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

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.