The present article examines the influence of measurement errors of characteristic technological process parameters on the evaluation of process compliance with standards. Quantitative control charts are utilized for the evaluation of technological process compliance, with the a priori probability of decision errors also being taken into consideration. In order to enhance the statistical reliability of such assessments, the use of a posteriori probabilities is proposed. To illustrate this point, the paper undertakes a rigorous analysis of the efficacy of compliance assessment in scenarios where both the parameter values and their measurement errors adhere to uniform probability distributions. Using a Bayesian-based approach to assess a control procedure reduces ambiguity by half. The coefficient of efficiency is introduced in the context of the a posteriori probability, thereby enhancing the statistical reliability of the conformity assessment. The analysis revealed that this coefficient grows as the tolerance limit (action line) nears the value at which the probability density of the controlled parameter approaches zero.

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Determining the Reliability of Assessments of Technological Process Conformance to Standards

  • Yevhen Volodarskyi,
  • Oleh Kozyr,
  • Zygmunt L. Warsza

摘要

The present article examines the influence of measurement errors of characteristic technological process parameters on the evaluation of process compliance with standards. Quantitative control charts are utilized for the evaluation of technological process compliance, with the a priori probability of decision errors also being taken into consideration. In order to enhance the statistical reliability of such assessments, the use of a posteriori probabilities is proposed. To illustrate this point, the paper undertakes a rigorous analysis of the efficacy of compliance assessment in scenarios where both the parameter values and their measurement errors adhere to uniform probability distributions. Using a Bayesian-based approach to assess a control procedure reduces ambiguity by half. The coefficient of efficiency is introduced in the context of the a posteriori probability, thereby enhancing the statistical reliability of the conformity assessment. The analysis revealed that this coefficient grows as the tolerance limit (action line) nears the value at which the probability density of the controlled parameter approaches zero.