Sage: Open Source Mathematics Software. Www-personal.umich.edu/~kikuchi/Research/rsm_amago.pdf. Rsm_amago.pdf. Rsm. Response-Surface Methods in R, Using rsm. Rs-illus. Www.brad.ac.uk/staff/vtoropov/burgeon/thesis_luis/chapter3.pdf. Monte Carlo Pi. Monte Carlo method. Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results; typically one runs simulations many times over in order to obtain the distribution of an unknown probabilistic entity. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to obtain a closed-form expression, or infeasible to apply a deterministic algorithm. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration and generation of draws from a probability distribution.
The modern version of the Monte Carlo method was invented in the late 1940s by Stanislaw Ulam, while he was working on nuclear weapons projects at the Los Alamos National Laboratory. Immediately after Ulam's breakthrough, John von Neumann understood its importance and programmed the ENIAC computer to carry out Monte Carlo calculations. Introduction[edit] Latin Hypercube Sampling | Mathieu Fenniak. Introduction Latin hypercube sampling (LHS) is a form of stratified sampling that can be applied to multiple variables. The method commonly used to reduce the number or runs necessary for a Monte Carlo simulation to achieve a reasonably accurate random distribution. LHS can be incorporated into an existing Monte Carlo model fairly easily, and work with variables following any analytical probability distribution.
Monte-Carlo simulations provide statistical answers to problems by performing many calculations with randomized variables, and analyzing the trends in the output data. There are many resources available describing Monte-Carlo (history, examples, software). The concept behind LHS is not overly complex. Variables are sampled using a even sampling method, and then randomly combined sets of those variables are used for one calculation of the target function. The sampling algorithm ensures that the distribution function is sampled evenly, but still with the same probability trend. Taguchi's Orthogonal Arrays. Response Surface Methods. Prof. Dr. Ulrike Grömping - Design of Experiments - Beuth Hochschule für Technik Berlin. Design of Experiments :: Overview :: The Quality Portal. The order of tasks to using this tool starts with identifying the input variables and the response (output) that is to be measured. For each input variable, a number of levels are defined that represent the range for which the effect of that variable is desired to be known.
An experimental plan is produced which tells the experimenter where to set each test parameter for each run of the test. The response is then measured for each run. The method of analysis is to look for differences between response (output) readings for different groups of the input changes. These differences are then attributed to the input variables acting alone (called a single effect) or in combination with another input variable (called an interaction). DOE is team oriented and a variety backgrounds (e.g. design, manufacturing, statistics etc.) should be involved when identifying factors and levels and developing the matrix as this is the most skilled part. Tikhonov regularization. When the following problem is not well posed (either because of non-existence or non-uniqueness of where may be ill-conditioned or singular).
In the latter case this is no better than the original problem. In order to give preference to a particular solution with desirable properties, the regularization term is included in this minimization: for some suitably chosen Tikhonov matrix, . , is given by: The effect of regularization may be varied via the scale of matrix . This reduces to the unregularized least squares solution provided that (ATA)−1 exists.
History[edit] Tikhonov regularization has been invented independently in many different contexts. Generalized Tikhonov regularization[edit] For general multivariate normal distributions for and the data error, one can apply a transformation of the variables to reduce to the case above. To minimize where we have used to stand for the weighted norm (compare with the Mahalanobis distance). Is the inverse covariance matrix of is the expected value of , and. Lean Manufacturing Glossary & Definitions. 5S: 5S is a housekeeping methodology for the shop floor. There are five rules of housekeeping for a lean environment and they help to expose waste and support the discipline needed to implement the Toyota Production System.
The five S’s are described below: 1. Seiri (Organization): Keep just what is needed, clearly distinguish between what is needed and kept and what is unneeded and thrown away. 2. Seiton (Orderliness): Have a place for everything and implement a system whereby everything is in its place. 3. 4. 5. If a company does not have the discipline to execute the five S’s, it will not have the discipline to complete standard work, pull systems, and other lean techniques. 5S is the very first step on a company’s learn journey. Andon: Simply means “light” in Japanese. Automation: Employing machines to do the work of people. Automatic Time: The time when a machine is running on an automatic cycle and a person is not needed to operate the equipment. Return to top | W, X, Y and Z | Why Six Sigma Projects Often Fail. SixSigma - making customers feel quality.
SEMATECH e-Handbook of Statistical Methods.