SPCQCharts for a Poisson Parameter λ: Short or Long Runs

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Abstract
Approximately normalized control charts, called Q Charts, have been given by the author in other work for charting variables and for a binomial attributes chart. We consider here the corresponding transformations for Poisson distributions, and give the Q charts technology for controlling a Poisson parameter λ. Charts are given for the two cases when the Poisson parameter λ is known and when it is unknown. The chart for the case when λ is unknown is useful both for short runs and for charting processes at start up before enough data are available to assume that λ is essentially known. The chart for the case when the parameter is assumed known gives probabilities of exceeding the control limits that are better approximated by the nominal normal distribution probabilities than the classical c or u charts. We give some tabular results to compare the goodness of the normal approximation to the probabilities for these charts with the c or u charts, and also with a chart made using a square root normalizing transformation.

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