Quality control. Methods for evaluating technological processes

where Ki are partial quality indicators,

P is the sign of the work.

In turn, individual indicators are defined as

where Kf is the actual level of quality,

Ke - the level of the best sample (standard).

With a comprehensive assessment of the quality of p

The average weighted arithmetic indicator can also be used for production, when the averaged initial relative indicators Ki differ relatively little from each other:

, (2.7)

where Ki is private relative indicator quality;

Wi - coefficients of weighting indicators (determined by experts).

If the value of the summary quality indicator is greater than one, then we can conclude that the product sample in question is better in terms of the quality of the base sample.

Much more often, the method of relative linear estimates is used to assess the quality level. In this case, the integral assessment of the quality level is found by the formula:

, (2.8)

where Кfi is the actual level of quality,

Kei - reference (normative) level.

Formula (2.6) can also be used to assess the instability of the technological process, while the formula for calculating the summary indicator of instability (Kn) takes the following form:

, (2.9) AAAAAAAAAAAAAAAAAAAAAAAAAAA

where Kni are the actual process parameters,

Pni - normative (specified by the technological regulations) parameters;

i is the number of parameters;

n is the number of measurements.

The considered approaches can also be used in tasks when it is necessary to give a summary assessment of the quality of the enterprise, taking into account many indicators. For their application necessary condition is the presence of standard (reference) values ​​with which you can compare the actual levels of indicators.

Example 1. According to the methodology of the generalized assessment of the quality of the State Standard of Russia, check the compliance of the quality of electric lamps with the standard. The average duration of burning of electric lamps of a certain power, manufactured by the enterprise, is 420 hours. The reference value of the service life is 450 hours. Coefficient useful action has a reference value of 20 lm/W and an actual coefficient of 19 lm/W.

The actual level of quality of produced electric lamps is 11.3% lower than the reference one.

Example 2. There is data on the quality levels of the same type of automatic washing machines manufactured by Vesta (Vyatka-Alenka) and Ariston according to passport data. Give a comparative assessment of the quality levels of machine tools, if the weight coefficients of each factor determined by the expert are 0.31, 0.29, 0.03, 0.07, 0.3, respectively.

Level of quality washing machine	Units	"Alenka"	"Ariston"
Water consumption per main wash cycle
Longest wash cycle time at 90°C with cold water only
Power consumption
Warranty period

In order to determine the relative level of quality of washing machines, a composite quality factor is calculated according to the method proposed by Professor V.A. Trapeznikov. When calculating the coefficients, the nature of the indicators is also taken into account. For "positive" indicators, with an increase in the values ​​of which the quality increases, formula (2.4) is chosen, and for "negative" indicators, with an increase in the values ​​of which the quality of the product decreases, the inverse formula is used.

The relative quality level of the Ariston automatic washing machine is 11% higher than the quality level of the Vyatka-Alenka automatic washing machine.

Example 3. There are data on the results of measurements of the concentrated parameters of the technological process during the work shift.

By technological regulations standard values are: pressure - 100 kPa, acidity - 6.0.

Determine by the method of relative linear estimates the summary relative indicator of the instability of the technological process.

Measurement number	Pressure	Acidity	Sum of relative deviations

In the process machining workpiece, any technological process, the accuracy of its manufacture is affected by a fairly large number of different factors. So, for example, when processing parts on a machine, a machine tool, a device for installing and fixing parts and a cutting tool, a cutting tool, the workpieces themselves, an equipment adjuster, environment etc. Due to the action of various production factors the indicators of the final result of the selected technological process are also constantly changing.

Therefore, despite the fact that the parts are manufactured using the same technological process, with constant processing modes and in automatic mode, that is, without human intervention, they all differ from each other and from the calculated “ideal” prototype. This phenomenon is called the dispersion of a random variable, in particular, the accuracy of manufacturing the output parameters of the part.

To analyze the accuracy of manufacturing parts by the selected technological process, we use various methods, allowing to take into account the influence of various production factors. These methods include: the method of direct observation or the method of scatter plots, analytical and statistical methods.

Most commonly used in manufacturing scatter plot method, which allows you to determine the influence of regularly changing factors on manufacturing accuracy. The method requires enough a large number observations and is used in large-scale production.

Analytical method requires a mathematical description of all primary factors affecting the processing error, the method is quite laborious and is used in individual cases.

Statistical Method based on the principles of probability theory and mathematical statistics. It is known from probability theory that if the scattering of any quantity (size, surface roughness, material hardness, etc.) depends on the combined action of many factors of the same order of magnitude, which are random, independent or weakly dependent on each other, then the scattering obeys the law normal distribution or Gaussian law.

The theoretical law of normal distribution in a coordinate system in which the origin coincides with the axis of symmetry of the curve Z.2 or with an average deviation value, expressed by the formula

Y \u003d j (x) \u003d e - (3.2)

where is the standard deviation of a random variable;

- frequency corresponding to the value X.

To analyze the accuracy of the selected technological process, the actual dimensions of the batch of parts are measured and a distribution curve is built.

Difference between minimum and maximum actual dimensions

measured parts are divided into equal intervals.

Determine the number of sizes of parts in each Fig.3.2

interval.

