![]() The target duration for the packages is specified as between 8 days (LSL - Lower Specification Limit) and 12 days (USL - Upper Specification Limit). The height of the line indicates the number of times that the package duration was at the duration of the value. The above curve shows the results (Values) for the number of days between the send date and the arrival date of a package. The curve is characterized by two variables: µ (mean) and σ (standard deviation. The curve shown above is Normal Distribution. The above calculator and exposition show how to analyze and interpret the values (mean and standard deviation) derived from data acquisition and processing.The sigma value is a statistical term that is explained in the following bell-shape curve. Enter values into the green data windows, then press Enter or press the Compute button: What is the numerical value of 5σ when expressed as a p-value? ( Click here for a more detailed description of this problem.)įeel free to compute solutions for problems of your own. To justify announcing a new discovery like the Higgs Boson, experimental physicists require that their data have a p-value equal to or less than 5σ. (1) $ \displaystyle f(x,\mu,\sigma) = \frac$ = percentage rejected.) Figure 1 shows the proportions and percentages one expects to see in a data set for which a Gaussian analysis is appropriate.Ĭaveat: it cannot be overemphasized that many data sets have properties that make them unsuitable for this treatment, and there are any number of stories of misapplication of the Gaussian distribution where another kind of analysis would better fit the data and circumstances.Ī normal (Gaussian) distribution is defined this way: In the analysis method described here, this uncertainty is quantified by the "standard error" value, which is computed along with the values described above and which provides a measure of confidence in the analysis.Īnalysis based on a normal or Gaussian distribution is most appropriate for data sets having an innate normal distribution of its own, that is to say, a centrally weighted grouping of data with decreasing examples far from the average value of the data (the "mean"). It should be noted that this kind of statistical analysis has a degree of uncertainty related to the number of samples or measurements taken. There are many applications for these methods in everyday life - measures of people's height, weight, IQ, and many similar quantities are appropriate to these methods and can provide insight into them. The above is just an example of statistical data analysis. Use the acquired values, the established manufacturing aceptance limits, and a Gaussian curve calculator (also included in this article) to estimate the rate of manufacturing rejects.Process the data set and acquire mean, variance and standard deviation (square root of variance) values using a data processor like that included in this article.Acquire a set of measurements of typical manufactured items, as many measurements as practical.Using statistical analysis methods, you would: You want to be able to predict the number of production rejects based on quality control acceptance limits and a limited set of production measurements. Here's an example - let's say you build widgets that are expected to be 100 cm long but that, when constructed, have some variation in their lengths. With these values in hand, one can predict the properties of the system from which the measurements were acquired. A standard error, an indication of how well the analysis reflects reality. ![]() A standard deviation, which is the variance in a more useful form.A "variance", which quantifies how much the samples differ from the mean value. ![]()
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