Summary
Due to the particularities of the sugar agro-industrial companies in terms of technology, as well as the limitations in terms of financial resources to develop, the fundamental strategy must focus on reducing costs, and one way is given by reducing variability in the process, an essential element that still today at the international level constitutes a problem not solved fundamentally in the process industries, where according to Juran there are the largest reserves, so for Cuba it is a challenge, which implies going beyond the traditional in the procedure for analysis and process control. The work starts with a traditional statistical analysis that characterizes the technological variables, evaluates the state of process control, to continue with the use of time series,based on the Box-Jenkins methodology, which allows identifying the models that describe the variables studied. The presence of assignable causes of variation in the control charts of the residuals of the ARIMA model allow evaluating the amount of their effect on the variability of the process, the identification of the moments that such behavior occurs and the possibility of attenuating such effect with consequent reduction of variability, also proceeded to the evaluation of the inputs to the process. All this with the aim of evaluating the effect of autocorrelation in the extraction process of the sugar company "Melanio Hernández".They allow evaluating the amount of their effect on the variability of the process, the identification of the moments that such behavior occurs and the possibility of attenuating such effect with the consequent reduction of variability, in addition, the inputs to the process were evaluated. All this with the aim of evaluating the effect of autocorrelation in the extraction process of the sugar company "Melanio Hernández".They allow evaluating the amount of their effect on the variability of the process, the identification of the moments that such behavior occurs and the possibility of attenuating such effect with the consequent reduction of variability, in addition, the inputs to the process were evaluated. All this with the aim of evaluating the effect of autocorrelation in the extraction process of the sugar company "Melanio Hernández".All this with the aim of evaluating the effect of autocorrelation in the extraction process of the sugar company "Melanio Hernández".All this with the aim of evaluating the effect of autocorrelation in the extraction process of the sugar company "Melanio Hernández".
Keywords: Structured time series, Sugar industry, extraction process, quality.
Introduction.
For the manufacturing environment, the quality engineering practiced is changing rapidly, many organizations are facing high demands, for which the introduction of new systems and new products is required.
Systems transitions are becoming the most significant part of overall operations and there is increased pressure for quality engineering as well as other manufacturing activities to support the entity's economic objectives and profitability, a situation that requires to quality engineering the use of tools to face these changes as well as the intense international competition.
Due to the particularities of agroindustrial sugar companies in terms of technology, as well as the limitations in terms of financial resources to develop, the fundamental strategies have to focus specifically on reducing costs. Of particular importance, in order to reduce the costs of sugar and its derivatives, is the rational use of the company's resources and capacities.
Process Control Engineering has in Statistical Process Control a rich collection of tools to monitor a system. Shewhart (1926) proposed the first Control Charts (CG), which are still the most widely used in industrial systems today.
GCs are used to model the stability of processes. In this context, a process is said to be in statistical control if the probability distribution that represents the quality characteristic is constant over time. This traditional definition of the SPC has been generalized over the years to include cases in which a basic statistical model of the quality characteristic is stable over time. These useful generalizations include, for example, regression, variance components, and time series models.
Autocorrelation has long been recognized as a natural phenomenon in process industries. Only in recent years has autocorrelation become an outlet for SPC applications, particularly in the parts industries, where autocorrelation is seen as a problem that can undermine the interpretation of control charts. When control charts are constructed with autocorrelated measurements, the result can give many false signals, causing the LCs to appear too tight.
Other evidences are reported in measurements carried out by (Alwan and Roberts, 1995), when finding that more than 85% of the controls in the process industries, apply graphical results with misplaced control limits. In many cases, this situation is given by the presence of autocorrelations of the observed processes and violations of the basic assumptions associated with Shewhart's graphs (Woodall, 2000).
Structured time series are common occurrences in data from many process industries, complicating the effort of quality researchers to correctly place LCs. In the literature consulted in Cuba and in the rest of the world, there is no reference to the use of structured time series in the sugar industry.
Precisely the problem situation that led to the realization of this work is based on the need for the country to adapt to the world market, through the adoption of new approaches and the difficulties detected in previous studies in the sugar company "Melanio Hernandez". specifically in the Tandem.
The objective is to apply the structured time series to evaluate the influence of autocorrelation in reducing variability in the extraction process of the sugar company "Melanio Hernandez", which allows explaining the existing variability in this process.
For the development of the research, the sugar company "Melanio Hernandez" from the Province of Sancti Spíritus was taken as the object of study. And as a field of action, study of the variables involved in the variability in the extraction process.
