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# Regression Analysis

The regression analysis determines the relationship between the behavior of a characteristic cause (response variables), and a potential cause (descriptive variables). Hence, the technique aims at understanding the potential causes of change in the response while determining the contribution of each of these factors accomplished through establishing a statistical relationship between the changes in the response variables and changes in the descriptive variables. The analysis can indicate the most effective method of minimizing the difference between the real and the ideal answers.

1.2.1.5.1 Applications

Regression analysis has the following applications:

• • Examination of the assumptions related to the effect of independent descriptive variables on dependent variables (response) and predicting the value of the dependent variables (response) for the values of these independent descriptive variables. (Identifying the most important factors in processes and assessing their contributions to the variability of the desired features as well as forecasting the outputs of a test or study related to the past, present, and future conditions of a specified production.)
• • Estimation of the direction and degree of the relationship between a dependent variable (response) and an independent descriptive variable. Of course, this does not imply the existence of a cause-and-effect relationship. (For example, determining the effect of changing a factor like temperature on the output of the process while the other factors remain constant.)
• • Modeling different characteristics of a process. (For example, efficiency, output, performance, cycle time, probability of failure of the test, and various stoppages in the process.)
• • Verifying the replacement of a measurement method. (Such as replacing a time-consuming method with a faster and more accurate one.)
• • Non-linear applications. (For example, obtaining a production formula for a product as a function of time and volume of demand or obtaining a formula for a chemical interaction as a function of time, temperature, and pressure.)

Regression analysis can provide the relationship between various factors and the desired response, and thereby help in the making of a decision related to the process under study, and can ultimately improve the process. The main capability of this technique is to accurately describe the patterns of response data, to compare differences and explain related sets of data, and to provide the acceptable estimate of the impact of independent variables on a dependent variable (the response). This type of information aids the realm of controlling or improving the outputs of a process. The regression technique can also estimate the response rate in a satisfactory manner as well as the source of the effects of factors that are either not measured or eliminated in the analysis. In general, the analytical capability of the technique, especially in predicting the effect of independent variables on a given response, can prove useful, especially for processes requiring time and cost.

The use of regression analysis for modeling linear, exponential, multivariate, and other processes, in the absence of sufficient skill and experience in those working with the model, can lead to measurement errors and other sources of changes that can make the structured model too complicated. In some cases, as well, for creating a model, the accuracy of the available data may not be taken into consideration while checking the accuracy of such data is essential. As such, adding or removing this type of data from the analysis causes an incorrect estimation of the parameters related to the model, consequently affecting the response. Another important point is the existence of additional independent descriptive variables which can also prevent the discovery of the real effect of other independent descriptive variables on the dependent variable (response), whose elimination may seriously damage the validity of the model's results.

# Reliability Analysis

Reliability analysis makes use of analytical and engineering methods for evaluating, predicting, and ensuring the correct operation of a product or system under study over time. The techniques used in reliability analyses often require the use of statistical methods to resolve uncertainties, random attributes, or probabilities of failure, etc. In this kind of analysis, parameters such as the time to failure or the time between failures are dealt with. The technique includes other techniques like analyzing the malfunctions and their effects which focus on the physical nature and causes of failures.

• 1.2.1.6.1 Applications Reliability analysis applies to:
• • Validating key indices related to the reliability and predictability of the performance of various components and systems (e.g., time to failure or time between failures for a certain number of test units in a limited time)
• • Providing statistical data for design parameters for predicting the cost of the product life cycle, as a consequence of which a new product is introduced
• • Identifying critical components or parts of a high-risk process accurately to discover the causes of the product failure or weaknesses in the implementation of processes eventually providing the necessary background for corrective and preventive measures
• • Supplying guidance for making decisions on manufacturing or buying general products
• • Determining the major characteristics of product degradation to improve the product design or scheduling appropriately for the maintenance and repair