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Engineering Statistics Handbook Episode 4 Part 12

Tham khảo tài liệu 'engineering statistics handbook episode 4 part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 3.2.2. Continuous Linear Model ENGINEERING STATISTICS HANDBOOK hW tools raids lỉEÂtCH BACK Nixf 3. Production Process Characterization 3.2. Assumptions Prerequisites 3.2.2. Continuous Linear Model Description The continuous linear model CLM is probably the most commonly used model in PPC. It is applicable in many instances ranging from simple control charts to response surface models. The CLM is a mathematical function that relates explanatory variables either discrete or continuous to a single continuous response variable. It is called linear because the coefficients of the terms are expressed as a linear sum. The terms themselves do not have to be linear. Model The general form of the CLM is p y Ofl e i l This equation just says that if we have p explanatory variables then the response is modeled by a constant term plus a sum of functions of those explanatory variables plus some random error term. This will become clear as we look at some examples below. Estimation The coefficients for the parameters in the CLM are estimated by the method of least squares. This is a method that gives estimates which minimize the sum of the squared distances from the observations to the fitted line or plane. See the chapter on Process Modeling for a more complete discussion on estimating the coefficients for these models. Testing The tests for the CLM involve testing that the model as a whole is a good representation of the process and whether any of the coefficients in the model are zero or have no effect on the overall fit. Again the details for testing are given in the chapter on Process Modeling. Assumptions For estimation purposes there are no additional assumptions necessary for the CLM beyond those stated in the assumptions section. For testing purposes however it is necessary to assume that the error term is adequately modeled by a Gaussian distribution. http www.itl.nist.gov div898 handbook ppc section2 ppc22.htm 1 of 2 5 1 2006 10 17 23 AM 3.2.2. Continuous Linear Model