stored in the objective model storage portion 15. This relationship is 
a relationship as shown in FIG. 14 when the parameter H1 is taken as an 
example. As can be seen from FIG. 14, the degree to which a fault 
phenomenon occurs is 0.9 when the degraded state is D1, while being 1.24 
when the degraded state is Dn. 
In the substance model shown in the table 2 or the parameter model shown in 
FIG. 11, the relationship between the time elapsed after the objective 
machine starts to be used and the degraded state may be estimated and set 
with respect to each of parameters H1, D, Vn, .beta., Vb, .gamma.O, .zeta. 
and Asp basic to the construction of the objective machine, sensor 
parameters X, Vs and Os obtained from the sensors, and parameters which 
may be degraded, and is stored in the objective model storage portion 15. 
In this case, this relationship is a relationship as shown in Table 3 with 
respect to, for example, the parameter H1. 
TABLE 3 
______________________________________ 
degree to which 
elapsed time FQ value of H1 
phenomenon occurs 
______________________________________ 
after one month 
N : 1.0 0.9 
after two (0, N) : 0.05 
0.92 
months N : 0.95 
after three (0, N) : 0.07 
0.93 
months N : 0.93 
: : : 
: : : 
: : : 
after n months 
(0, N) : 0.085 
1.24 
N : 0.915 
: : : 
: : : 
: : : 
______________________________________ 
From the relationship shown in the table 3, it is possible to immediately 
find the fuzzy qualitative value of the parameter H1 and the degree to 
which a fault phenomenon occurs (more specifically, the degree in the 
present embodiment is the degree to which there occurs a phenomenon that a 
halogen lamp is cut off) after an elapse of time, for example, after one 
month, after two months, . . . . 
Description is now made by giving several examples utilizing the foregoing 
description as a premise. 
EXAMPLE 1 
Example in which machine is normal one month (T1) after it is new 
The values obtained by the above described sensors 1a, 1b and 1c are 
previously converted into fuzzy qualitative values. 
More specifically, the quantity of light measured using the sensor 1a is 
used as the value of a parameter X. In addition, a surface potential Vs 
after exposure and a toner density Os on output paper are respectively 
measured by the sensor 1b and the sensor 1c. The values of the parameters 
obtained by the measurement are respectively mapped on the qualitative 
fuzzy quantity space as shown in FIG. 13 which is set for each parameter, 
to obtain, for example, the following sensor values of the parameters: 
X=((0, N): 0.1, N: 0.9) 
Vs=(N: 1.0) 
Os=((0, N): 0.1, N: 0.9) 
(1) Forecast of present degraded state 
Time information applied from the timer 19 are added up, to find the time T 
elapsed after the objective machine starts to be used. The time T is 
applied to the graph of the degraded state against the time elapsed after 
the objective machine starts to be used for each parameter as shown in 
FIG. 12, to estimate the present degraded state. As a result, the value of 
the parameter is found as an estimated value. The value of the parameter 
H1 is D1 because one month has elapsed since the objective machine started 
to be used (T=T1). 
(2) Examination of effects of degradation 
The value of the parameter H1 found in the foregoing item (1) is applied to 
FIG. 13, to obtain the following result: 
H1=(N: 1.0) 
Furthermore, the above described value of the parameter H1 is applied to 
FIG. 14, to obtain data, in which the degree to which there occurs a 
phenomenon that a halogen lamp (H1Cut) is cut off is 0.9, that is, to 
obtain the following result: 
p (H1Cut)=0.9 
When the table 3 is used, the results are as follows: Time information 
applied from the timer 19 are added up, thereby to find the elapsed time 
T=T1 of the objective machine. The elapsed time T1 is applied to the table 
3, to obtain the following results: 
H1=(N: 1.0) p1 (H1Cut)=0.9 
(3) Inference of present state of entire machine using result of above item 
(2) by SSIM 
The SSIM is made on the basis of the result of the foregoing item (2) 
(H1=(N: 1.0)) and the initial conditions (in this case, the amount of 
degradation is not calculated with respect to parameters other than H1 and 
thus, the remaining parameters are all (N: 1.0)). As a result of the SSIM, 
the values of all the parameters are (N: 1.0) as described below: 
______________________________________ 
H1 = (N : 1.0) .gamma. 0 = (N : 1.0) 
D = (N : 1.0) Vt = (N : 1.0) 
.beta. = (N : 1.0) .zeta. = (N : 1.0) 
Vn = (N : 1.0) Asp = (N : 1.0) 
Vb = (N : 1.0) 
______________________________________ 
(4) Fault judgment 
The following knowledge is used as the reference for fault judgment. This 
knowledge is previously stored in the objective model storage portion 15 
(see FIG. 3). 
