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.
The Gaussian distribution is sometimes informally called the bell curve. A normal distribution is The factor . . 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. 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. A few different types of FMEA analyses exist, such as Functional,Design, andProcess FMEA. Sometimes FMEA is extended to FMECA to indicate that criticality analysis is performed too. Introduction[edit] Functional analysis[edit] Ground rules[edit] Benefits[edit] Basic terms :-[edit] Failure Failure mode Failure cause and/or mechanism.
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. The categories typically include: Overview[edit] Ishikawa diagram, in fishbone shape, showing factors of Equipment, Process, People, Materials, Environment and Management, all affecting the overall problem. Ishikawa diagrams were popularized by Kaoru Ishikawa[3] in the 1960s, who pioneered quality management processes in the Kawasaki shipyards, and in the process became one of the founding fathers of modern management. Causes[edit] Causes can be derived from brainstorming sessions. 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. 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.
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 Very good fit The analysis of variance can be used as an exploratory tool to explain observations.
Background and terminology[edit] Additionally: Design-of-experiments terms[edit] Blocking. A-Flowchart-to-Help-You-Determine-if-Yoursquore-Having-a-Rational-Discussion.jpg (JPEG Image, 622x866 pixels) Wikiversity. Dunning–Kruger effect. Cognitive bias about one's own skill The Dunning–Kruger effect is a cognitive bias in which people with limited competence in a particular domain overestimate their abilities. Some researchers also include the opposite effect for high performers: their tendency to underestimate their skills. In popular culture, the Dunning–Kruger effect is often misunderstood as a claim about general overconfidence of people with low intelligence instead of specific overconfidence of people unskilled at a particular task.
The Dunning–Kruger effect is usually measured by comparing self-assessment with objective performance. For example, participants may take a quiz and estimate their performance afterward, which is then compared to their actual results. There are disagreements about what causes the Dunning–Kruger effect. There are disagreements about the Dunning–Kruger effect's magnitude and practical consequences. Definition[edit] David Dunning Measurement, analysis, and investigated tasks[edit] [edit] Six Sigma. The common Six Sigma symbol Six Sigma is a set of techniques and tools for process improvement. 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. 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.
Variations and sub-classes[edit] The testing process[edit] An alternative process is commonly used: Interpretation[edit] 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 . , then. W. Edwards Deming. William Edwards Deming (October 14, 1900 – December 20, 1993) was an American engineer, statistician, professor, author, lecturer, and management consultant.
Educated initially as an electrical engineer and later specializing in mathematical physics, he helped develop the sampling techniques still used by the U.S. Department of the Census and the Bureau of Labor Statistics. In his book, The New Economics for Industry, Government, and Education,[1] Deming championed the work of Walter Shewhart, including statistical process control, operational definitions, and what Deming called the "Shewhart Cycle"[2] which had evolved into Plan-Do-Study-Act (PDSA). This was in response to the growing popularity of PDCA, which Deming viewed as tampering with the meaning of Shewhart's original work.[3] Deming is best known for his work in Japan after WWII, particularly his work with the leaders of Japanese industry. Deming is best known in the United States for his 14 Points (Out of the Crisis, by 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. 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. Fixing values for minimum "acceptable" process capability targets is a matter of personal opinion, and what consensus exists varies by industry, facility, and the process under consideration.
Since the process capability is a function of the specification, the Process Capability Index is only as good as the specification . At least one academic expert recommends[3] the following: It should be noted though that where a process produces a characteristic with a capability index greater than 2.5, the unnecessary precision may be expensive.[4] Example[edit] If and. 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). For specifications that only have a lower limit, ; for those that only have an upper limit, Practitioners may also encounter , a metric that does not account for process performance that is not exactly centered between the specification limits, and therefore is interpreted as what the process would be capable of achieving if it could be centered and stabilized.
Interpretation[edit] Larger values of Ppk may be interpreted to indicate that a process is more capable of producing output within the specification limits, though this interpretation is controversial. and Example[edit] If See also[edit] 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. Because the reasons are in decreasing order, the cumulative function is a concave function. To take the example above, in order to lower the amount of late arriving by 78%, it is sufficient to solve the first three issues. The purpose of the Pareto chart is to highlight the most important among a (typically large) set of factors. See also[edit] References[edit] Hart, K. 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. In addition, data from the process can be used to predict the future performance of the process. The control chart is one of the seven basic tools of quality control.[3] Typically control charts are used for time-series data, though they can be used for data that have logical comparability (i.e. you want to compare samples that were taken all at the same time, or the performance of different individuals), however the type of chart used to do this requires consideration.[4] History[edit] 1. 2.
EnterpriseTrack Login. On-demand Project Portfolio Management Software | EnterpriseTrack | Instantis. 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. Minitab began as a light version of OMNITAB, a statistical analysis program by NIST; the documentation for OMNITAB was published 1986, and there has been no significant development since then.[2] Minitab is distributed by Minitab Inc, a privately owned company headquartered in State College, Pennsylvania, with subsidiaries in Coventry, England (Minitab Ltd.), Paris, France (Minitab SARL) and Sydney, Australia (Minitab Pty.).
Today, Minitab is often used in conjunction with the implementation of Six sigma, CMMI and other statistics-based process improvement methods. Minitab 17, the latest version of the software, is available in 8 languages: English, French, German, Japanese, Korean, Portuguese, Simplified Chinese, & Spanish. Uses of Minitab[edit] See also[edit] References[edit] "Minitab Statistical Software Features - Minitab. "