Development
Understanding the variation in the values of the quality characteristics is of primary importance in Statistical Process Control, the «Common Cause» is considered a variation due to the inherent nature of the processes and cannot be altered by an external change of the process itself. "Assignable or special cause" of variation are usual shocks or interruptions, which can be separated. The purpose of Statistical Process Control (SPC) is to distinguish between these two types of variation to prevent a reaction or overreaction.
For continuous quality characteristics, specification limits are frequently given in practice. An article is considered compliant if the value of its quality characteristic is within the specification limits and it is not compliant when it is outside.
Deming (1986) and other authors have argued that being within specification limits is not enough to ensure good quality and that the variability of quality characteristics has to be reduced. Thus, for many quality characteristics, quality improvement corresponds to centering the probability distribution of the quality characteristic on a target value and reducing variability. Taguchi (1981) urges reducing variability until it appears economical and disadvantageous to reduce it later.
The estimation by the ARIMA model of the parameters may not be reliable in these cases, if the assignable causes are present in the data, in addition to a misplacement of the LCs if the inputs are dynamic, exhibiting a structured time series. The time series explain most of the variations in the data regardless of independence and the identical distribution of the residuals.
If the series is contaminated by periods of external disturbances for the process, the ARIMA model may be incorrectly specified, the variability of the residuals is overestimated and the control limits are incorrectly placed.
Box and Tiao (1978) with the Transfer Function Model, describe the observed quality characteristic () as a function of three causes of variability, given by the following equation:
= Dynamic inputs + Intervention + ARIMA
Dynamic inputs representing a pulse function, applied for input with a delay of time periods. If the dynamic relationship between the input and the output of the time series exists, the lagged value of the process can be modeled, resulting in a considerable reduction of the unexplained variance.
The intervention term identifies periods of time when assignable causes are present in the process. Box, Jenkins and Reisel (1994). The intervention term is a polynomial ratio that defines the nature of the disturbance (instability).
ARIMA basic model.
The main objective pursued when grinding cane is to extract as much sucrose as possible that it contains, hence the importance of this area.
Understand as extraction: The total sugar extracted by the tandem, as percent of the sugar in the cane. As defined by the International Society of Sugarcane Technologists, it is the sucrose in the mixed juice, for every one hundred parts of sucrose in the cane.
The loss of sucrose due to non-extraction varies between 4 and 7% of the total sucrose in the cane and that is why the milling process must be aimed at obtaining the highest possible extraction of the juice contained with the minimum cost. Pérez de Alejo (1979), shows that extraction in the Tandem is the one that most affects the profits in a sugar mill, this criterion being shared with Riera (1996).
For the analysis of the extraction process, the Quality Characteristics (QC) that identify the two products resulting from this process were taken: Bagasse (B) and Mixed Juice (JM) and the variables Pol of bagasse, Bagasse moisture, Brix were studied. of mixed juice, Pol of mixed juice, acidity of mixed juice and purity of mixed juice.
First, a descriptive study was made of all the technological variables that influence the extraction process. The results are shown below:
Table 1. Descriptive statistics of the CC that identify the B and JM.
|
Parameters \ Variables |
Pol in B |
B humidity |
JM Brix |
Pol from JM |
JM purity |
JM acidity |
|
N |
100 |
99 |
100 |
100 |
100 |
100 |
|
Half |
2.3804 |
50.7579 |
15.4366 |
13,2092 |
85.5312 |
0.5940 |
|
fashion |
2.20 |
50.08 |
15.56 |
12.79 |
84.02 |
0.55 |
|
DT |
0.25379 |
1.21619 |
0.69993 |
0.63007 |
1.81035 |
0.09081 |
|
Asymmetry (A) |
1,243 |
0.696 |
-0.069 |
-0.078 |
-0.315 |
0.506 |
|
Kurtosis (C) |
1,380 |
4,490 |
-0,400 |
-0.788 |
-0.343 |
0.441 |
|
Minimum |
1.97 |
46.17 |
13.80 |
11.82 |
79.90 |
0.38 |
|
Maximum |
3.35 |
55.40 |
17.31 |
14.44 |
88.49 |
0.87 |
The type of CG to be used depends on the characteristics of the process and its elaboration is carried out from the distribution followed by the analyzed variables, for the selection of the constants with the information obtained by the SPSS. The evaluation of the state of control of the process is carried out in an apparent way according to the graphical representation obtained from the CG and by variability analysis proposed by Ishikawa (1992).
