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<p>The process capability index (PCI) is a valuable tool for evaluating how effectively a product meets customer expectations and for assessing overall process performance. When the quality characteristics of a process follow a normal distribution, conventional PCIs typically provide reliable and accurate results. However, these traditional indices may lead to incorrect conclusions when applied to non-normally distributed processes, potentially resulting in flawed decisions. In light of this challenge, the present study focuses on the process capability index <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(C_{pc}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mrow> <mi mathvariant="italic">pc</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>, which remains suitable for both normal and non-normal process distributions. Specifically, we consider a process that follows the Dhillon distribution. Further, classical estimation along with classical confidence intervals and bootstrap confidence intervals for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(C_{pc}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mrow> <mi mathvariant="italic">pc</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> are constructed and evaluated based on their average widths and coverage probabilities. Additionally, Bayesian estimation of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(C_{pc}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mrow> <mi mathvariant="italic">pc</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> is carried out using both the product spacing and likelihood functions under symmetric and asymmetric loss functions assuming objective priors for the model parameters through Markov Chain Monte Carlo algorithm. A detailed Monte Carlo simulation study is conducted to evaluate the performance of the proposed estimators. Finally, the methodology is illustrated using three real datasets, thereby confirming the practicality, flexibility, and reliability of the proposed inferential framework for process capability evaluation.</p>

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Classical and Objective Bayesian Approaches to Estimating the Process Capability Index \( C_{pc} \) for the Dhillon Process Distribution

  • 期刊论文

  • 发表日期：

    2026年3月2日

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  • Sanku Dey,
  • Abhimanyu Singh Yadav

摘要

The process capability index (PCI) is a valuable tool for evaluating how effectively a product meets customer expectations and for assessing overall process performance. When the quality characteristics of a process follow a normal distribution, conventional PCIs typically provide reliable and accurate results. However, these traditional indices may lead to incorrect conclusions when applied to non-normally distributed processes, potentially resulting in flawed decisions. In light of this challenge, the present study focuses on the process capability index \(C_{pc}\) C pc , which remains suitable for both normal and non-normal process distributions. Specifically, we consider a process that follows the Dhillon distribution. Further, classical estimation along with classical confidence intervals and bootstrap confidence intervals for \(C_{pc}\) C pc are constructed and evaluated based on their average widths and coverage probabilities. Additionally, Bayesian estimation of \(C_{pc}\) C pc is carried out using both the product spacing and likelihood functions under symmetric and asymmetric loss functions assuming objective priors for the model parameters through Markov Chain Monte Carlo algorithm. A detailed Monte Carlo simulation study is conducted to evaluate the performance of the proposed estimators. Finally, the methodology is illustrated using three real datasets, thereby confirming the practicality, flexibility, and reliability of the proposed inferential framework for process capability evaluation.