# Six Sigma

Normal distribution. In probability theory, the normal (or Gaussian) distribution is a very commonly occurring continuous probability distribution—a function that tells the probability that an observation in some context will fall between any two real numbers.

Normal distributions are extremely important in statistics and are often used in the natural and social sciences for real-valued random variables whose distributions are not known.[1][2] The normal distribution is immensely useful because of the central limit theorem, which states that, under mild conditions, the mean of many random variables independently drawn from the same distribution is distributed approximately normally, irrespective of the form of the original distribution: physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have a distribution very close to the normal.

Failure mode and effects analysis. Failure Mode and Effects Analysis (FMEA) was one of the first systematic techniques for failure analysis.

It was developed by reliability engineers in the 1950s to study problems that might arise from malfunctions of military systems. An FMEA is often the first step of a system reliability study. It involves reviewing as many components, assemblies, and subsystems as possible to identify failure modes, and their causes and effects. Ishikawa diagram. Ishikawa diagrams (also called fishbone diagrams, herringbone diagrams, cause-and-effect diagrams, or Fishikawa) are causal diagrams created by Kaoru Ishikawa (1968) that show the causes of a specific event.[1][2] Common uses of the Ishikawa diagram are product design and quality defect prevention, to identify potential factors causing an overall effect.

Each cause or reason for imperfection is a source of variation. Causes are usually grouped into major categories to identify these sources of variation. 5S (methodology) Tools drawer at a 5S working place 5S is the name of a workplace organization method that uses a list of five Japanese words: seiri, seiton, seiso, seiketsu, and shitsuke.

Transliterated or translated into English, they all start with the letter "S".[1] The list describes how to organize a work space for efficiency and effectiveness by identifying and storing the items used, maintaining the area and items, and sustaining the new order. The decision-making process usually comes from a dialogue about standardization, which builds understanding among employees of how they should do the work. There are five primary 5S phases: They can be translated from the Japanese as Sort, Systematize, Shine, Standardize and Self-Discipline.

Other translations are possible. Analysis of variance. Analysis of variance (ANOVA) is a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups), developed by R.A.

Fisher. In the ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are equal, and therefore generalizes the t-test to more than two groups.

Doing multiple two-sample t-tests would result in an increased chance of committing a type I error. For this reason, ANOVAs are useful in comparing (testing) three or more means (groups or variables) for statistical significance. A-Flowchart-to-Help-You-Determine-if-Yoursquore-Having-a-Rational-Discussion.jpg (JPEG Image, 622x866 pixels) Wikiversity. Dunning–Kruger effect. The Dunning–Kruger effect is a cognitive bias in which unskilled individuals suffer from illusory superiority, mistakenly rating their ability much higher than is accurate.

This bias is attributed to a metacognitive inability of the unskilled to recognize their ineptitude.[1] Actual competence may weaken self-confidence, as competent individuals may falsely assume that others have an equivalent understanding. David Dunning and Justin Kruger of Cornell University conclude, "the miscalibration of the incompetent stems from an error about the self, whereas the miscalibration of the highly competent stems from an error about others".[2] Six Sigma. The oft-used Six Sigma symbol Six Sigma is a set of techniques and tools for process improvement.

It was developed by Motorola in 1986,[1][2] coinciding with the Japanese asset price bubble which is reflected in its terminology. [citation needed] Jack Welch made it central to his business strategy at General Electric in 1995.[3] Today, it is used in many industrial sectors.[4] Six Sigma seeks to improve the quality of process outputs by identifying and removing the causes of defects (errors) and minimizing variability in manufacturing and business processes.

Statistical hypothesis testing. A statistical hypothesis test is a method of statistical inference using data from a scientific study.

In statistics, a result is called statistically significant if it has been predicted as unlikely to have occurred by chance alone, according to a pre-determined threshold probability, the significance level. The phrase "test of significance" was coined by statistician Ronald Fisher.[1] These tests are used in determining what outcomes of a study would lead to a rejection of the null hypothesis for a pre-specified level of significance; this can help to decide whether results contain enough information to cast doubt on conventional wisdom, given that conventional wisdom has been used to establish the null hypothesis.

The critical region of a hypothesis test is the set of all outcomes which cause the null hypothesis to be rejected in favor of the alternative hypothesis. P-value. In statistical significance testing, the p-value is the probability of obtaining a test statistic result at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.[1][2] A researcher will often "reject the null hypothesis" when the p-value turns out to be less than a certain significance level, often 0.05 or 0.01.

Such a result indicates that the observed result would be highly unlikely under the null hypothesis. Many common statistical tests, such as chi-squared tests or Student's t-test, produce test statistics which can be interpreted using p-values. In a statistical test, the p-value is the probability of getting the same value for a model built around two hypotheses, one is the "neutral" (or "null") hypothesis, the other is the hypothesis under testing.

If this p-value is less than or equal to the threshold value previously set (traditionally 5% or 1% [5]), one rejects the neutral hypothesis and accepts the test hypothesis as valid . W. Edwards Deming. William Edwards Deming (October 14, 1900 – December 20, 1993) was an American statistician, professor, author, lecturer, and consultant.

Trained as a mathematical physicist, he helped develop the sampling techniques still used by the Department of the Census and the Bureau of Labor Statistics, championed the work of Dr. Walter Shewhart, including Statistical Process Control, Operational Definitions, and what he called The Shewhart Cycle[1] which evolved into "PDSA" (Plan-Do-Study-Act) in his book The New Economics for Industry, Government, Education.[2] as a response to the growing popularity of PDCA, which he viewed as tampering with the meaning of Dr. Process capability index. And the estimated variability of the process (expressed as a standard deviation) is , then commonly accepted process capability indices include: is estimated using the sample standard deviation.

Recommended values[edit] Process performance index. , and the estimated variability of the process (expressed as a standard deviation) is , then the process performance index is defined as: is estimated using the sample standard deviation. Ppk may be negative if the process mean falls outside the specification limits (because the process is producing a large proportion of defective output). Some specifications may only be one sided (for example, strength).

Pareto chart. A Pareto chart, named after Vilfredo Pareto, is a type of chart that contains both bars and a line graph, where individual values are represented in descending order by bars, and the cumulative total is represented by the line. Simple example of a Pareto chart using hypothetical data showing the relative frequency of reasons for arriving late at work The left vertical axis is the frequency of occurrence, but it can alternatively represent cost or another important unit of measure. The right vertical axis is the cumulative percentage of the total number of occurrences, total cost, or total of the particular unit of measure. Control chart. Control charts, also known as Shewhart charts (after Walter A. Shewhart) or process-behavior charts, in statistical process control are tools used to determine if a manufacturing or business process is in a state of statistical control. Overview[edit] If analysis of the control chart indicates that the process is currently under control (i.e., is stable, with variation only coming from sources common to the process), then no corrections or changes to process control parameters are needed or desired.

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