EVALUATION OF PRODUCT QUALITY WITH DECIBELS

In modern Quality Engineering, the quality of process results, the quality of measuring instruments, and the quality of completed processes are considered according to their quality characteristics. However, in traditional engineering, only the quality of measuring instruments and the quality of completed processes (precision or accuracy indices PCI, PPI) can be successfully defined, while the quality of process results (semi-finished product, product, software, service) can only be described (has or does not have the required quality), good or bad quality, better or worse quality). In the modern consideration of quality, the quality of process results is now defined by the number of decibels [dB], according to the discovery of the genius Japanese scientist Genichi Taguchi (1924-2012), with the methods of Robust Technology Development and Standard Ratio (S/N). This paper discusses definition of the quality of process results with one input variable and continuous characteristics with three illustrative examples.


INTRODUCTION
The business of organization, in order to satisfy users more fully, stakeholders and employees, largely depends on the achieved quality of the results of the process, which is considered in Quality Engineering. The quality of process results is the level to which a set of quality characteristics effectively meets planned requirements and tasks. Quality engineering is a way of approach to predict or prevent problems that may occur in the market, after the customer sells and uses the product in various circumstances and applied conditions, during the projected life of the product. Quality characteristics are more often continual because they can be calculated accurately while discrete characteristics are only estimated. The set of quality characteristics of the process results can be: Semi-finished product, Product, Software or Service. Dependability is the probability to which a process result can perform its function, i. e. a set of characteristic quantities: Availability, Reliability, Safety, Confidentiality, Integrity and Maintainability.
The traditional understanding of quality includes consideration of the quality of process results, the quality of measurement systems, or the quality of completed processes. The quality of measurement systems and completed processes can be defined using a standardized (ISO 8258) process capability index (PCI). Cp) or Process Performance Index, PPI, Pp). In consideration of the quality of process results, input quantities can be continuous and attributive, with continuous having a great advantage. Unfortunately, the quality of process results can only be described in attribute terms (quality or poor quality, good or bad quality, better or worse quality, etc.).
One of the most important quality assessments with decibels is Phred. A Phred quality score is a measure of the quality of identification of the nucleobases generated by automated DNA sequencing (Hillier & Green, 1998). It was originally developed for the computer program Phred to help in the automation of DNA sequencing in the Human Genome Project. Phred quality scores are assigned to each nucleotide base call in automated sequencer traces. The FASTQ format encodes Phred scores as ASCII characters alongside the read sequences. Phred quality scores have become widely accepted to characterize the quality of DNA sequences, and can be used to compare the efficacy of different sequencing methods. Perhaps the most important use of Phred quality scores is the automatic determination of accurate, quality-based consensus sequences.

METHODOLOGY
The standard S/N ratio (signal/noise ratio, S/N) establishes the appropriate ratio of input quantity (S) and variability (N), which Taguchi used for application in the communications industry, to check the quality of the results. starting from the fact that the radio receives a signal or voice wave emitted from broadcast stations and converts it into sound, the voice is the input quantity (signal), the received voice is the output signal (response), where the input is mixed in space with the variability of the output signal (noise), so the sound quality is expressed by the ratio of the input signal and the variability in decibels [dB]. Of course, the higher the ratio (S/N) the better the quality. The ratio (S/N) has a real value of the input quantity (signal, S) in the counter and a value of variability of the input quantity (noise, N) in the denominator, so that higher quality is always obtained with the actual value of input value (S) and the highest value of variability (N). Primary ratios (S/N) for the quality of process results with continuous characteristics include:  known true values of the input quantity (zero proportional function, proportional function with reference point, linear function),  known levels of the magnitude value interval,  known ratios of (S/N) levels of the input quantity, unknown true values of the input quantity level and  unknown input quantities (non-dynamic characteristics: nominal is-best, less-is-better, bigger-is-better, non-dynamic operations).
There are many different advantages of primary (S/N) ratios in Quality Engineering but the code is most often defined with regression coefficient (β) and variance (σ 2 ): A factor is any parameter or variable that can affect the operation of a product or process. The signal factor is used to adjust the output (response). The noise factor is an uncontrolled factor that distinguishes levels of quality and products, there are (variability due to external causes: temperature, humidity, operator, vibration, etc., variability due to internal causes: wear, aging, etc. and variability due to differences between parts or products (length, voltage, etc.). Response factor is the output result (response) of the effect. Environmental noise factors are sources of variability due to environmental conditions when using the product. The ideal function is the ideal standard state relationship between the output (response) and the input quantities. Robust technology development is a special approach to maximize the functionality of a product group at the earliest stage, such as those in the product research and development phase, minimizing product development time. Robustness is the condition of using and describing a product plan or process that operates with limited variability, despite different and changing environmental conditions. Robust design is a special process within quality engineering to create a product or process insensitive to variability, without removing the source. Signal-to-noise ratio (S/N), the ratio of magnitude to variability, any set of special functions in an experimental design to find the optimal set of factor levels.
The (S/N) ratio in the approach of considering the quality of process results is observed in:  traditional approach when planning a new product,  in advanced approach when considering the quality of the whole group of process results with the same function within a certain range,  dynamic mode when there is a fixed goal and no adjustment is required,  non-dynamic mode when adjusting the input to the target (nominal-is-best, less-is-better, bigger-is-better),  generic function with physical laws, objective function when all data is missing,  an ideal function that is defined on the basis of the process result function,  with a passive (S/N) ratio with measured values,  an active (S/N) ratio with an adjusted value input, and  according to the number of input quantities.
Starting from the collected data on the quality of the process results according to Table 1, with one input quantity M i (i = 1,2,3,…,k) and its values y ij (i = 1,2,3,..,.k; j = 1,2,3,..r 0 ) and the principal quantities y i (i = 1,2,3,…,k). The quality of process results with continuous characteristics is most often taken into account when a larger number of data can be seen according to Figure 1. The regression line passes to: a) zero ideal function through the origin of diagram and reference data (M=0, y=0) usually for measuring instruments, b) proportional ideal function through the reference point and reference data (M=M s , y= S y ) usually for products or c) linear ideal function through reference ( MM  , y=m) usually for completed processes.

