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The seven basic tools of quality are a fixed set of visual exercises identified as being most helpful in troubleshooting issues related to quality. [1] They are called basic because they are suitable for people with little formal training in statistics and because they can be used to solve the vast majority of quality-related issues.
When the quality of the output is satisfactory the A.R.L. is a measure of the expense incurred by the scheme when it gives false alarms, i.e., Type I errors (Neyman & Pearson, 1936 [4]). On the other hand, for constant poor quality the A.R.L. measures the delay and thus the amount of scrap produced before the rectifying action is taken, i.e ...
Nelson rules are a method in process control of determining whether some measured variable is out of control (unpredictable versus consistent). Rules for detecting "out-of-control" or non-random conditions were first postulated by Walter A. Shewhart [1] in the 1920s.
In statistics, efficiency is a measure of quality of an estimator, of an experimental design, [1] or of a hypothesis testing procedure. [2] Essentially, a more efficient estimator needs fewer input data or observations than a less efficient one to achieve the Cramér–Rao bound.
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
The Foundations of Statistics are the mathematical and philosophical bases for statistical methods. These bases are the theoretical frameworks that ground and justify methods of statistical inference , estimation , hypothesis testing , uncertainty quantification , and the interpretation of statistical conclusions.
Mathematical statistics is the application of probability theory and other mathematical concepts to statistics, as opposed to techniques for collecting statistical data. [1] Specific mathematical techniques that are commonly used in statistics include mathematical analysis , linear algebra , stochastic analysis , differential equations , and ...
The notable unsolved problems in statistics are generally of a different flavor; according to John Tukey, [1] "difficulties in identifying problems have delayed statistics far more than difficulties in solving problems." A list of "one or two open problems" (in fact 22 of them) was given by David Cox. [2]