Printing Quality Control--Subjective Evaluation (1)

Subjective assessment of print quality

One, multidimensional scaling method

The multidimensional scale is a scale technique based on mathematical statistics. When comparing the differences between samples or determining the degree of satisfaction with the samples in pairs, multidimensional scaling methods can be used to analyze and identify the main parameters used in people's assessment. When evaluating printed samples in this way, the relative importance of the main printing quality parameters can be determined; the value obtained from the evaluation can make the subjective evaluation and the objective evaluation or intrinsic relationship with the nature of the paper; it can also obtain the quality of each print. The reliability of the evaluation, the consistency of each evaluation staff (for example, printing, papermaking experts, readers, advertising staff, etc.) and the evaluation team's evaluation and other information.

Multidimensional scaling technology was proposed by Tokosson. Its content is: If there is a perceived difference between two elements, then the difference can be expressed in a geometric distance. If this difference is recorded on a scale scale, then the scale value on the scale shows the distance, and then the distance can be used to create more than one-dimensional geometric models that reflect the relationships between the samples.

Figure 6-1 and Figure 6-2 show a five-element system model (A~E). If the present sensory differences of each pair of evaluation objects are converted into linear distance representations, then there is a unique solution to the distribution of each sample in space. For example, if the observed difference is as shown in Figure 6-1, the resulting solution is a two-dimensional model; if the reported difference is as shown in Figure 6-2, the solution is a three-dimensional model. Are all unique. In other words, in Figure 6-1, the evaluation result is determined by two independent parameters, and Figure 6-2 is determined by three independent parameters. The distance coordinates of the elements can be marked with numbers.

In order to convert the distance between elements to a multidimensional diagram like that in Figure 6-1 and Figure 6-2, the Pythagorean theorem can be used. This is the simplest method, namely:

In the formula:
Dij - the linear distance of the difference between the elements i and j;

Xim, Xjm - coordinates along the mth axis.

Multidimensional scaling involves determining multidimensional coordinates for each element based on the difference between the recorded elements. The method of determination is the maximum natural fit method. Sheppard once pointed out that the relative position model of an element can be fitted with a monotonic function. This function is a function that contains the order relationship of the sample when converting the sensory disparity into a multidimensional distance.

Because of the subjective response to most stimuli, the best form of expression is expressed as a power function of the values ​​of the responding physical quantities, so Ramsay made the following improvements to equation (6-1):

V and P are scalar and power indices, respectively, and V and P are used to fit each evaluator's response style difference without changing the monotonicity of Equation (6-1).

Because people's evaluations are rarely as consistent as shown in Figure 6-1 and Figure 6-2, the use of an alignment model to fit the differences in the evaluation will bring about some deviations. In order to reduce this deviation, we must stack The steps of the generation correct the parameters of the model until the best fit is obtained. In the case that the dimension or parameters cannot be determined, the dimension can be determined according to the highest dimension selected, because the higher the dimension is, the larger the proportion that produces the evaluation bias. The method of choice is to first obtain the natural logarithm of the ordering model of different dimensions and compare the natural logarithm with the squared table.

After the model parameters are given, the standard deviation of each evaluator can be calculated.

In the formula:
d - observed differences;
d* - model for predicting deviations;
N - number of observations;
n - the number of parameters of the model.

The standard deviation is a measure of an evaluator and a measure of the degree of fit of the multidimensional response model of the evaluator. If the opinion of a judge is inconsistent with the opinions of most people in the evaluator or the evaluator is unreasonable, the evaluator's criteria The deviation is relatively large.

Obviously, it is better to distinguish the two kinds of biases existing in an evaluator. Therefore, the computer program used in the multi-dimensional scaling study also provides each evaluator with an error map (see Figure 6-3). The nature of the evaluator's bias can be seen on the graph, whether it is a random feature or the opinion of the evaluator is different from others. The deviation graph also provides a means of preventing significant record deviations because some incorrect values ​​will appear as far away points.

Figure 6-1 Figure 6-2 may be a physical element (such as an experimental print), or it may be conceptual. For example, there may be five different fruits, such as bananas, lemons, watermelons, cherries, oranges, etc. There may be ten pairs of these five fruits, and the judges are required to report the differences he feels. If the judge is using two parameters to distinguish, then a two-dimensional graph will be obtained. The two dimensions may be easily identifiable (such as size or shape). However, there are some acceptable parameters, such as: color, texture And sturdiness, the number of dimensions in the arrangement of fruits should reflect the number of parameters that have a significant effect on the bias reported by the evaluator.

In fact, most evaluators use 2 or 3 parameters (with 4 being few) to judge the difference between elements, and only use the significance x2 test to limit the number of parameters in the multidimensional model.

An important feature of multidimensional scaling techniques is that multidimensional scaling of the subjective psychological factors of the judges can be performed. The role of each parameter in an evaluation can be represented by a desired vector, which will be described below. (to be continued)