379
COMPLEX ESTIMATION OF ELECTRONIC TECHNICAL EQUIPMENT
PRODUCTS QUALITY ON THE BASIS OF IMAGE RECOGNITION
THEORY
Y.V. Zakharov1
1Mari
State Technical University, Lenin Sq., 3, Yoshkar-Ola, Mari El, 424000, Russia,
tel.: 8(8362) 455412. E-mail: [email protected]
Issues of complex estimation of electronic technical equipment products quality in view
of absence or presence of correlation ties between individual parameters are considered.
In case of dependence on individual parameters of a product the method of image
recognition theory, the method of statistical decision, is applied to solve the problem.
Nowadays the problem of complex estimation
of electronic technical equipment products
quality (ETP) in view of the set of individual
parameters (IP) describing special properties
of a product is getting more and more important. Average weighted arithmetic, geometric and harmonic parameters have widely been
applied for complex estimation of ETP quality.
The basic restriction for using average
weighted parameters is the fact that they do
not take into account correlation ties of ETP
IP. In this case it is recommended to use one
of methods of image recognition theory – the
method of statistical decision.
The essence of the method with reference to
the problem being solved consists in the following. For single-type ETP under consideration IP quality values are measured. In kdimensional space of controllable parameters
each product i has certain corresponding values of vector x {хij} of IP measured values
(j=1,2...,k). Using the method of casual selection the training sample including two classes
of products is formed: qualitative (with number n1) and having poor quality in at least one
IP (n2). The elements of vectors of average
values and the elements of co-variation matrixes are estimated applying the material of
the training sample. For the co-variation matrixes not happen to be singular several requirements are necessary to be met: n1≥k;
n2≥k. The results are usually good when the
ratio of products number to IP number exceeds
10.
Then the deciding rule is constructed allowing
to attribute a product, the quality of which is
estimated in aggregate k IP, to a certain class
in view of value of vector х. For this purpose
the ratio logarithm for functions of probabili

ties f1( x ) and f2( x ) density in classes is calcu


lated: ln[f1( x )/f2( x )] ≡ L( x ).

The obtained value L( x ) is compared to


threshold value Lпор( x ) ≡ λ. Given L( x ) > λ
the product is attributed to the class of qualita
tive production, given L( x ) ≤ λ – to the class
of poor-quality production. To choose λ
threshold various approaches are used, but
more often than not its value is set taking into
account the condition of minimum average
risk caused by 1st and 2nd type mistakes and
providing the maximum rate of correct distribution of all the products within the classes of
qualitative and non-qualitative production.
In spite of the fact that the method of statistical
decisions is based on the assumption of normal
distribution of products quality IP in classes, it
allows to receive satisfactory results for a
broad class of distributions distinct from normal. Therefore its application does not need
checking of a hypothesis about the normality
of distributions, it may be used in all the cases
where a required level of mistake probability
in quality estimation is provided. In view of
above-stated the following algorithm of com-
380
plex estimation of ETP quality is offered on
the basis of the images recognition theory.
Mathematical equations used in the algorithm
are given in [1].
1. Training
Given the results of measurements k of IPs,
classification of n products into two classes is
realized: 1 class – appropriate (n1); 2 class –
inappropriate in at least one IP quality (n2) as
to the requirements of the specifications and
technical documentation (STD) for a product.
Values L(x) for all n products are calculated:
 
 

Li( ) = 0,5[-( x - m1 )*Д1( x - m1 ) + ( x -
 
 

Д -1
 
2
m 2 )*Д2( x - m 2 ) + ln
],
(1)
Д1-1
where x
– vector of measured IP values
for a concrete i product;
m1, m2
– vectors of average IP values
for products of 1st and 2nd classes;
* – the sign of transposing;
Д1,Д2 – co-variation matrixes for the 1st and
2nd class products;
Д1-1, Д2-1
– inverse matrixes for Д1 and
Д2;
i = 1,2,...,n; n1+n2 = n.

The calculated values Li( x ) are listed in a de
crease order of L( x ) values. Thus «the picture
of recognition» is obtained. Using «the picture
of recognition» the threshold λ of a deciding
rule providing maximum ratio of correct
recognition Р of all products when classifying
them as appropriate and inappropriate as to the
requirements of STD.
 n  n21 
Р = 1  12
(2)
  100% ,
n


where n12 (n21) – number of products of the
first (second) class, attributed by the deciding
rule to the second (first) class.
2. Control and complex estimation of products quality
Given the results of measurements k of IP
quality for a controllable product nfin, the value

Lкон( x ) is calculated using equation (1). When

calculating Lкон( x ) statistical data obtained at

a training level are used. Lкон( x )> λ, nкон Є to

the first class; Lкон( x )≤λ, nкон Є to the second
class.
A numerical value of complex quality parame
ter (CQP) Q = Li( x )/λ is derived from the
whole number of controllable products satisfy
ing the Lкон( x ) > λ, i = 1,2,…,q. The product
with value Qmax possesses a maximum level of
the generalized quality in the whole k of IPs.
Classification of products according to CQP is
made using descending sort of Q value.
In complex estimation of ETP quality in case
of independence of IPs it is necessary to use
the average weighted parameters and in case
of statistical dependence – the instrument of
the image recognition theory.
References
1. Барабаш Ю.Л. Bопросы статистической теории
распознавания образов. - М.: Советское радио, 1987.