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In the empirical sciences, the so-called three-sigma rule of thumb (or 3 σ rule) expresses a conventional heuristic that nearly all values are taken to lie within three standard deviations of the mean, and thus it is empirically useful to treat 99.7% probability as near certainty.
Mechanical movement is the predominant failure mechanism causing mechanical and electromechanical devices to wear out. For many devices, the wear-out failure point is measured by the number of cycles performed before the device fails, and can be discovered by cycle testing. In cycle testing, a device is cycled as rapidly as practical until it ...
where B 10 is the number of operations that a device will operate prior to 10% of a sample of those devices would fail and n op is number of operations. B 10d is the same calculation, but where 10% of the sample would fail to danger. n op is the number of operations/cycle in one year. [11]
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]
Fastest possible cycle time is 1.5 seconds, hence only 21,600 seconds would have been needed to produce the 14,400 parts. The remaining 7,200 seconds or 2 hours were lost. The OEE is now the 21,600 seconds divided by 28,800 seconds (same as minimal 1.5 seconds per part divided by 2 actual seconds per part), or 75%.
In this case, 70/100 = 0.70 or 70% yield. The same example using first pass yield (FPY) would take into account rework: (# units leaving process A as good parts with no rework) / (# units put into the process) 100 units enter process A, 5 were reworked, and 90 leave as good parts. The FPY for process A is (90-5)/100 = 85/100 = 0.8500
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. [1] [2] The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches.
Statistics is a field of inquiry that studies the collection, analysis, interpretation, and presentation of data. It is applicable to a wide variety of academic disciplines , from the physical and social sciences to the humanities ; it is also used and misused for making informed decisions in all areas of business and government .