Читать книгу The ABC of Qualimetry. The Toolkit for Measuring Immeasurable - Garry G. Azgaldov, Alexander V. Kostin - Страница 6

Let us denote a given time point byt₁and a time point in the future by t₂ (obviously, t₂>t₁). Let us denote by ΔT the time elapsed from t₁ to t₂: ΔT= t₂ – t₁.

Let us define our terms:

Pre-settime ΔT_SET: a time period ΔT, the value of which is pre-set by a human controller.

Indefinite period of time ΔT_i: a time period ΔT_i the value of which is not pre-set/defined by human controller.

Let us introduce some terms:

Object state: the state of an object at an instant defined by its quality whose index has the value k^K.

Given object state: the state of an object at a given (initial) instantt₁at which the value of its quality index is k₁^K.

Future object state: the state of an object at a future instant t₂at which its quality index will be k₂^K.

Quality variation: a value given by the expression ΔK^K = k₂^K– k₁^K.

Pre-set quality variation ΔK^K_PRE: a quality variationΔK^K the value of which is given in advance by a human controller.

Indefinite quality variation ΔK^K?: a quality variation ΔK^K the value of which is not given by a human controller.

Object quality control: the transfer of an object from a given state k₁^K to a future state k₂^K at ΔK^K_PRE with in ΔT_PRE (To rephrase it, to control the quality of an object is to ensure in the object a pre-set quality variation ΔK^K_PRE with in a pre-set time ΔT_PRE).

It follows from this definition that if any of these conditions were not met (e.g., indefinite timeΔT? instead of pre-set time ΔT_PRE or in definite quality variation ΔK^K? instead of pre-set quality variation ΔK^K_PRE is used) it would be improper to refer to it as quality control. In actual fact a different process is in progress. Table 1 shows different processes and their relation to the quality control process.

Table 1. Kinds of processes related to variation in the quality of objects. NOTE: Lines 10 and 11 represent situations, in which quality control in the ordinary sense is indeed exercised

Table 1 lists twelve situations differing in their combinations of ΔK^K (quality variation) and ΔT (time variation). Each has an associated process type related to quality variation, from total uncertainty to quality control, which may vary within pre-set limits within a pre-set time.

Regrettably, in practice the term quality control is frequently applied to processes that can at best be described as quality improvement (see, e.g., line 4 above).In these processes (which in most cases concern industrial products) the value of an object’s property index could be improved by so many per cent within a pre-set time; e.g., the life of a component part could be increased by 30%.It is then concluded that the quality of the object improved by the selfsame 30% supposedly as a result of quality control.

There are two principal fallacies here. One is that the magnitude of increase in the value of the quality index was determined incorrectly, taking no account of the fact that an improvement in the value of a property of an object by α% almost always leads to an improvement in its quality index by β% (with α<β).

The second fallacy is neglect the following: a quality improvement in one property of an object will result in an improved quality index of the object to the extent that none of its other property indices has deteriorated. Yet, this is a fairly common occurrence. Let us suppose that in the above case a 30% increase in the life of a component part is often accompanied by an increase in its mass. This leads to a deterioration of its “product mass” property by so many percent. Unless we make a qualimetric calculation we cannot say a priori whether – and by how many per cent – the quality of the product deteriorated or improved. (Proofs of both these assertions are to be found in books on theoretical qualimetry; see, e.g., [2]).

Therefore, it often happens in practice that the term quality control is applied to processes which, in control theoretic terms, cannot be considered quality control and, not infrequently, cannot be even called quality improvement because in reality they only ensure some indefinite quality variation (see lines 2 and 5 in Table 1 above).

The grey background in Table 1 is used to highlight two lines, 10 and 11, which represent the criteria to be met if we are to have a real quality control process. Line 10 describes the conditions under which, as common sense tells us, quality control is really achievable. That is to say, it is about a quality improvement is achievable to a pre-set extent within a pre-set time.

The case introduced by line 11 also belongs to control processes, though it is less apparent in the usual sense. Its only difference from case 10 is that the latter achieves a quality improvement (accordingly, ΔK^K > 0), whereas in case11 no improvement is envisioned, the only intention being to keep quality from deteriorating within a pre-set time period, i.e., to set it at a constant level, ΔK^K = 0).

The process described in line 12 is also related to quality control is totally unobvious to common sense. In pure theory, however, one can imagine a situation where the goal is not to increase but to decrease the quality of a product within pre-set limits and within a pre-set time, e.g., in order to cut production costs so as to boost demand. Since this is more academic than a real-life situation the respective line (12) in Table 1 was not highlighted with grey.

The foregoing interpretation of quality and quality control suggests that if we are to control quality we must be able to calculate the values of ΔK^K. To do it we must, in turn, be able to quantify or estimate quality using its index K^K. Consequently, we need a tool for the quantification of quality, which is provided by qualimetry.

There were also other factors, which made the appearance of qualimetry necessary, even inevitable. They will be discussed in the section that follows.