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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 distribution

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] Failure mode and effects analysis. Failure mode and effects analysis (FMEA)—also "failure modes," plural, in many publications—was one of the first systematic techniques for failure analysis.

Failure mode and effects analysis

It was developed by reliability engineers in the late 1940s 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. For each component, the failure modes and their resulting effects on the rest of the system are recorded in a specific FMEA worksheet. There are numerous variations of such worksheets. 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.

Ishikawa diagram

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.

5S (methodology)

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. Remove unnecessary items and dispose of them properlyMake work easy by eliminating obstaclesProvide no chance of being disturbed with unnecessary itemsPrevent accumulation of unnecessary items The phase, "Security", can also be added. 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.

Analysis of variance

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.

Motivating example[edit] No fit. Fair fit. 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 low-ability individuals suffer from illusory superiority, mistakenly assessing their ability as much higher than it really is.

Dunning–Kruger effect

Dunning and Kruger attributed this bias to a metacognitive incapacity, on the part of those with low ability, to recognize their ineptitude and evaluate their competence accurately. Their research also suggests corollaries: high-ability individuals may underestimate their relative competence and may erroneously assume that tasks which are easy for them are also easy for others.[1] Six Sigma. The common Six Sigma symbol Six Sigma is a set of techniques and tools for process improvement.

Six Sigma

It was developed by Motorola in 1986.[1][2] 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. It uses a set of quality management methods, mainly empirical, statistical methods, and creates a special infrastructure of people within the organization ("Champions", "Black Belts", "Green Belts", "Yellow Belts", etc.) who are experts in these methods. Each Six Sigma project carried out within an organization follows a defined sequence of steps and has quantified value targets, for example: reduce process cycle time, reduce pollution, reduce costs, increase customer satisfaction, and increase profits.

Doctrine[edit] Methodologies[edit] Statistical hypothesis testing. A statistical hypothesis test is a method of statistical inference using data from a scientific study.

Statistical hypothesis testing

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. 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. He is best known in the United States for his 14 Points (Out of Crisis, by Dr.

W. 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.

Process capability index

Recommended values[edit] Process capability indices are constructed to express more desirable capability with increasingly higher values. Values near or below zero indicate processes operating off target ( far from T) or with high variation. 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). Pareto chart. 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.

EnterpriseTrack Login. On-demand Project Portfolio Management Software. 16. Minitab. Minitab is a statistics package developed at the Pennsylvania State University by researchers Barbara F. Ryan, Thomas A. Ryan, Jr., and Brian L. Joiner in 1972.