The CGs used were of the X-Rm type (individual values and mobile paths) due to the suggestion of Juran (1988), NC 92.11.80, about the applications of these graphs, when it is not possible to form rational subgroups (SGR) by the characteristics of the data, given the nature of the process that is relatively uniform (due to the effect of mixtures that occur in the production process).
For all the variables analyzed (Campos, A. Y, Blanco, G. E, 2004) a process out of statistical control was manifested, not only due to the presence of points outside the LC, but also because adhesions were observed: at the higher LC at the beginning of the harvest, characterizing the deficient operation in this period and in the lower LC in the normal period of operation, which could be the result of the intervention of man to achieve values that are closest to the plans by which they are evaluated and stimulated.
By identifying non-random patterns, it is required to deepen the study of the process through STs, which cannot be studied with basic regression techniques, because in most cases, the values of the series are autocorrelated. In the works of (Gómez, 1998), when using moving average GC, the presence of autocorrelation was evidenced in the extraction process, as very narrow LCs were obtained, an element that the literature identifies as a manifestation of this phenomenon.
The Box-Jenkins methodology for the study of non-seasonal TS is used in the determination of the ARIMA model of the variables. The evaluation was carried out with the SPSS. As an example, the treatment given to the variable Purity of the mixed juice is explained below.
1. Plot of the series. The graph obtained gives the possibility of visualizing the non-stationarity presented by the Mixed Juice Test (PJM) and therefore the need for a differentiation of order 1.
2. Plotting the Autocorrelation Function (ACF) and the Partial Autocorrelation Function (PACF). The correlograms shown in Figure 1 allow us to reaffirm the stationarity provided by the previous step, so it is possible to proceed to the identification of the model that each series follows.
To see the graph select the "Download" option from the top menu
Fig. 1. Correlograms of the ACF and PACF of the PJM.
3. Identification of the model. With the analysis of the ACF and PACF graphs, the models that characterize the series were identified; in the case of the PJM, the selected model is an ARIMA (0,1,1).
4. Plot of ACF and PACF residuals. The plotting of the residuals obtained in figure 2 (ACF, with similar behavior to the PACF), allows to know if the model obtained for the series is adequate or not, through the analysis of the existence of white noise.
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Fig. 2. Plotting of residuals ACF and PACF of the PJM.
Once the PJM quality characteristic had been modeled, the control graphs of the residuals shown below were made:
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Fig 3. Control graphs of the residuals of the ARIMA model.
The presence of assignable causes of variation in the GC of the residuals of the ARIMA model (figure 3), allow evaluating the amount of their effect on the variability of the process, the identification of the moments that such behaviors occur and the possibility of attenuating such effects. with the consequent reduction of variability. For this, an intervention analysis was carried out. The control charts are shown below once the analysis of the interventions has been performed.
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Once the analysis of the assignable causes related to the operation of the process had been carried out, we proceeded to the evaluation of the inputs to the process, obtaining only for the model referred to the Purity of the JM a dependence on foreign matters and the percentage of back cane..
The model obtained was the following:
The models obtained allowed to evaluate the contribution to the reduction of variability of the extraction process as shown in Table 3.
|
Parameters / Variables |
Mixed Juice Acidity |
Purity of Mixed Juice |
Bagasse moisture |
Bagasse pol |
|
Initial standard deviation |
0.08854142 |
1.2195183 |
1,1346052 |
0.1391749 |
|
Final standard deviation |
0.0769999 |
1.0165379 |
0.7275653 |
0.09319682 |
|
Variability reduction percentage |
13.04% |
16.64% |
35.86% |
33.04% |
Table 3.1. Summary of variability reduction for each variable.
With the use of the developed tools, the model that characterizes the analyzed process is concretized, so that it can be used in quality monitoring. This modeling has the disadvantage of the loss of simplicity of the Shewhart graphs, but it guarantees greater accuracy in the calculation of the variability of the process and therefore minimizes the problem of misplacing the LCs and thus a contribution to the improvement.
Conclusions
Structured time series were applied for the first time in the Cuban sugar industry to evaluate the influence of autocorrelation in reducing variability in the extraction process of the sugar company "Melanio Hernández".
Autocorrelation analyzes were carried out that allowed obtaining the models that explain the variability of the process, for whose adjustments assignable causes were identified, which allow a reduction of variability in: 13.04% for the Acidity of the JM; 16.64% for JM Purity; 35.84% for B Moisture; 33.04% for Pol del B.
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