Two Inverse Normalizing Transformation methods for the process capability analysis of non-normal process data

- An Inverse Normalizing Transformation (INT) method is presented for PCIs of non-normal processes.
- A Simplified INT method using cubic spline interpolation is proposed to simplify its calculation.
- Simulation results show the INT method and Simplified INT method are superior to the existed ones.
- An example is given to show the advantage of these methods in terms of p value and non-conforming rate.

For process capability analysis of non-normal processes, the non-normal data are often converted into normal data using transformation techniques, then use the conventional normal method to estimate the process capability indices (PCIs), and they are heavily affected by the transformation accuracy of the transformation methods. To enhance the transformation accuracy and improve the PCIs estimation, an Inverse Normalizing Transformation (INT) method is introduced to estimate PCIs for non-normal processes, and a Simplified INT method using cubic spline interpolation is further proposed to simplify its calculation. The performance of the proposed methods is assessed by a simulation study under Gamma, Lognormal and Weibull distributions, and simulation results show that the INT method and Simplified INT method perform better than the existed ones on the whole. Finally, a real case study is presented to show the application of the proposed methods.

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