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Related Concept Videos

Bootstrapping01:24

Bootstrapping

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The term "bootstrap" originated in the 19th century as a metaphor for self-improvement or achieving something independently, without external assistance. This concept extends to statistical bootstrapping, a self-contained method for estimating population parameters through resampling, even though it can be computationally intensive. Developed by the American statistician Dr. Bradley Efron in 1979, bootstrapping provides a robust way to perform inference when the original sample size is...
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A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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A contingency table provides a way of portraying data that can facilitate calculating probabilities. It is a method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other; The table helps determine conditional probabilities quite quickly and can help systematically organize, analyze and quantify data. The table displays sample values concerning two variables that may be dependent or contingent on one...
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A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
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Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
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Control chart for geometrically distributed data based on Bayesian fast double bootstrap.

Muhammad Yahya Matdoan1,2, Muhammad Mashuri1, Muhammad Ahsan1

  • 1Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Kampus ITS-Sukolilo, Surabaya 60111, Indonesia.

Methodsx
|April 23, 2025
PubMed
Summary
This summary is machine-generated.

A new Bayesian fast double bootstrap (BFDB) method improves parameter estimation for g charts, especially with small sample sizes. BFDB offers superior sensitivity and efficiency for process monitoring compared to traditional methods.

Keywords:
Bayesian fast double bootstrapMinimum variance unbiasedg-Chart Using MVU Estimator and BDFB Estimator

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Area of Science:

  • Industrial Engineering
  • Statistical Process Control
  • Quality Assurance

Background:

  • Accurate parameter estimation is crucial for effective process control using g charts.
  • Traditional methods like maximum likelihood and Bayesian estimation can be inaccurate with small sample sizes.
  • Minimum variance unbiased (MVU) estimators and bootstrap-based Bayesian estimators have limitations in detecting large process shifts.

Purpose of the Study:

  • To introduce a novel Bayesian fast double bootstrap (BFDB) approach for parameter estimation in g-charts.
  • To enhance the accuracy and reliability of process monitoring, particularly in small sample size scenarios.
  • To improve the detection of significant process shifts.

Main Methods:

  • Development of a Bayesian fast double bootstrap (BFDB) algorithm for parameter estimation in g-charts.
  • Comparative analysis of BFDB with existing methods, including minimum variance unbiased (MVU) estimators.
  • Evaluation of sensitivity and computational efficiency in high-quality process monitoring scenarios.

Main Results:

  • The BFDB approach demonstrated superior sensitivity and computational efficiency compared to MVU estimators.
  • BFDB consistently outperformed MVU in high-quality process monitoring scenarios.
  • The method effectively handles small sample sizes and detects large process shifts.

Conclusions:

  • The proposed BFDB method offers a significant advancement in parameter estimation for g-charts.
  • BFDB provides a more accurate and reliable approach to process monitoring, especially under challenging data conditions.
  • This advancement is expected to improve industrial process control and quality assurance.