# Analysis of scales of measurement in qualification testing methods

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<ul><li><p>Chemistry. and Technology of Fuels and Oils. Vol. 33. No. 2, 1997 </p><p>METHODS OF ANALYSIS </p><p>.,-~NALYSIS OF SCALES OF MEASIoR1EMENT E-N </p><p>QUAL IF ICAT ION TESTENG :METHODS </p><p>V. G. Gorodetski i UDC 620.1.08:662.75 </p><p>Chemmotology is among the scientific disciplines in which mathematical methods of investigation have not yet come </p><p>into general use. In particular, the introduction of such methods is being hindered by the inadequacy of the qualification test </p><p>methods used to evaluate the service properties of fuels and lubricants. </p><p>Abstract mathematical apparatus can be applied only under the condition that a particular empirical system is expressed </p><p>in numbers having a structure of ratios corresponding to the structure of this empirical system. If this condition is met, real empirical systems can be studied by means of the corresponding numerical systems. </p><p>The conversion of empirical systems to numerical systems is accomplished by means of measurements. According to </p><p>the tenets of the formalized mathematical approach, measurement is defined as a procedure of assigning to an empirical element </p><p>a i of the set A (a i E A) a numerical element ni from the set N (n i E N). This procedure ensures that the relationship between different numerical and empirical elements will be single-valued (isomorphous or homomorphous). </p><p>In order to perform a measurement, it is necessary to establish a system of relationships R, i.e., a set of rules, in </p><p>accordance with which the quantities to be measured are given numerical values . The selected system of relationships R i </p><p>is true for the set of numbers obtained as a result of the measurements. Such systems of relationship are called scales of </p><p>measurements . </p><p>Depending on the type of scale that is used, the numbers obtained as a result of a measurement may not have all the </p><p>properties of numbers, and hence it is not always permissible to perform all mathematical operations with these numbers. Scales </p><p>of four types are used for technical measurements. Each scale has its own structure of relationships among the numbers that </p><p>are determined on its basis . </p><p>The simplest is the scale of classification, or names, defined as one-to-one (injective) mapping of empirical (A; =) </p><p>and numerical (N; =) systems. This scale reflects one-to-one correspondence between classes of empirical objects, identically </p><p>manifesting the property under consideration, and real numbers. The numbers furnished in correspondence to individual objects </p><p>permit only a determination of whether two objects are identical or not. </p><p>The procedure for measurement of an element a E A consists of comparing it with standard elements n E A. The </p><p>symbol standard is given to those elements that are equivalent to the standard. </p><p>For example, aviation kerosines are tested in accordance with a list of methods given in the technical standardization </p><p>documentation (TU, GOST, or set of qualification test methods). Those products that meet the requirements for a given grade </p><p>according to the standardized quality indexes are assigned the Code name for this grade: T-1. T-2, T-6, or T-8. The numbers. </p><p>which are used in marking the product, serve to distinguish one grade from another, and they do not have any informational </p><p>significance. These aviation kerosines do not differ from each other in any of their property indexes by a factor of 2, 6, or 8. Any mathematical operation on these numbers will be completely meaningless. </p><p>With a better scale, objects can not only be distin~maished, but also ranked according to some indicator. Here we have </p><p>a scale of order, which provides a monotonically increasing, continuous mapping of an empirical system (A; = ; &lt; ) by a </p><p>numerical system (N; = ; </p></li><li><p>The only characteristic feature of the numbers that are obtained is that they are ordered. Operations of addition, </p><p>subtraction, multiplication, and division cannot be performed on these numbers, hence it is impossible to estimate by how much </p><p>or by how many times one particular measured value is greater or less than another. A classic example of a scale of order is </p><p>the Mobs hardness scale for minerals. </p><p>In chemmotology, most of the methods for evaluating service properties provide for the determination of scales of </p><p>order. The simplest of these are realized in procedures for rating the results of stand or service tests on fuels and oils in gas </p><p>turbine engines. The rating is given by means of a comparison of the number and character of failures, and also the technical </p><p>conditions of the engines in testing or service on the test fuels and lubricants, in comparison with operation on standard </p><p>materials. </p><p>The finaI result of such tests does not have any numerical expression, but instead is represente'2 in the form of a </p><p>conclusion: The specific sample in the specific engine has "passed" or "failed" the test; it is either "worse" or "better" in its </p><p>service properties in comparison with a standard material, or it "does not differ" from the standard material. There is no </p><p>possibility of comparing results from tests on several samples with each other. </p><p>For piston engines, the results are rated in a "negative system of rating hard carbon and varnish deposits," the results </p><p>of which are expressed as arbitrary numerical ratings. There are five versions of such a procedure. The coefficients of rank </p><p>correlation between the results of tests using these methods may range from 0.1 to 0.9 . In other words, depending on the </p><p>method used for evaluation, test oils may be rated at one level of properties or another. </p><p>The reason for these discrepancies is found in the arbitrary definition of relationships between the quantity of deposits, </p><p>the hardness of the deposits, and the numerical demerit rating. Such relationships differ from one method to another. Also, </p><p>a relationship selected for a particular method may vary over the different sections of the interval of measurements, owing to </p><p>specific features of visual evaluation. This is responsible for obtaining a scale of order and hence the ranking of any quantity </p><p>of test results, not only with test results on a standard sample, but also against each