The aluminum manufacturing company faces many operational challenges. They have to analyze the performance of different sections. To do that they have at data from previous year about main inputs that go into aluminum production. In addition, they use other chemicals as a part of manufacturing process. In terms of output they produce four grades of metal. They have also to account for some about of production loss and level of impurities. Finally, as a measure of ultimate performance, they have to take into account power consumption and percentage efficiency.
As a part of efficiency improvement exercise, statistical analysis of various parameters was undertaken. The amount of Grade-A aluminum from all the four sections was analyzed. The results were found to be very similar besides the fact that total production of Section 3 was less than the other three. Upon analyzing the relation between Grade-A and Grade-B, it was found that the relationship is linear and moderately strong. Also, the relationship between the efficiency and power consumption was found to be linear and moderately negative. It was analyzed that 84% of power consumption was attributed to variation in current efficiency. From this we infer, that if the aluminum company wants to cut down power consumption, they should increase the efficiency of their operations. The latter would influence the reduction in power consumption by 84%. Finally, the residual analysis shows that the variance of the error variable is near constant.
Statistics has many functions in operations of the industry. Tools such as summary statistics and descriptive statistics give basic information which may of relevance in decision making. Examples of such measures include, mean, standard deviation and coefficient of correlation. Then there are much more powerful tools such as regression analysis that help us predict values and analyze the strength of relationship. We will be applying these concepts and tools in relation to the aluminum manufacturing company.
The aluminum manufacturing company produce four grades of aluminum, Grade – A, Grade-B, Grade-C, and Grade-D. It has four different sections to manufacture aluminum. And manufacturing process requires pots, which are compared for their quality, power consumption and efficiency.
I would like to provide summary statistical analysis of the Grade – A aluminum produced by each of the sections separately. Then I will compare and discuss these statistics. The detailed statistical analysis tables are presented in Appendix A. For the Section 1, the mean or average production of Grade-A aluminum is 0.089 tons; standard deviation from average production is 0.057; the median value or the centre most value is 0.0804 tons; mode or the most commonly produced value is 0.054; the minimum tonnage is 0.007 and maximum tonnage is 0.192; and total production is 1.87 tons. For Section 2, the mean or average production of Grade-A aluminum is 0.0889 tons; standard deviation from average production is 0.057; the median values or the centre most value is 0.088 tons; the minimum tonnage is 0.001 tons and maximum tonnage is 0.188 tons; and total production is 1.7785 tons. For Section 3, the mean or average production of Grade-A aluminum is 0.071 tons; standard deviation from average production is 0.044; the median value or the centre most value is 0.068 tons; the minimum tonnage is 0.0125 and maximum tonnage is 0.148 tons; and total production is 1.36 tons. Finally for Section 4, the mean or average production of Grade-A aluminum is 0.094; standard deviation from average production is 0.064; the median value or the centre most value is 0.100; the minimum tonnage is 0.0019 and maximum tonnage is 0.1833; and total production is 1.893 tons.
- The means are comparable; ranging from 0.071 to 0.095 tons.
- Their standard deviations vary from 0.044 to 0.064, with two of the middle figures at 0.057. This would mean that their bell curve is equally symmetrical.
- Regarding their total production, that of Section 3 stands as minimum at 1.36 tons. Whereas that of other three Sections hovers around 1.88 tons.
Next we would like to evaluate how the amount of Grade-A aluminum produced at the plant is different to the amount of Grade-B produced. We would set the Null Hypothesis that there is no difference between the amount of Grade-A and Grade-B produced. The data on statistical analysis is available on Appendix B.
The Pearson Coefficient of Correlation between the amount of Grade-A and Grade-B produced is -0.5745. This coefficient is used to measure the strength of association between two variables; particularly the linear relationship between the two variables – amount of Grada-A and Grade-B. In this case as the coefficient is negative, there is a negative linear relationship. Also it tells us that the linear relationship is not very strong. The equation of trend-line is
The value of R2 is 0.3301, which is the Coefficient of Determination. This means that 33% of variation is not explained by the variation in x. At the 95% confidence level, the average level of Grade-A production, at .0.086 tons, is much less than that of Grade-B, which is at 0.3797 tons. The Standard Deviation is almost identical at 0.056. The total production of Grade-B is almost 5 times that of Grade-A. The total of Grade-B is 30.4 tons, whereas that of Grade-B is 6.8 tons.
Here the plan manager is required to determine the amount of cryolite to purchase. At this time the decisions are made based on average cryolite consumption of 2.75kg per pot. Doing descriptive analysis on Cryolite consumption we infer that the average consumption is 2.493 kg/pot. From this we infer that they have been purchasing more Cryolite than required.
The aluminum company believes that when the plant is operating at a lower efficiency level, more energy is consumed. Using the sample of power consumption and current efficiency, we discuss further. The details are in Appendix C
- Among the power consumption and current efficiency, power consumption will be response or dependent variable and current efficiency will be explanatory or independent variable.
- Presuming Y is power consumption and X is current efficiency, the regression coefficients will be
The equation will be Y = 16.0102 – 3.83X
- The plot of the data-points and the estimated regression line of the same chart will be as follows
- Evaluating whether the regression line provides an adequate fit of the data, we will study the graph and the R2.
The value of R2 is .8485, which means that the 84.85% of the variation in Y, which is power consumption, is explained by the variation in X, which is Current efficiency. Also the R2 and Adjusted R Square are so close to each other. Which means no matter how we measure the coefficient of determination, the model’s fit is good to very good.
The gradient of the slope of t Stat is -20.904. That calculated at the confidence level 95% would be considered as a significant relationship.
Comparing the Grade-A aluminum across various sections, we observe from the summary statistics that the results are very similar. Only major difference lies in the total production, where the production of Section 3 is less than others. Evaluating the relation between Grade-A and Grade-B, we find that the relationship is linear and moderately strong. Also there is a negative moderately linear relationship between efficiency and power consumption. With R2 and Adjusted R Square value as high as .84 and close to each, other, it means that 84% of variation in power consumption can be explained by efficiency. So, if the aluminum company wants to cut down power consumption, they should increase the efficiency of their operations. Finally, residual plot analysis shows homoscedasticity, which means variance of the error variable, is near constant.
The one thing that stands out upon doing the analysis is the impact of current efficiency on power consumption. 84% of reduction in power consumption can be attributed to the current efficiency. So, the major recommendation would to make concerted effort to increase the current efficiency so as to cut down power consumption. That also will have significant impact in terms of cost savings.