A study of process monitoring based on inverse Gaussian distribution

The average run length unbiased control charts are proposed.The parameter estimation seriously affects the performance of the proposed charts.The shape control chart with desired ARL 0 is developed when the parameter is estimated.The sample size largely affects the performance of the location chart.The coefficient of variation greatly influences the ability of the location chart. The inverse Gaussian distribution has considerable applications in describing product life, employee service times, and so on. In this paper, the average run length (ARL) unbiased control charts, which monitor the shape and location parameters of the inverse Gaussian distribution respectively, are proposed when the in-control parameters are known. The effects of parameter estimation on the performance of the proposed control charts are also studied. An ARL-unbiased control chart for the shape parameter with the desired ARL 0 , which takes the variability of the parameter estimate into account, is further developed. The performance of the proposed control charts is investigated in terms of the ARL and standard deviation of the run length. Finally, an example is used to illustrate the proposed control charts.

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