Distributional Properties and Implications of the Estimated Process Incapability Index Ĉⁿ_pp

SYNOPTIC ABSTRACT

Chen (1998) proposed an adjusted incapability index Cⁿ_pp to handle processes with both symmetric and asymmetric tolerances. The incapability index Cⁿ_pp provides an uncontaminated separation between information concerning the process accuracy and the process precision. In order to test whether a normally distributed process is capable or not using the theory of testing statistical hypothesis, we first derive explicit form for the probability density function of the natural estimator of the index Cⁿ_pp. Then, we develop a decision-making rule based on the estimated index Ĉⁿ_pp.

Key Words and Phrases:

• asymmetric tolerances
• decision-making rule
• incapability index
• normal underlying distributions
• sampling distributions