Distributions of the Estimated Process Capability Index Cpk
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G. H. Lin
Abstract
Process capability indices Cp and Cpk have been widely used to provide numerical measures on process potential and process performance. While Cp measures process variation relative to the specification tolerance, which only reflects process potential, Cpk considers process variation as well as process centering, which gives an approximate measure of process yield. In this paper, the statistical properties of the estimated Cpk for two classes of stable processes are investigated under different real-world conditions: (1) normal processes with constant mean, and (2) normal processes with known probability P(μ ≥ m) = p, 0 ≤ p ≤ 1, where m is the mid-point of the specification interval. For the two classes of processes, the distributions, the probability density functions, the asymptotic behaviors, and other statistical properties of their estimators are derived.
© Heldermann Verlag
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Articles in the same Issue
- NP-Optimal Kernels for Nonparametric Sequential Detection Rules
- Availability Formulas and Performance Measures for Separable Degradable Networks
- Bayesian Predictions for Exponentially Distributed Failure Times With One Change-Point
- Bayes Inference Problems in Failure-Repair Processes
- Forecasting of Categorical Time Series Using a Regression Model
- Estimation of a Threshold-Value in the Context of Air Pollution and Health
- Estimation of the Jump-Point in a Hazard Function
- Distributions of the Estimated Process Capability Index Cpk
