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Transforming the Exponential for SPC Applications

Summary: The long-tailed, positively skewed exponential distribution can be made into an almost symmetric distribution by taking the fourth root of the data. The transformed data can then be plotted conveniently on an individuals chart , an exponentially weighted moving average chart, or a cumulative sum chart for statistical process control (SPC). The log transformation of the exponential distribution, used for proper analysis of variance calculations, does stabilize the variance, but produces a very negatively skewed distribution that is not suitable for SPC applications. The observations for the fourth root can be easily calculated with a pocket calculator by depressing the square root key twice.

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  • Topics: Statistical Process Control (SPC)
  • Keywords: Exponentially weighted moving average control charts (EWMA),Individuals charts,Poisson distribution,Shewhart control chart,Statistical process control (SPC),Cumulative sum control chart (CUSUM)
  • Author: Kittlitz, Rudolf G. Jr.
  • Journal: Journal of Quality Technology