Accuracy Analysis of the Percentile Method for Estimating Non Normal Manufacturing Quality

Abstract

Vännman (1995) proposed a superstructure C_p (u, v) of capability indices for processes with normal distributions, which include C_p, C_pk, C_pm, and C_pmk as special cases. Pearn and Chen (1997) considered a generalization of C_p (u, v), called C_Np (u, v), to cover processes with non normal distributions. Pearn and Chen (1997) also proposed a sample percentile estimator for the generalization C_Np (u, v). In this article, we investigate the performance of the sample percentile estimator. We perform some simulation study, which covers the normal distribution and various non normal distributions including the uniform distribution, chi-square distribution, student's t distributions, F distribution, beta distribution, gamma distribution, Weibull distribution, lognormal distribution, triangular distribution, and Laplace distribution, with selected parameter values. Extensive simulation results, comparisons, and analysis are provided.

Keywords:

• Flexible capability indices
• Non normal distributions
• Relative bias
• Sample percentile estimator
• Simulation

Mathematics Subject Classification:

• Primary 62G05
• Secondary 62P30