Apply a general percentile method to evaluate process capability indices

Several process capability indices (PCIs) such as Cp Cpk and Cpm have been used to evaluate process capability by monitoring whether the process tolerance is less than the allowable product tolerance interval. Using the traditional PCI assumes that the underlying distribution is a normal distribution and “six sigma” is adopted to be the process tolerance. However, this assumption may be too restrictive for some practical processes when an underlying probability distribution is skewed. The proposed method for calculating PCI uses a 3-parameters function expressed in terms of its cumulative probability function to approximate a quantile function for given data. Using this approach to derive the extreme percentiles PO.GGB65 and Pooom for a normal or skew process distribution is easy and accurate. The new percentile method is tested on several real data to verify its estimating capability.