The curve is constructed in the following sequence. The abscissa shows the size dispersion field, which is defined as the difference between the actual maximum and minimum size X f.max - X f.min. = 6, in the chosen scale. From the middle of each interval, along the y-axis, the relative frequency is plotted W \u003d m / N, where m is the number of sizes of parts that fall into this interval, N is the total number of parts in the measured batch. Based on the points obtained, a broken curve of the actual size distribution is built. The larger the batch of parts, the smoother the broken curve becomes, and in its appearance approaches the curve of the normal distribution law (Gaussian curve) Fig. 3.3. On the graph, the designations X d min and X d max determine allowable max and min values ​​of the controlled size or tolerance limits, the value specified by the constructor. Regions A i and B i correspond to the value of a correctable and irreparable marriage, and the value of a i defines the offset of the dimension grouping center relative to the middle of the tolerance field. The normal distribution curve is symmetrical about the axis corresponding to the abscissa M (x) or X CP, the arithmetic mean of the deviations. The arithmetic mean of the deviations is called the center of size grouping or the center of dispersion of a random variable.

Fig.3.3

The theoretical curve of normal size scattering extends in both directions along the abscissa axis indefinitely, asymptotically approaching this axis. For theoretical calculations, limit deviations (when using the law of normal scattering), expressed in fractions of the standard deviation, are usually limited by the values ​​\u200b\u200band the scattering field 6.

The area under the curve of the normal distribution, which is in

in the zone limited to 6, is 99.73% of the total area and only 0.27% go beyond the scattering field.

If the entire area under the normal distribution curve is taken as 100% or as a unit, then its unshaded area will correspond to the fraction of deviations of the random variable that fits into the interval .

With an increase in the scattering interval more than the area under the curve increases slightly, with a decrease to the area under the curve sharply

is shrinking.

The nature of the dispersion of sizes is most clearly revealed by drawing up the so-called distribution curves. To obtain a reliable distribution curve, it is recommended to obtain at least 200 - 300 measurements of the actual values ​​​​of a given size, in many cases, however, practically acceptable results can be obtained with a number of measurements of about 100.

The number of parts to be measured to determine the standard deviation depends on the accuracy with which you want to determine this deviation.

It is known from mathematical statistics that the root mean square error in determining the root mean square value is:

where N is the number of measurements, and E is the error in fractions of .

To obtain with an accuracy of 5%, it is necessary to solve the equation

, whence N 200.

To determine the standard deviation with an accuracy of 10%, 50 parts must be measured.

The form of the actual distribution curve depends on the considered manufacturing process, the number of parts subjected to measurements and a number of other factors.

The difference between the maximum dimensions of the parts of a given batch, the "dispersion field" - characterizes the magnitude of random errors. The systematic error, which is constant within the batch, does not affect the shape of the distribution curve - it only causes a shift of the entire curve in the direction of the x-axis.

If the manufacturing accuracy is affected by regularly changing production factors, then the normal distribution curve will be asymmetric about the grouping center. The construction and study of distribution curves for various operations allow us to draw a number of conclusions related to the accuracy of processing; and, first of all, they make it possible to separate the influence of constant systematic errors from the influence of random errors.

Further, the same studies make it possible in some cases to predict the value of random errors, based on the batch of parts examined earlier. A number of works on the study of the distribution curves of the sizes of parts show

close coincidence of the actual distribution curves with the normal distribution curve, the equation of which is:

(3.4)

where x i are the current coordinates of the curve,

X is the arithmetic mean of all values,

(3.5)

here … m n- number of parts with deviations, x 1, x 2 .... x n

The mean square deviation of dimensions, is determined by the formula

(3.7)

In formulas (3.26 and 3.27)

N is the total number of measured parts, and

m is the number of parts with the same size deviation.

If the actual distribution of sizes (or deviations) is practically

Fig.3.4

comes close to the normal distribution law, then it can be quite fully characterized by the value of the standard deviation. From here, a mandatory inequality can be derived that relates the tolerance value for a given size () and the value of the standard deviation:.

In Fig.3.4. the case is given when the tolerance field is equal to the size dispersion field, in the absence of a systematic error caused by incorrect machine settings.

To obtain the required dimensions of the part, in the process of machining, the machine is set up with the expectation of obtaining a grouping center () in the middle of the tolerance field. In practice, various options for the influence of random factors on the nature of the location and the magnitude of the dispersion field relative to the tolerance field are possible. In particular, Fig.3.5 and Fig.3.6 show cases when the grouping center coincides with the middle of the field

Fig.3.5 Fig.3.6

tolerance, and or . In the first case, all parts meet the requirements for manufacturing accuracy. In the second case, marriage appears as a correctable A i, and incorrigible B i. To exclude the possibility of a defect, it is necessary to change the technological process of processing, and in particular, change the processing modes or use more high-precision equipment.

If the setting of the machine, to perform a given size, is made with an error of a i, and the value of Fig.3.7 or Fig.3.8, then a defect appears, correctable or irreparable, or both at the same time.

Fig.3.7 Fig.3.8

The amount of marriage depends both on the magnitude of the systematic error and on the selected manufacturing process.

The value of the systematic error a i determined by the formula

(3.9)

The amount of marriage or the number of deviations that go beyond the boundaries of the tolerance field will be determined by the formulas.

Area А А i = 0.5 where t a = (3.10)

Area B B i = 0.5 Central limit theorem: the sum of arbitrarily distributed independent random variables, subject to their equal influence, obeys

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