EXAMPLE FOR ZERO IDEAL FUNCTION
Evaluation of the quality of process results, for zero proportional function with: input values M (M 1 , M 2 ,..,M k ), input values y ij (i= 1, 2,..., k; j= 1, 2,…, r 0 ), outputs y (y 1 , y 2 ,..,y k ), and errors (e ij ), include the sum of the squares of the data (r) and the ideal function (Taguchi, & Rajesh, 2002;G. Taguchi, Rajesh, & S. Taguchi, 2004): Analysis of variance is essential in the calculation. Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the variation among and between groups) used to analyze the differences among means. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the t-test beyond two means. ANOVA was developed by the statistician Ronald Fisher (1890 -1962).  Applying the Analysis of Variance, the following values are obtained, shown in

EXAMPLE OF IDEAL PROPORTIONAL FUNCTION AND REFERENCE POINT
Evaluation of the quality of process results, with an ideal proportional function and a reference point, usually occurs in products, when a regression line with a linear regression coefficient (β) passes through the reference point and reference data. The product quality is calculated with calibration according to the reference point (M s ), with two types of calibration according to point calibration and according to the slope calibration (Rosa et al., 2009).
Evaluation of product quality in the proportional function includes: input value M (M 1 , M 2 ,..,M k ), input values y ij (i= 1, 2,…,k; j= 1,2,..., r 0 ), reference point (M s ), input reference values y ij (i= 1, 2,..., k; j= 1,2,..., r 0 ), average values ( S y ), sensitivity coefficient (β), sum of squares difference (r) and ideal proportional function, according to Table 4: (17) The calculation of the (S/N) ratio includes total sum of squares variability (S T ), linear effect of input quantity (S ) and error variability (S e ): For example, the quality of the Density Analyzer should be evaluated according to the ideal proportional function with a reference point of 5% of the standard solution. Solutions of four different densities with four different densities (5 %, 10 %, 15 %, 10 %) were observed and the data

B. Popović
Evaluation of product quality with decibels JEMC, VOL. 11, NO. 2, 2021, 106-114 111 in Table 5. were obtained, after two measurements (R 1 , R 2 ). With the average (M S = 5 %), the of the calibration values reference points are obtained according to  The obtained results of the analysis of variance are also shown in Table 7:  After the calculation, it was found that the quality of the new INSTRUMENT DENSITY ANALYZER with four different densities (5%, 10%, 15%, 10%) can be compared with the correct instrument, due to the positive and higher value of the ratio (S/N = 16.10 [dB]).

EXAMPLE OF IDEAL LINEAR FUNCTION
Evaluation of the quality of process results, with an ideal linear function, occurs when there are no special constraints between inputs and outputs, or when the regression line passes through reference data ( MM  , y=m), usually for completed processes (Selden, 1997). Evaluation of the quality of process results with an ideal linear function, includes input value M (M 1 , M 2 ,.., M k ), input values y ij (i= 1, 2,..., k; j= 1,2,..., r 0 ), number of repetitions of each level of input quantity (r o ), output result y (y 1 , y 2 ,..,y k ), regression coefficient (β), mean value ( M ) and the sum of squares of difference of input values (r): ..
It should be noted that for ideal linear functions, the total variability (S T ) is obtained subtracting the value (S m ) from the total sum of the squares of the individual data, so the variability is the mean:   The calculation of the ratio (S/N) includes the total variability of the average value (S m ), the total linear effect of the input quantity (S β ), the error variance (V e ) and the true value of the ratio (S/N):

RESULTS AND CONCLUSIONS
In traditional engineering, only the quality of measuring instruments and the quality of completed processes (PCI precision or accuracy indices, PPI) can be successfully defined, while the quality of process results (semi-finished product, product, software, service) can only be described (has or does not have the required quality), good or bad quality, better or worse quality). In modern quality consideration, the quality of process results is now defined by the number of decibels [dB], according to the discovery of the Japanese scientist Genichi Taguchi, with the methods of Robust Technology Development and Standard Ratio (S/N). The standard (S/N) ratio (signal/noise ratio, S/N) establishes the appropriate ratio of input quantity (S) and variability (N), which Taguchi used for application in the communications industry, to check the quality of results. starting from the fact that the radio receives a signal or a wave of voice that is broadcast from broadcasting stations and converts it into sound, the voice is the input quantity (signal), the received voice is the output signal (response), where the input is mixed in space with the output signal variability (noise), so the sound quality is expressed by the ratio of the input signal and the variability in decibels [dB]. In this paper, the definition of the quality of process results with one input quantity and continuous characteristics with three illustrative examples is considered.
After the performed calculations, the following results were achieved:  now the qualities of the process results (semifinished product, product, software, service) can be defined, which previously could only be described (there is or is not the required quality, good or bad quality, better or worse quality),  it was found that the quality of the new INSTRUMENT DENSITY ANALYZER with four different densities (5%, 10%, 15%, 10%) can be compared with the correct instrument, due to the positive and higher value of the ratio (S/N) = 16.10 [dB]).