8/29/2023 0 Comments Six sigma math formulasThe area under the distribution curve also represents the probability. The curve is symmetrical about the mean, and the tails extend to infinity. The area under the curve represents 100% of the possible observations. The normal distribution is completely described by its mean and standard deviation. This new plot is called a standard normal histogram. This is called the Z-Transform: Z = (point of interest-μ)/σ. The histogram can be made dimensionless for analysis by setting the mean to zero and scaling the units on the horizontal axis by dividing by the standard deviation. The equation for the variance of the population is σ² = Σ(X-μ)²/ N, and the standard deviation, σ, is the square root of the variance. The mean of the population is the central tendency of the data. The sample mean and standard deviation are used to estimate the population mean and standard deviation, which are denoted by the Greek letters μ and σ. If you have your data in an Excel spreadsheet, you can easily calculate the mean and standard deviation by using the built-in functions, AVE and STDEV. The square root of the variance provides the standard deviation of the sample, s. The equation for variance is s²=Σ (X )²/(N 1). The variance is calculated by squaring and summing the deviation of the individual data points from the mean. The most common measure of variability is the variance. Another measure calculated from the data is the variability, or the degree to which the individuals cluster about the mean. The equation for the mean is (X1+X2+X3+.+XN)/N, also denoted by ΣXi/N. The average value of the data is called the mean or X-bar. Some of the useful characteristics that can be calculated from the data are described below. The confidence in the correctness of that prediction is dependent upon the size of the sample and the behavior of the data. It is more useful to study a sample of that population and infer from the analysis what the entire population most likely looks like. The analysis of the data in this fashion is called descriptive statistics.ĭata about the entire population is not usually studied. For stable processes, the curve would most likely be a normal, or bell-shaped, curve. If you were to acquire metrics on features of 100 "identical" parts and plot the values relative to frequency, you would be plotting a histogram. There exist small variations from part to part or measure to measure. In nature and most manufacturing processes no two things are ever exactly the same. (This information supports an article appearing in the January 2008 issue of Vision Systems Design, "Quality Numbers: Six Sigma.") By Valerie Bolhouse, Certified Six Sigma Blackbelt
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