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Related Concept Videos

Confidence Intervals01:21

Confidence Intervals

An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A confidence...
Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...
Hazard Rate01:11

Hazard Rate

The hazard rate, also known as the hazard function or failure rate, is a statistical measure used to describe the instantaneous rate at which an event occurs, given that the event has not yet happened. From a probabilistic perspective, it represents the likelihood that a subject will experience the event in a very small time interval, conditional on surviving up to the beginning of that interval. In terms of frequency, the hazard rate can be viewed as the ratio of the number of events to the...
Confidence Coefficient01:24

Confidence Coefficient

The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under both the...
Prediction Intervals01:03

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
The...

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An R-Based Landscape Validation of a Competing Risk Model
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An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Confidence interval procedures for system reliability and applications to competing risks models.

Yili Hong1, William Q Meeker

  • 1Department of Statistics, Virginia Tech, Blacksburg, VA, 24061, USA, yilihong@vt.edu.

Lifetime Data Analysis
|February 6, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces new methods for estimating system reliability, focusing on confidence intervals for system failure-time quantile functions and cumulative distribution functions. These techniques improve accuracy for complex systems, especially in competing risks scenarios.

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Applied Probability

Background:

  • System reliability is crucial and depends on component reliability and system structure.
  • Estimating system reliability, especially for complex systems like competing risks models, requires accurate confidence intervals (CIs).
  • Existing methods for system reliability CIs can be complex and lack optimal properties.

Purpose of the Study:

  • To develop a general procedure for constructing confidence intervals for the system failure-time quantile function.
  • To develop general procedures for constructing confidence intervals for the system's cumulative distribution function (cdf).
  • To ensure these procedures have good statistical properties and are asymptotically valid.

Main Methods:

  • Utilizing the implicit delta method for quantile function CI construction.
  • Developing general procedures for cumulative distribution function (cdf) CI construction.
  • Conducting simulations to evaluate finite-sample coverage properties and comparing with existing methods.

Main Results:

  • The proposed procedures for system reliability CIs are shown to be asymptotically valid.
  • Simulations indicate good finite-sample coverage properties for the new methods.
  • The procedures demonstrate effectiveness in applications involving competing risks and k-out-of-s systems.

Conclusions:

  • The developed general procedures provide reliable confidence intervals for system reliability metrics.
  • These methods offer improved statistical properties for complex system reliability analysis.
  • The study highlights potential for future research in advanced reliability modeling and estimation.