Bayesian and Shrinkage Estimation of Process Capability Index C_p

ABSTRACT

Recent developments in statistical quality control include the study of the process capability. Much attention has been given to the estimation and the test of hypotheses in this regard. Due to considerable handling of parameter(s) in the past,one may have some prior information in the form of either a point,an interval or in the form of prior distribution. This article provides a class of shrinkage estimators for C _p when apriori or guessed value, say σ₀ of standard deviation σ, is available. Subsequently, the Bayesian estimation of C _p has been done under squared error loss function by assuming quasi-prior distributions of σ and (1/σ). Bayesian estimation of C _p around (1/σ₀) is further tried. The investigation is supported by numerical illustrations wherever necessary.

Keywords:

• Normal distribution
• Process capability index (PCI)
• Guessed value
• Shrinkage estimator
• Bayesian estimation
• Squared error loss function (SELF)

Mathematics Subject Classification:

• 62N10
• 62A15