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Estimation of process performance index for the two-parameter exponential distribution with measurement error.

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Area of Science:

  • Industrial Engineering
  • Statistical Quality Control
  • Metrology

Background:

  • Existing process performance indices do not account for inevitable measurement errors.
  • This limitation affects the accuracy of process performance assessment in real-world applications.
  • A robust estimation method is needed to address these inaccuracies.

Purpose of the Study:

  • To propose an estimation method for process performance index in two-parameter exponential distributions considering measurement errors.
  • To fill the gap in current methodologies by incorporating a full error model.
  • To provide a more accurate and reliable assessment of process performance.

Main Methods:

  • Utilized a full error model to describe the relationship between actual and measured values.
  • Employed the maximum likelihood estimation method to determine unknown parameters.
  • Applied the Bootstrap method for constructing confidence intervals of the process performance index.

Main Results:

  • The proposed estimator was evaluated based on bias, mean square error (MSE), and average interval length.
  • Simulation results demonstrated that the new estimator surpasses existing methods in performance.
  • The method was illustrated using mileage data from military personnel carriers.

Conclusions:

  • The developed estimation method effectively incorporates measurement errors into process performance index calculations.
  • The proposed approach offers superior accuracy and reliability compared to traditional methods.
  • This research provides a valuable tool for quality control and process improvement in the presence of measurement uncertainty.