| Process capability indices Cp, Cpk, C pm, and Cpmk have been used in manufacturing industries to assess a quantitative measure of process potential and performance. Many studies have pointed out that the normally-based process capability indices (PCIs) are very sensitive to non-normal process. Also these capability indices are calculated using the process mean mu and standard deviation sigma, which are almost always unknown and conventionally replaced with the sample mean X¯ and standard deviation S. Since it is well known that the distribution of X¯ is not stable to non-normality when sample size n is small, say n < 30, and S is not reliable for non-normality, none of the estimates of process capability indices are robust to non-normality.; For the above reasons, this research uses the smooth adaptive estimator, SA, proposed by Han and Hawkins (1994) to construct new and robust process capability indices, Cp, Cpk, C pm, and Cpmk. These indices are called smooth adaptive PCIs to improve the measure performance when the processes are non-normally distributed and sample sizes are small. The main idea of this estimator is to set the weight sequence, wi, with probability one, constant "in the middle" observations and decreasing "toward and extremes" for observations at either end. The smooth adaptive PCIs will be compared with the normally-based (classical), median, and Clements PCIs in term of bias and mean square error.; To investigate the effect of sample size and non-normal processes for the estimated PCIs, we use the bootstrap method and four bootstrap confidence intervals to make the comparisons in a Monte Carlo study. The sample sizes considered are n = 10, 20, 30, and 50. The distributions used in the simulation are the beta distribution, and some bell-shaped (e.g., student-t) and right-skewed (e.g., Gamma) distributions. |
