Process capability analysis for non-normal relay test data

Abstract

Process capability is the performance of a process under normal and in-control conditions. Its indices are to measure the inherent variability of a process and thus to reflect its performance. To calculate the C p and C pk indices for key characteristics, most industries normally assume the distribution of their process output is normal. It has not been proved that the collected data match the assumption of normality, nor has the accuracy of its process capability indices been proved. Therefore, it is doubtful whether the C p or C pk indices can really reflect the performance of a process. This study concentrates on the investigation of process capability indices for non-normal data, and the quality characteristics are broken down into the following three categories and discussed thoroughly: bilateral specifications; unilateral specification with target value; and unilateral specification without target value. Comparison is made under several theoretical, non-normal distributions. One can see the difference between the non-normal process capability indices and the normal process capability indices by overlooking its theoretical distributions. Finally, this paper provides a decision flow chart on how to calculate the process capability indices for normal and non-normal data. Using S-plus computer language, a program was written to simplify the tedious calculation of the non-normal process capability indices. A realistic example is also given to explain and demonstrate the application of the above method.