A Statistical Analysis of Industry Data with Particular Reference to the Low Grade End Factory Operations

Industry data from the low grade end of the factory have been statistically analysed with a view to deriving empirical relationships that could be of assistance in two important areas: (a) evaluation of factory performances and (b) provision of new insights into the significance of operating variables and techniques. Based on the industry data, the best fit equation for evaluating backend performance takes the following form: Molasses true purity = 39,82 15,91 log (Rsla) An equation of this form indicates that the factories with high Rsla ratios have greater difficulty achieving target purity than do their low RS/a ratio counterparts and this suggests that the existing SMRI log formula could be marginally biased in favour of the low Rs/a ratio operator. Regarding correlations, it has been established that a very strong relationship exists between molasses true purity and C-massecuite purity: with a one unit change in the latter being equivalent to 0,3-0,35 units of true purity in the average case. Introduction In South Africa factories pol losses in molasses are substantial, averaging out at approximately 8,5 % on pol in cane. This represents by far the largest single factor in relation to overall recoveries. For this reason, process personnel at all levels devote considerable time and energy to the backend of the factory in an endeavour to minimize losses. In line with practice followed in other parts of the world, notably Australia and Hawaii, the South African sugar industry has set about developing its own standard for measuring and comparing the performances of individual factories. In 1973 the Sugar Milling Research Institute recommended the use of the following relationship as a standard for evaluating molasses exhaustion: Target (true) purity = 39,94 19,6 log (Rsla) While the SMRI log formula has proved of great value to the Industry it has at the same time come in for a fair amount of criticism in regard to its apparent inequity at high reducing sugarslash ratios. The present statistical analysis was undertaken with a view to (i) checking out the validity of this claim and (ii) identifying the process variables (physical as well as chemical) that influence the achievement of optimum backend performances and results. Discussion EVALUATION OF FACTORY PERFORMANCES Background comments on source of the input data and evaluation technique used The data presented in Figures 1-3 have been obtained from routine laboratory analyses performed on final molasses composite samples. These data cover the vast bulk of the season's results, with only one or two data points excluded at each end of the season. This excision has been made to ensure that the quality of the final product is not affected by the a-typical results normally associated with factory startup and liquidation. The approach adopted in the preparation of these figures has been to select a number of operating variables that could possibly affect the molasses true purity and, in turn, the target (true) purity difference, and to statistically test their significance both singularly or in combination with each other. Analysis of data from Huletts' factories (normal conditions: 1975176) In reference specifically to Figure 1, it is readily apparent that the Rs/a ratio is the only factor that is of any real significance with respect to molasses true purity. This same trend is discernable for all the Huletts' factories and is a most gratifying result. Taking Empangeni as example, the correlation coefficient/"t"-value of the coefficient, are respectively 0,7911 7,31. Both these values are significant at above the 0,1% level. , Furthermore it is noteworthy that combining the Rs/a ratio with almost any other variable viz. MJ purity, C-massecuite purity, equipment loading, makes practically no difference to the correlation coefficient; which rises to only 0,798 in the maximum case. Again in reference to Figure 1, it is equally apparent that in no instance does the Rs/a ratio exert a significant effect on the target purity difference. In considering target purity difference, as opposed to true purity, it is important to note that the SMRI log formula should successfully eliminate all vestiges of the influence of Rsla ratio; and any general evidence of residual Rs/a effects must be seen as a measure of the log formula's inability to fulfil its role. In the event, the formula is fully vindicated and the results shown in Figure 1 are much as expected. Analysis of data from Huletts' factories (abnormal conditions: 1974175) During the second half of the 1974175 season (mid September to the end of the crop), the full force of the 1973174 drought manifested itself with drought stressed and fire cane accounting for the bulk of the supplies to a number of factories. The factories principally affected were the four northern Natal mills owned by Huletts, namely: Darnall, Amatikulu, Felixton and Empangeni. The midlands factories also suffered to a greater or lesser extent. In all these factories juice purities plunged between 3 and 7 units and besides the obvious adverse effect that a change of such magnitude would have on recoveries, the position was further aggravated by the presence of refractory juices which gave rise to poor boiling characteristics. In Figure 2, data are presented for the 1974175 season and reveal a very different picture to that seen in the 1975176 season already discussed. Not only is the correlation coefficient between Rs/a ratio and true purity much lower than previously but also there is a very substantial residual effect of the Rs/a ratio on target purity difference. In point of fact, the correlation is very much better for Rs/a -target purity difference than for Rs/a true purity. This is clearly in conflict with the format of the SMRI log formula and demonstrates the Proceedings of The South African Sugar Technologists' Association -June 1976 199 inapplicability of this formula to situations that vary grossly from "normality". In this context it is of passing interest that a single sample of final molasses drawn from Amatikulu factory about this time, and which was subjected to a boiling down test at the SMRI, could do no better than approach target by + 4,5 units following exhaustion under standard laboratory conditions. That this leads one to the inescapable conclusion that the SMRI formula does not apply under all circumstances should not be regarded as in any way heretical or even unusual: the only new feature is that speculation and fact have been brought somewhat closer together. Analysis of all industry data One of the major disadvantages inherent in analysing