(a) Fault evaluation of machine 
N value.gtoreq.0.5 
.fwdarw.normal 
.fwdarw.compare the degree of coincidence between the value on the model 
and the measured value 
N value&gt;0.5 
.fwdarw.abnormal 
.fwdarw.fault diagnosis 
(b) Comparison between value on model and measured value 
the degree of coincidence between the value on the model and the measured 
value.gtoreq.0.5 
.fwdarw.no fault 
the degree of coincidence between the value on the model and the measured 
value&gt;0.5 
.fwdarw.display message such as "there is a possibility that the sensor is 
abnormal" 
In the present embodiment, (a) the function evaluation of the machine is 
first carried out. In this case, comparison may be made with respect to 
Os. Accordingly, comparison is made using Os=((0, N): 0.1, N: 0.9) 
obtained by converting the measured value of Os into a fuzzy qualitative 
value. In this case, the value of N is 0.9. Accordingly, N .gtoreq.0.5, so 
that the result of (a) the function evaluation becomes normal. 
Then, (b) comparison is made between the value on the model and the 
measured value. 
Comparison is made between each of the sensor values and the value on the 
model obtained as the result of the above described item (3), to find the 
degree of coincidence therebetween from the following conditions: degree 
of coincidence=max (min (grade of each item)) Consequently, the following 
results are obtained: 
______________________________________ 
sensor value 
model value min value 
______________________________________ 
x : (0, N) 
0.1 0 
N 0.9 1.0 0.9 
max 0.9 
Vs : N 1.0 1.0 1.0 
max 1.0 
Os : (0, N) 
0.1 0 0 
N 0.9 1.0 0.9 
max 0.9 
______________________________________ 
Furthermore, the degree of coincidence in the entire machine is as follows: 
the degree of coincidence in the entire machine 
=the average of the degrees of coincidence between the values of the 
respective sensors and the value on the model 
=(0.9+1.0+0.9)/3=0.93 
Meanwhile, the degree of coincidence in the entire machine may be found 
under more strict conditions by taking not the average value but the 
minimum value of the degrees of coincidence between the values of the 
respective sensors and the value on the model. 
When the above described reference for fault judgment (b) is applied, the 
average of the degrees of coincidence exceeds 0.5, so that it is judged 
that the result is normal. More specifically, the results of both (a) and 
(b) are normal, so that the objective machine can continue to be used. In 
the above described embodiment, when the result of (a) the function 
evaluation of the machine is normal and the result of (b) the comparison 
between the value on the model and the measured value is abnormal (a case 
where the program proceeds from the step S8 to the step S9 in FIG. 8), 
there is a possibility that the sensor for measuring the parameter 
relating to the function evaluation, that is, Os is abnormal, so that a 
message "there is a possibility that the sensor is abnormal" is displayed. 
EXAMPLE 2 
Example in which machine fails one month (T1) after it is new, similarly to 
Example 1 
The values of the sensor parameters X, Vs and Os are as follows: 
X=(0: 0.9, (0, N): 0.1) 
Vs=(N: 0.1, (N, nil): 0.9) 
Os=(N: 0.1, (N, nil): 0.9) 
Furthermore, when (2) the effect of the amount of degradation is examined 
after (1) forecast of present degraded state, the following results are 
obtained as the values of the parameters: 
H1=(N: 1.0) 
P (H1Cut)=0.9 
When (3) the SSIM is made in such a state, the values of all the parameters 
on the model obtained become (N: 1.0). 
(4) Fault judgment 
(a) Function evaluation of machine 
N=0.1 from the fuzzy qualitative value of Os, so that N&lt;0.5. Accordingly, 
the result of the function evaluation is abnormal. Consequently, a fault 
is diagnosed. 
(5) Derivation of fault candidate 
The following information are previously stored as fault candidates in the 
objective model storage portion 15. 
H1Cut: H1=0 
H1Out: H1=(0, N) 
VtOut: Vt=(0, N) 
PaperOut: .zeta.=(0, N ) 
VbOut: Vb=(N, nil) 
TonnerOut: .gamma.0=(0, N) 
MCOut: Vn=(0, N) 
Meanwhile, Out means being faulty. 
