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Related Concept Videos

The R Chart01:02

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In statistical process control, control charts, particularly R charts, are instrumental in monitoring process variations and identifying non-random patterns that run charts might miss. R charts track the variability within process subgroups, which is crucial when standard deviation use is impractical or unknown process variations exist.
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Interpreting R Charts01:22

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R chart, or range chart, is a fundamental tool in statistical process control used to monitor the variability within a process. It complements the X-bar (x̄) chart by focusing on the range of the data, rather than individual values, providing a clear picture of the process dispersion over time.
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Interpreting x̄ charts, a type of control chart used in statistical process control helps monitor the variation in processes over time. The x̄ chart is based on the sample mean and allows for monitoring variations in the process mean over time. These charts are pivotal for quality assurance in manufacturing and other sectors.
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Statistical Process Control (SPC) is a method used to monitor and control quality within processes, particularly in manufacturing and service delivery, by employing statistical methods. SPC aims to distinguish between natural (common cause) variation and variation due to specific changes or events (special cause), allowing for timely improvements and sustained quality. The control chart, a pivotal tool in SPC, visually displays data over time alongside a central line of upper and lower control...
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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
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Run charts serve as an essential instrument for visualizing the performance of various processes over time, enabling the identification of trends and patterns crucial for quality improvement. These charts map out a series of data points chronologically, offering insights into the stability and efficiency of a process. A run chart's creation involves plotting data points on a graph, with the time intervals on the horizontal axis and the specific measurements on the vertical axis. For...
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Adaptive EWMA control chart using Bayesian approach under ranked set sampling schemes with application to Hard Bake

Imad Khan1, Muhammad Noor-Ul-Amin2, Dost Muhammad Khan1

  • 1Department of Statistics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa, Pakistan.

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This study introduces a new Bayesian adaptive EWMA (AEWMA) control chart using ranked set sampling (RSS) for improved process monitoring. The proposed method enhances detection of mean shifts compared to traditional simple random sampling techniques.

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Area of Science:

  • Industrial Engineering
  • Statistical Quality Control
  • Bayesian Statistics

Background:

  • Memory-type control charts like CUSUM and EWMA are effective for detecting small to moderate process shifts.
  • Existing methods often rely on simple random sampling (SRS), which may limit sensitivity.

Purpose of the Study:

  • To propose a novel Bayesian adaptive EWMA (AEWMA) control chart using ranked set sampling (RSS).
  • To monitor the mean shift of a normally distributed process under square error loss function (SELF) and linex loss function (LLF).

Main Methods:

  • Development of a Bayesian AEWMA control chart incorporating RSS designs.
  • Performance evaluation using Monte Carlo simulations.
  • Comparison with existing Bayesian AEWMA charts based on SRS.

Main Results:

  • The proposed Bayesian AEWMA control chart with RSS schemes demonstrates higher sensitivity in detecting mean shifts.
  • The average run length (ARL) and standard deviation of run length (SDRL) metrics confirm improved performance.
  • A numerical example in semiconductor fabrication validates the superiority of the proposed method.

Conclusions:

  • The Bayesian AEWMA control chart utilizing RSS designs is more effective than SRS-based methods for detecting process mean shifts.
  • The proposed chart offers enhanced sensitivity and out-of-control signal detection capabilities.