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**Industrial Statistics** is the branch of **economic statistics** which is concerned with the production activities of industries. It can also be defined as a science that utilizes general statistical theory, tools and techniques to develop a system of complex indices which describe the distribution and composition of industries; the functioning of enterprises, sectors and associations; the industry as a whole; and the result of industrial activity. It also refers to the practical work of collecting, analyzing and drawing inferences from industrial data to evaluate the implementation of government strategies as well as to describe the efficiency of production activity. Improving and maintaining the quality of goods and services produced by the industries of a nation is the main objective of industrial statistics. It involves the use of a wide variety of statistical tools even though the effort to improve and maintain quality requires a broader approach to managing industrial processes and goes beyond the application of specific tools.

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Industrial statistics is as much a discipline of science as it is of statistics and economics (**Economics Homework Help**). In this regard, it is defined as a discipline which involves the development of quantitative paradigms and methods for inquiry and typical decision making for industrial activity. Here, empirical inquiry provides the framework of statistical techniques which are applied to projects of industrial production and process improvement such as Six Sigma. Typical decision making on the other hand is the context in which industrial statistics techniques such as control-charting and sampling inspections are applied. Industrial statistical is therefore methodological research by nature. It needs to be mentioned here that methodology is not based on empirical science, and the research methods and paradigms used by empirical researchers cannot be used by researchers in the field of industrial statistics. Methodological research in industrial statistics is often characterized as logical reconstruction and at times as foundational research. Logical reconstruction focuses on elaborate explanation of phenomena, whereas foundational research investigates actions and their rationality

Mathematics, especially **mathematical statistics** has a central role in the science of industrial statistics. Mathematical concepts and techniques are the basis on which most industrial statistics methods and paradigms have been developed. For example, the concepts of **Acceptable Quality Level (AQL), Limiting Quality Level (LQL) and Operating Characteristic curve (OC)** can only be explained using mathematical concepts or research, even though there development is based on logical reconstruction. Statistical reasoning however is quite different from just mathematics and follows three steps:

**Experimental model:** It is hypothetical system or a model that imitates the real system being studied which means that the behavior it displays is similar to the real aspect or system of an industry. Aspects of the real system which are to be investigated are translated into statistical questions in terms of model parameters. The real system defined in terms of an experimental unit, population, population parameters and variables is governed by the natural law, whereas the experimental model defined in terms of probability while accounting for a canonical model for a test statistic and sampling error is governed by the laws and axioms of probability.

**Deduction:** To make a deduction, first a sample is taken from the population being studied and a realization of the specific test statistic is calculated on the basis of findings. The investigator then deduces conclusions that are true for the hypothetical system using the reasoning methodology for the given experimental model.

**Inference:** In last step, making the assumption that the behavior of the model represents the behavior of the real system, conclusions and inferences are made about the real system. Drawing relevant inferences involves a number of inductive steps which are not related to mathematics. These steps usually include defining the population and the experimental unit; making assumptions about the raw observations and the realization of the test statistic; making assumption that all other factors are constant; and translating the statistical conclusion into meaningful inferences about the real system.

The **Six Sigma** program which emerged in the last decades of the 20th century is by nature an inherent part of industrial statistics. Closely in line with industrial statistics which seeks to continuously improve and maintain the quality of industrial activity, Six Sigma asserts that substantial efforts of organizations should be invested towards systematically improving their routine functions. It also says that improvement initiatives should not only focus on manufacturing and delivery of services but equally on other organizational activities including marketing, sales, accounting, processes and product development. The Six Sigma program in this regard is the next step in the adoption of increasingly more scientific and professional approaches to managing and improving organizational processes.

Other than a managerial framework, Six Sigma also provides a comprehensive methodology for projects of industrial improvement. The methodology comprises of an inquiry framework and a series of statistical tools and techniques. A major leap over previous quality improvement methods, it foster an attitude of business economics, and reduces the gap between scientific, especially engineering and management contexts of business. As more and more organizations adopt Six Sigma methodologies, it has helped familiarize the general public with considerable levels of statistical methods. An ever-growing number of business leaders are now trained in using design experiments, analysis of variance (ANOVA) and non-normal capability analysis to name just a few of the statistical tools.

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