Such functional abnormality that Os is large, that is, Os=(N, nil) which is 
found in the foregoing item (4) is traced on the parameter model shown in 
FIG. 11, to obtain FIG. 15. In FIG. 15, parameters marked with upward 
arrows are parameters whose value may be changed into (N, nil), parameters 
marked with downward arrows are parameters whose value may be changed into 
(0, N) or (0), and parameters marked with no arrows are parameters whose 
value remains normal. As a result, H1Cut and H1Out out of the above 
described fault candidates are taken out as fault candidates. 
(6) The SSIM is made with respect to the two fault candidates found in the 
foregoing item (5), to infer the fault state at that time. More 
specifically, the SSIM is made with respect to H1Out, to obtain the 
following two types of models: 
______________________________________ 
H1 = ((0, N) : 1.0) 
D = (N : 1.0) 
X = (0 : 1.0) or ((0, N) : 1.0) 
.beta. = (N : 1.0) 
Vs = ((N, nil) : 1.0) 
Yn = (N : 1.0) 
Vb = (N : 1.0) 
.gamma. O = (N : 1.0) 
Ds = ((N, nil) : 1.0) 
Vt = (N : 1.0) 
.zeta. = (N : 1.0) 
Os = ((N, nil) : 1.0) 
Asp = (N : 1.0) 
Sp = ((N, nil) : 1.0) 
______________________________________ 
Two types of models are obtained because X takes two types of values. The 
reason for this is as follows: The value of X is a value obtained by 
subtracting D from Hi. However, H1=(0, N) and D=(N) . Accordingly, if 
"Normal" is subtracted from "Smaller than normal", two types of cases are 
considered as a results of the fuzzy operation, that is, "Smaller than 
normal" remains or the answer becomes zero. 
Furthermore, the SSIM is made with respect to H1Cut, to obtain the 
following two types of models: 
______________________________________ 
H1 = (0 : 1.0) 
D = (N : 1.0) 
X = (0 : 1.0) or ((0, N) : 1.0) 
.beta. = (N : 1.0) 
Vs = ((N, nil) : 1.0) 
Yn = (N : 1.0) 
Vb = (N : 1.0) 
.gamma. 0 = (N : 1.0) 
Ds = ((N, nil) : 1.0) 
Vt = (N : 1.0) 
.zeta. = (N : 1.0) 
Os = ((N, nil) : 1.0) 
Asp = (N : 1.0) 
Sp = ((N, nil) : 1.0) 
______________________________________ 
(7) Specification of causes of fault 
The causes of the fault are assigned priority and are narrowed down from 
the degree of coincidence between the model and the sensor and the degree 
to which a phenomenon occurs. 
(i) Degree of coincidence between model and sensor 
______________________________________ 
A. H1Out X = 0 B. H1Out X = (0, N) 
X 0.9 X 0.1 
Vs 0.9 Vs 0.9 
Os 0.9 Os 0.9 
whole 0.9 whole 0.63 
C. H1Cut X = 0 D. H1Cut X = (0, N) 
X 0.9 X 0.1 
Vs 0.9 Vs 0.9 
Os 0.9 Os 0.9 
Whole 0.9 whole 0.63 
______________________________________ 
The degree of coincidence between the model obtained as a result of making 
the SSIM with respect to each of the fault candidates in the item (6) and 
the sensor is found as described above. 
The model obtained in the item (6) is a parameter model on which the causes 
of the fault (for example, H1=((0, N): 1.0) for H1Out) are set and the 
effect of the causes of the fault on the other parameters is traced. 
Consequently, the higher the degree of coincidence between the value of 
the sensor paid attention to and the value of a parameter corresponding 
thereto on the model is, the closer the present state of the objective 
machine is to the model. In other words, the possibility that the causes 
of the fault assumed so as to derive the model are the present causes of 
the fault is high. 
In the present embodiment, the degrees of coincidence between the models 
with respect to H1Out and H1Cut and the sensor are simultaneously 0.9, so 
that H1Out and H1Cut are both considered as the causes of the fault. 
The above described four models are assigned priority as follows: 
Priority 1. A, C: 0.9 
2. B, D: 0.63 
The priority of the causes of the fault may be previously stored in the 
objective model storage portion 15 shown in FIG. 3 or the like when a 
plurality of causes are thus derived, to narrow down the causes of the 
fault in accordance with the priority. In the present embodiment, the 
following operation is performed so as to further narrow down the causes 
of the fault. 
