The paradigm that mathematics is a subject to be taught and learned is not correct. Mathematics is to be
produced. However, without hermeneutics, it would be difficult to do so. Unfortunately, hermeneutics was
all that have been neglected in mathematics education. Meanwhile, only with hermeneutics, teaching
and learning mathematics and also research in mathematics could flourish and be fruitful. Without it,
it would be extremely hard for students to come up with a new creation in mathematics. This paper
aims to shift the paradigm of mathematics education from learning (only) of mathematics into producing
mathematics. Some examples are presented to illustrate the power of hermeneutics in developing
mathematical imagination, ideas, and creativity towards mathematical discovery or invention.
Industrial statistics is an important part of the management system in any industry that strives to continuously improve quality and increase productivity and efficiency. That system covers supply chain management, production design and prototyping, production process and marketing. Industrial statisticians, industrial engineers and industrial leaders should work together hand in hand, in the same language, to ensure that the process and products are as expected. The system itself is never complete. Thus, the usefulness, manageability and reliability of all statistical models used in the system are to be considered as first priority, but those skills are not sufficient. Industrial statisticians should also, of course, be able to come and go between the two poles: statistics and industry. This requirement needs a good understanding about the culture of these poles and how to conduct a mutual symbiosis. One of the principal bridges between these cultures is statistical process control (SPC). This paper is to show that modern industry cannot escape from SPC, especially in a multivariate setting. This setting, which characterizes modern industry, consists of two philosophical problems: how to order data and how to measure process variability. Our recent research results sponsored by the Government of Malaysia will be presented to illustrate the challenging statistical problems in modern industry.
Almost a half century after it was introduced, Wilks’ statistic has come into application in industrial manufacturing process variability monitoring. This is an important breakthrough in the way experts monitor the variability of manufacturing processes which is vital in modern industry. It leaves behind the traditional practice characterized by the use of sample size n which equals 1, if the process variability monitoring is based on individual observations and is greater than the number of variables p if one works with subgroup observations. The use of Wilks’ statistic allows us to work with n < p. This paper contains a review on process variability monitoring based on individual observations. First, some historical backgrounds of process variability monitoring in the general scheme was reviewed before it was revealed where the philosophy of Wilks’ statistic could be further interpreted. Subsequently it was indicated that the way to monitor the process variability depended on how the variability itself was measured. Finally, a new statistic for detecting the shift in variability based on individual observations was introduced and then a new control chart was proposed. The performance of the proposed chart as compared with Wilks chart, was quite promising. Therefore, some recommendations were given to better understand the history of manufacturing process variability.
A monitoring procedure was introduced for process variability in a multivariate setting based on individual observations which was a combination of (i) robust high breakdown point approach in the set-up stage to determine the reference sample and (ii) the use of Wilks chart in the mass production stage. This setting is what the Malaysian manufacturing industry is currently lacking in, especially when a robust approach must be used. The advantage of this procedure was revealed by using the case of a female shrouded connector production process in a Malaysian industry. Moreover, this procedure could also be used in any process quality monitoring and for any industry. A recommendation for quality practitioners was also addressed.
We had reviewed the current practice in stocks market analysis where stock is represented by its closing price, and then found that this approach may be misleading. In actuality, in the daily activity of stocks market, stock is represented by four prices, namely opening, highest, lowest, and closing prices. Thus, stock is a multivariate time series of those four prices and not a univariate time series of closing price only. In this paper all four prices will be considered. Then, the notion of multivariate time series similarity among stocks will be developed as a generalisation of univariate time series similarity. The results are used to construct stocks network in multivariate setting. To filter the economic information contained in that network, the standard tools in econophysics is used. Furthermore, the topological properties of stocks are analysed by using the most common centrality measures. As an example, Bursa Malaysia data are investigated and we show that the proposed approach can better figure out the real situation compared to the current one.