Process Capability Index for Simple Linear Profile in the Presence of Within- and Between-Profile Autocorrelation

Aylin Pakzad (), Ali Yeganeh, Rassoul Noorossana and Sandile Charles Shongwe
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Aylin Pakzad: Department of Industrial Engineering, Kosar University of Bojnord, Bojnord 9453155168, Iran
Ali Yeganeh: Department of Mathematical Statistics and Actuarial Science, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9301, South Africa
Rassoul Noorossana: Information Systems and Operations Management Department, College of Business, University of Central Oklahoma, Edmond, OK 73034, USA
Sandile Charles Shongwe: Department of Mathematical Statistics and Actuarial Science, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9301, South Africa

Mathematics, 2024, vol. 12, issue 16, 1-40

Abstract: In many situations, the quality of a process or product can be characterized by a functional relationship or profile. It is well-known that the independence assumptions of the error terms within or between profiles are not always valid and could be violated due to within or between profile autocorrelation. Since most of the process capability indices (PCIs) have been developed for simple linear profiles (SLPs) without considering autocorrelation, this paper provides some novel methods to analyze the capability of SLP under each of the two different autocorrelation effects separately, as well as the case where both autocorrelation effects are present. We assume that the first-order autoregressive AR(1) model explains the within- and between-profile autocorrelation in error terms. To evaluate the process capability, a new functional index called C p ‴ ( P r o f i l e ) is introduced for SLP with independent errors, and then it is modified to include the three possible cases of within, between, and simultaneous autocorrelation. The simulation results demonstrate that the proposed schemes outperform existing schemes regarding bias and mean square error (MSE) criteria. Moreover, bootstrap confidence intervals for the proposed index are obtained. Finally, an illustrative example in the chemical industry is used to demonstrate the applicability of the proposed method.

Keywords: autocorrelated simple linear profiles; functional approach; process capability analysis; statistical analysis; within- and between-profile autocorrelation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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