Properties of Estimators of the Process Capability Index

Abstract

The capability index is designed for an in-control process with asymmetric tolerances. In this article, the density function of the natural estimator is derived. The expression is in terms of finite sum and only involves standard normal distribution. Four ensemble estimators for are proposed. A simulation study is conducted due to the complexity of the mean-squared error of the estimators. The comparisons among estimators are based on the mean-squared error, standard error and absolute bias of estimators. Furthermore, the ability for an estimator to reach a given capability level is also considered.

Keywords:

• Asymmetric tolerance
• Indirect estimator
• Probability density function
• Ensemble estimator

Mathematics Subject Classification:

• Primary 62F10
• Secondary 62P30

Notes

where

θ₀ is a guessed value of θ and available in addition to sample information.

Note: For those without specific pattern we leave the cells blank.

Note: (a) N ∖A because as and σ = 3.33, μ must equal T; (b) for those without specific trend we leave the cells blank.