other. </p><p>Performance of operations of addition and subtraction on the results of measurements is provided by a scale of </p><p>intervals. Characteristic for this scale is the presence of relationships of order and equivalence not only between results of </p><p>measurement, but also between differences in pairs of numbers. In obtaining such a scale, a unit of measurement is necessary; </p><p>just what interval of the scale it may occupy is not important. The main concern is that the unit of measurement must remain </p><p>unchanged over the entire range of measurements. Numbers obtained on the scale of intervals have the properties of order and </p><p>additivity. </p><p>The most widely encountered scale of intervals is the scale of time measurement. An evaluation of the interval of time </p><p>between two events does not present any difficulty. However, in order to determine "by what factor is the time consumed </p><p>longer or shorter," a zero point must be indicated, i.e., a point at which the timing is started. </p><p>If a natural zero exists on a scale of intervals (the absence of the measured property), this scale is converted to a scale </p><p>of ratios. Thus, the temperature in degrees Celsius is measured on a scale of intervals, but the temperature in degrees Kelvin </p><p>is measured on a scale of ratios. The results of measurements obtained on a scale of ratios have all of the properties of </p><p>numbers. </p><p>Indirect evaluations of the properties of fuels and lubricants are used extensively in chemmotology. Here, properties </p><p>are expressed in terms of physical or chemical quantities that are measured on a scale of intervals or ratios. With such </p><p>measurements, it is necessary to take into account that scales of indirect indexes are valid for direct indexes if a linear </p><p>relationship exists between the direct and indirect indexes over the entire range of measurement. </p><p>If monotonic relationships exist, the scale of ratios of direct indexes changes over to a scale of order of indirect </p><p>indexes. If the relationship between the indirect and direct indexes is extremal or if it has a point of discontinuity, the indirect </p><p>index can serve to rate the particular property only within that range of measurements in which the monotonic section of the </p><p>relationship between these indexes is maintained. </p><p>Thus, as an indirect rating index of the thermooxidative stability of aviation kerosines, measured by means of a TsITO- </p><p>M unit, we have the rate of decrease of the temperature t at the cooler outlet , and as a direct index the rate of increase of </p><p>the hydraulic resistance coefficient ~ of the fuel filter. </p><p>The relationship between direct and indirect rating indexes is described by the equation </p><p>! r d </p><p>= at 2 + bt +'~c + </p><p>120 </p></li><li><p>where a, b, c. d are constants that are determined by the construction of the unit, the test conditions, and the properties of the </p><p>aviation kerosines that are being tested. </p><p>Depending on the combination of constants, the function will assume one of six different forms. All of them have </p><p>maxima or minima, and four of them have one or two discontinuities. In this connection, the TsITO-M unit gives a scale of </p><p>order only within a very narrow range of variation of the indirect index. </p><p>If results are expressed in dimensionless units (ratings), the scales are transformed in accordance with the rules set forth </p><p>above. For exampIe, the tendency of aviation kerosines to form deposits on heated surfaces is rated visually in tests performed </p><p>in accordance with ASTM D I660 and GOST 17751, by comparing the darkest sections of the deposits on the rating tube of </p><p>the heater with a standard color scale with five or six ratings . A direct rating index of this property is the mass or volume </p><p>of deposits. Owing to the physiological features of the eye, the relationship between direct and indirect rating indexes is </p><p>described by an indicator function. The increase of deposit mass corresponding to an increase of the visual evaluation by one rating level in the interval </p><p>from 7 to 8 is ten times the increase of deposit mass in the interval from 1 to 2. However, this relationship would be preserved </p><p>only under the condition of maintenance of the law of variation of deposit thickness along the length of the rating tube for </p><p>different aviation kerosines. Since this condition is not met, there is no guarantee that a scale of order will be obtained. </p><p>These deficiencies were eliminated by the use of a deposit-measuring device consisting of a photoresistor having an </p><p>S-shaped characteristic with a wide linear section. The change of deposit thickness along the rating tube is taken into account </p><p>by means of an integral evaluation of the quantity of deposits on the entire surface. The test conditions for aviation kerosines </p><p>and diesel fuels have been selected so that the thickness of deposits for all samples will fall within the linear section of the </p><p>characteristic of the photoresistor . As a result, a scale of ratios has been obtained successfully in this section. </p><p>Work is being conducted to develop methods for direct integral determination of deposit thickness on the rating tube, </p><p>which will make it possible to obtain a scale of ratios over the entire range of measurements . </p><p>In the development of qualification test methods, all of the attention is being given to obtaining the most highly </p><p>improved metrological characteristics. Questions of the scale of measurement have not even been raised, Therefore, the </p><p>overwhelming majority of qualification test methods provide for obtaining scales of order; and this is hindering the introduction </p><p>of mathematical methods of research into chemmotology and is retarding the growth of chemmotology as a scientific discipline. </p><p>REFERENCES </p><p>1. </p><p>9 </p><p>3. </p><p>4. </p><p>5. </p><p>L. Finkelstein, IMECO Acta., I1, 11-27 (1973). J. Pfanzagl, Theory of Measurement, Halsted Press, New York (1968). V. M. Korobkov and D. M. Aronov, in: Service-Technical Properties and Application of Automotive Fuels, Lubricants, and Special-Purpose Fluids [in Russian], Transport, Moscow (1970), No. 6, pp. 127-189. A. A. Gureev, E. P, Seregin, and V. S. Azev, Qualification Methods for Testing Petroleum Fuels [in Russian], Khimiya, Moscow (1984). </p><p>R. E. Morris and R. N. Hazlett, Energ. Fuel, 3, No. 2, 18 (1989). </p><p>121 </p></li></ul>