data from individual factories is that the spread in the operating variables is frequently small and this lack of resolution makes it difficult if not impossible to obtain a realistic picture of the "effect" of such variables on the overall result. One means of overcoming this type of problem is to look at data emanating from a large number of sources (such as all the factories in the industry) but even here the technique is not without problems; notably the considerable increase in the background "noise" introduced by such factors as differences in equipment and technique applied at the various factories. However, looking on the positive side, inclusion of data from all the factories does imply a vast increase in the number of data sets and seen from the statistical point of view this can only mean that such trends as do emerge can be accepted with a greater degree of confidence. Figure 3 is to be seen in the light of the above remarks. Before discussing the results given in Figure 3, it is considered important that a few words be said regarding the input data that has been included. Noteworthy points are: (i) the primary source data are analyses performed monthly by the SMRI laboratories on a weekly composite sample of molasses provided by each factory (third week of the operating month) (ii) consistent operating data is obtained from the SMRI publication "weekly summary of data" (the third week of the operating month again applying) (iii) the results of Malelane, Union Co-op and Entumeni factories have been excluded throughout as they appear to be incompatible with the balance of the data (iv) the results relate to the 1974175 and 1975176 seasons (v) the mass of the data have been processed in two sections all the Industry data, consisting of 230 data sets and abridged Industry data, consisting of 207 data sets, from which the results of DL, AK, FX, EM, JB and GD covering the period October 1974-February 1975 have been excised. The reasons for this decision appear in the earlier discussion. Some of the more important results of this study are given as follows : (a) the decision to separate the abnormal data from the normal data appears to have been fully justified in as much as the quality of the product is uniformly improved by this means. This effect is to be seen most noticeably in the case of the correlation coefficients but also, to a lesser extent, in the dispersion of the results. (see item 2 of Figure 3). Accordingly, the smaller data set is regarded as the more representative and is exclusively referred to in the subsequent discussion, irrespective of whether this fact is stated or not. (b) the very low correlation coefficient existing between backend loading and Rs/a ratio. This finding is completely in line with the results obtained for Huletts' factories operating under normal conditions. (c) the very low correlation existing between the Rs/a ratio and target purity difference. This result, together with the good correlation existing between the Rs/a ratio and true purity, is further verification of the soundness of a performance formula based on the Rs/a ratio. (d) the marginally better results obtained for the correlation of true purity with log Rs/a as opposed to a direct Rs/a relationship. Comparison of the values derived for the correlation coefficientlt-value of the coefficient, are respectively 0,595/9,32 versus 0,537/9,10. Again this finding is in line with the experimental work done by the SMRI. (e) the strong correlation found between C-massecuite purity and both true purity and target purity difference. The similarity in the size of the coefficient in these two cases lends strong support to the belief that the correlation is a genuine one. (f) the fair correlation found between backend loading and both true purity and target purity difference. Again the similarity in the size of the correlation in these two cases is a favourable factor. (g) the relationships of maximum correlation found between a combination of Rs/a ratio, C-massecuite purity on the one hand and true purity (or target purity difference) on the other. With reference to the latter relationship it is, however, noteworthy that the variable that correlates most strongly is C-massecuite purity and the appearance of the Rs/a ratio term in a marginally improved grouping could then be due to its residual influence or more probably via some indirect correlating route. Having discussed the main features of Figure 3 it only remains to look at the form of some of the relationships and to consider their practical implications. This is done in more detail in some of the following sections. The SMRI log formula In Figure 3 the best fit relationship between the Rs/a ratio and true purity is an equation of the form: Molasses true purity = 41,59 15,91 log (R/sa) This relationship is empirically derived from Industry data, and makes no claim at being the optimum level of attainment. On the contrary, factory results on the average are almost guaranteed to fall short of a standard performance level that has been established in terms of the SMRI log formula. What is then required for a direct comparison to be made between the factory derived formula and the SMRI log formula is some levelling technique. It is here contended that the mean target purity difference for the industry could perform this role. Adjustment of the factory data by this figure, namely +I ,77 units, alters the factory derived formula as follows: Molasses target purity = 39,82 15,91 log (Rs/a) The form of this equation is now very similar to the SMRI formula, the only significant difference being the slope of the lines. The various equations are plotted in Figure 4. If it is accepted that the difference in slope between the two lines is genuine then the implication of this finding is that factories with high Rs/a ratios are prejudiced in respect of their attempt at achievement of target purity whereas operators with low Rs/a ratios are favoured. Attaching actual values to this, it would appear that there is a bias of about 0,8 unit of purity on comparison of factories with Rs/a ratios differing by 0,5 of a unit. One or two additional comments need to be made in relation to Figure 4. Firstly, in some quarters it may be thought that the adjustment of the factory derived formula by the Proceedings of The South African Sugar Technologists' Association -June 1976 STATISTICAL ANALYSIS OF 1975176 SEASON RESULTS 1. Number of Data Sets . . . 3. Statistical Analysis of Data (correlation coefficients & Significance Levels) Mixed juice purity . . . . C-massecuitepurity . . . Backend loading . . . . RSA ratio in molasses . . True purity of molasses . . Target purity difference . . 2. Summary of Results EMPANGENI