(ii) Degree to which phenomenon occurs 
The causes of the fault are narrowed down by multiplying the value 
indicating the degree of coincidence by the value indicating the degree to 
which there occurs a phenomenon which is derived in the stage in which the 
effect of the amount of degradation obtained in the item (2) is examined, 
as described below: 
p (H1Out)=1 
(H1Cut)=0.9 
Priority 1. A: 0.9.times.1.0=0.9 1.0 when normalized 
2. C: 0.9.times.0.9=0.81 0.9 when normalized 
9. B: 0.63.times.1.0=0.63 0.7 when normalized 
4. D: 0.63.times.0.9=0.57 0.63 when normalized 
The highest calculated value of (degree of coincidence) .times.(degree) is 
assigned the highest priority. Accordingly, it is found that H1Out is most 
doubtful. Therefore, such a repair is made as to change the quantity of 
light of the halogen lamp. 
EXAMPLE 3 
Example in which machine is degraded n months (nT1) after it starts to be 
used 
The fuzzy qualitative values of the respective parameters are found as 
follows from the measured values obtained from the sensor: 
X=(N: 0.8, (0, N): 0.2) 
Vs=(N: 0.9, (N, nil): 0.1) 
Os=(N: 0.9, (N, nil): 0.1) 
(1) Forecast of the present degraded state 
As aresult of applying the condition nT1 to FIG.2, following is obtained: 
H1=Dn 
(2) Examination of effect of amount of degradation 
The following is obtained by applying the result H1=Dn found in the 
foregoing item (1) to FIG. 13: 
H1=(N: 0.915, (0, N): 0.085) 
On the other hand, the result is as follows by applying H1=Dn to FIG. 14: 
(H1Cut)=1.24 
(3) Inference of present state of entire machine using result of above item 
(2) by SSIM 
From the result in the foregoing item (2) and the initial conditions, the 
following results are obtained: 
H1=(N: 0.915, (0, N): 0.085) 
D=(N: 1.0) 
.beta.(N: 1.0) 
Vn=(N: 1.0) 
Vb=(N: 1.0) 
.gamma.0=(N: 1.0) 
Vt=(N: 1.0) 
.zeta.=(N: 1.0) 
Asp=(N: 1.0) 
The SSIM is made under the conditions, to obtain the following results: 
______________________________________ 
H1 = (N : 0.915, (0, N) : 0.085) 
D = (N : 1.0) 
X = (N : 0.915, (0, N) : 0.085) 
or 
(N : 0.915, 0 : 0.085) 
.beta. = (N : 1.0) 
Vs = (N : 0.915, (N, nil) : 0.085) 
Vn = (N : 1.0) 
Vb = (N : 1.0) 
.gamma. 0 = (N : 1.0) 
Ds = (N : 0.915, (N,nil) : 0.085) 
Vt = (N : 1.0) 
.zeta. = (N : 1.0) 
Os = (N : 0.915, (N, nil) : 0.085) 
Asp = (N : 0.1) 
Sp = (N : 0.915, (N, nil) : 0.085) 
______________________________________ 
The results indicate that an image may be high in density as the effect of 
the degradation of H1 (Os is raised). In addition, the combined effect of 
the degradation of a plurality of components and consequently, faults 
serially occurring can be generally inferred from the changes in value of 
the parameters. 
(4) Fault judgment 
(a) Function evaluation of machine 
N=0.9 from the fuzzy qualitative value of Os, so that N.gtoreq.0.5. 
Accordingly, the result of the function evaluation is normal. 
(b) Comparison between value on model and measured value 
Each of the sensor values and the value on the model obtained as the result 
in the foregoing item (3) are compared with each other, to find the degree 
of coincidence therebetween. 
A. Model of X=(N: 0.915, (0, N): 0.085) 
Degree of coincidence between the sensor and the model 
______________________________________ 
X : 0.8 
Vs : 0.8 
Os : 0.8 
whole 0.87 
______________________________________ 
B. Model of X=(N: 0.915, 0: 0.085) 
Degree off coincidence between the sensor and the model 
______________________________________ 
X : 0.8 
Vs : 0.9 
Os : 0.9 
whole 0.87 
______________________________________ 
Accordingly, it is found that the sensor value possibly coincides with the 
value on the model A or B. In conclusion, it is judged that the result of 
the function evaluation of the machine is normal, so that the machine can 
be normally used, through it is degraded to be brought into the state of 
the model A or B. 
