10: COMPLEX QUALITY ASSESSMENT

Lecture questions:

1. Comprehensive quality indicator

2. Calculation of the indicator based on weighted average arithmetic values ​​of properties

3. Calculation based on weighted geometric properties

1. Comprehensive quality indicator

A comprehensive assessment of the quality level involves the use of

The development of complex indicators of sets of properties. This is

Tod is used in cases where it is necessary to most accurately assess

quality of complex products. The need for the "convolution" of all

indicators of properties in order to obtain one complex

indicator is determined by practical feasibility.

Comprehensive indicator of the combination of properties of K depends

from the "weighted" parameters of the properties taken into account

ki i. from indicators of individual properties, taking into account their weight, significance

for K. Therefore, K = f ( k i), where

ki is a quantity characterizing the size of the i -th property, taking into account its significance;

i = 1, 2, 3, ..., p ; where n is the total number of properties taken into account.

Requirements for an integrated indicator

qualities are:

1) representativeness - the representation in it of all the

new product characteristics, by which its

honor;

2) the monotony of changes in the complex indicator

the quality of the product when changing any of the single indicators

quality at fixed values ​​of other indicators;

3) criticality (sensitivity) to varying para-

meters. This requirement is that the integrated display

The quality manager must respond in a coordinated manner to changes in each

from individual indicators. Comprehensive indicator is

the function of evaluating all indicators of properties, and its sensitivity

determined by the first derivative of this function. Value com

plex indicator should be especially sensitive in those

In cases where a single indicator goes beyond

allowable limits. At the same time, a comprehensive quality indicator

should significantly reduce its numerical value;

4) normalization - the numerical value of the complex

the indicator concluded between the greatest and least significant

relative quality indicators. This requirement

normalization determines the scale of the scale

rhenium complex indicator;

5) comparability

(comparability) of the results

full quality assessment is ensured by the uniformity of

Dov their calculations, in which indicators of the properties should be

razheny in dimensionless quantities.

Conversion of natural dimensions to dimensionless (reduced

d) units of measurement is carried out by appropriately

conversion.

For example, a linear dependence of the form is often used:

q = wx P,

where q is the value of the indicator in dimensionless numbers, in points or parts;

P - value of the indicator in physical units;

w is the conversion factor.

The use of linear dependence simplifies the conversion

single indicator, expressed in natural units

measurements in a dimensionless measure. However, in a number of cases

Tea needs to accept non-linear function dependency

q = f ( P )

. The formula for this relationship is derived from

or observing the nature of the change in P.

The level of product quality, determined by the complex

method is the ratio of the complex indicator

the properties of the estimated object (Kotz) to the corresponding indicator of the base sample ( K ots

bases), i.e .: Yk = Kotz / Kbaz

Comprehensive indicator of the combination of different properties

K must take into account the significance (weight) of each of them, i.e.

take into account the degree of influence of the values ​​of individual properties on the final

indicator

(level) quality. Quantitative characteristic

The significance of this indicator among other indicators is

weight coefficient. When finding the value of the complex

value of the aggregate characteristics of the properties necessary

parameter value of each of the many properties of "weigh",

those. multiply by the appropriate weight coefficient.

With a comprehensive method of quality assessment determine

the so-called weighted average of the aggregates of all

taken into account properties.

2. Calculation of the indicator based on weighted average arithmetic values ​​of properties

If the values ​​of the properties taken into account are proportional to the influence

on the final quantitative assessment of quality, then the value of K

find as a weighted average arithmetic by the formula:

Where

ai is the weight coefficient of the i- th parameter (property);

qi is the dimensionless quantity of the ith property;

n - the number of considered properties.

The quality level of the estimated object, determined by the weighted arithmetic indices of the aggregates

The properties of Ka.oc and Ka.oc are:

Another formula for calculating Yk.a is also known:

Subject to restrictions on the limiting values

properties, and considering their importance, it is recommended that

read the weighted arithmetic values ​​of such properties

according to the formulas:

Where

P iпр - the limiting value of the parameter of the i -th property;

ai is the weight coefficient of the i -th property.

If all indicators of properties have limitations

on their limiting values, the assessment (level) of the quality of the object

find the weighted average of the arithmetic values ​​of aggregate indicators of properties as

Another way to find a quantitative assessment of the quality

complex method is that initially

find the relative values ​​of the levels of all units considered

individual and generalized indicators of properties (if there is a generalized

indicators of property groups), that is, calculate Yi ( i = 1, 2, 3 .... n properties). Knowing the meanings of all

Yi, find the corresponding values ​​of Yk, i.e. Y.a. or Ykg

Consequently, a comprehensive indicator of the level of quality

determined by weighted average arithmetic values

separate levels of properties, calculated by the formula:

Where

ai is the weight coefficient of the i -th index of the level of the corresponding properties;

Yi is a relative indicator of the i -th property of the evaluated and base objects (samples).

3. Calculation based on weighted geometric properties

If the influence of the properties taken into account on the value of K

non-linear, power dependence, then calculate

weighted average of these properties

formula:

where m i = 1 / b - weight coefficient;

- the number of evaluated quality indicators;

bi is the denominator of the number of the i -th weight index (degree, root);

qi is the dimensionless (reduced by the conversion coefficient w ) value of the parameter of the i -th property;

n - the number of considered properties.

The calculation of the level of quality for "geometrically weighted"

indicators of sets of properties carried out according to the formula:

Where

Kgc - geometric index of the evaluated sample;

Kg base is the geometric index of the base sample.

Weighted average geometric complex display

the body of quality (quality level) is calculated by the formula:

Where

mi is the weight coefficient of the i- th property;

ki is the denominator of the number of the i -th weight index (degree, root);

Yi- level of property i ;

n - the number of considered properties.