An inference study on the process capabillity index for non-normal data based on modified weighted variance

When the distribution of a process quality characteristic is non-normal, using conventional process capability indices to calculate the process capability often lead to erroneous interpretation of the process’s capability. A new process capability index is proposed to improve the measurement of process performance when the process data are non-normally distributed. The new process capability index, called Modified Weighted Variance process capability indices (MWV PCIs), pertains to a non-transformation method to calculate the process capability with non-normal quality characteristic. The main idea of the MWV method is to divide a non-normal distribution into two normal distributions from its median to create two new distributions which have the same median but different standard deviations. MWV method is compared by Monte Carlo simulation with another two non-transformation methods, namely Weighted Variance control charting method proposed by BAI & CHOI and Weighted Variance method proposed by WU. When the underlying population is lognormal and Weibull, the MWV PCIs are found to perform better than weighted variance control charting method and Weighted Variance method as the skewness increases.