EXAMPLE 4 
Case where fault occurs under same conditions as Example 3 
The following data are obtained as sensor values: 
X=(N: 0.1, (0, N): 0.9) 
Vs=((N: nil): 1.0) 
Os=((N: nil): 1.0) 
Furthermore, the same results as those in the items (1) to (3) in the above 
described example 3 are obtained by applying values of H1 and T to FIG. 
12, FIG. 13 and FIG. 14. 
(4) Fault judgment 
(a) Function evaluation of machine 
N=0 from the fuzzy qualitative value of Os, so that N &lt;0.5. Accordingly, 
the result of the function evaluation is abnormal. Consequently, it is 
judged that the machine fails. 
(5) Derivation of fault candidate 
Fault candidates previously stored are the same as those described in the 
foregoing item (5) in the example 2. Therefore, Os=(N, nil) is traced on 
the parameter model shown in FIG. 11, to obtain H1Cut and H1Out as fault 
candidates. 
(6) Fault simulation by SSIM 
The same results as those in the item (6) in the example 2 are obtained 
with respect to H1Cut and H1Out. 
In the present embodiment, description is made considering that only an 
exposure portion is degraded for simplification. Accordingly, the results 
of the fault simulation in this example 4 are the same as those in the 
example 2. However, the same results are not generally obtained because 
the values of the other parameters are changed by the effect of the 
degradation. For example, when .zeta.=(N: 0.8, (0, N): 0.2) as the effect 
of the degradation of the output portion, the following results are 
obtained with respect to H1Out: 
______________________________________ 
H1 = ((0, N) : 1.0) 
D = (N : 1.0) 
X = ((0, N) : 1.0) 
or 
(0 : 1.0) 
.beta. = (N : 1.0) 
Vs = ((N, nil) : 1.0) 
Vn = (N : 1.0) 
Vb = (N : 1.0) 
.gamma. 0 = (N : 1.0) 
Ds = ((N, nil) : 1.0) 
Vt = (N : 1.0) 
.zeta. = (N : 0.8, (0, N) : 0.2) 
Os = ((0, N) : 0.2, N : 0.2, (N, nil) : 0.8) 
((0, N) : 0.18, N : 0.18, (N, nil) : 0.8) when 
normalized 
Asp = (N : 1.0) 
Sp = ((N, nil) : 1.0) 
______________________________________ 
(7) Specification of causes of fault 
The causes of the fault are assigned priority and are narrowed down from 
the degree of coincidence between the model and the sensor and the degree 
to which a phenomenon occurs. 
(i) Degree of coincidence between model and sensor 
______________________________________ 
A. H1Out X = 0 B. H1Out X = (0, N) 
X : 0.9 X : 0.1 
Vs : 1.0 Vs : 1.0 
Os : 1.0 Os : 1.0 
whole 0.97 whole 0.7 
C. H1Cut X = 0 D. H1Cut X = (0, N) 
X : 0.9 X : 0.1 
Vs : 1.0 Vs : 1.0 
Os : 1.0 Os : 1.0 
whole 0.97 whole 0.7 
______________________________________ 
Priority 1. A, C: 0.97 
2. B, D: 0.7 
(ii) Degree to which phenomenon occurs 
p (H1Out)=1 
p (H1Cut)=1.24 
Priority 1. C: 0.97.times.1.24=1.20 1.0 when normalized 
2. A: 0.97.times.1.0=0.97 0.81 when normalized 
3. D: 0.7.times.1.24=0.87 0.73 when normalized 
4. B: 0.7.times.1.0=0.7 0.58 when normalized 
Accordingly, C is most doubtful. In addition, at least H1Cut is doubtful. 
However, H1Cut means that the halogen lamp is cut off and the repair 
cannot be made, so that the repair is not made. 
Meanwhile, it can be judged by dividing the causes of the fault into the 
causes of the fault which can be repaired and the causes of the fault 
which cannot be repaired, storing the causes of the fault in the objective 
model storage portion 15 shown in FIG. 3, and suitably referring to the 
causes the fault whether the causes of the fault can be repaired. In 
addition, when the cause of the fault which cannot be repaired is derived 
as the highest priority one, a message "the repair cannot be made" may be 
displayed on the display portion. 
Although the present invention has been described and illustrated in 
detail, it is clearly understood that the same is by way of illustration 
and example only and is not to be taken by way of limitation, the spirit 
and scope of the present invention being limited only by the terms of the 
appended claims.