Bibliographic record
Abstract
A survival distribution is developed for exponential two-component systems that can survive as long as at least one of the two components in the system function. It is assumed that the two components are initially independent and non-identical. If one of the two components fail (repair is impossible), the surviving component is subject to a different failure rate due to the stress caused by the failure of the other. In this paper, we consider such an exponential two-component system failure model when the observed failure time data are (1) complete, (2) Type-I censored, (3) Type-I censored with partial information on component failures, (4) Type-II censored and (5) Type-II censored with partial information on component failures. In these situations, we discuss the maximum likelihood estimates (MLEs) of the parameters by assuming the lifetimes to be exponentially distributed. The exact distributions (whenever possible) of the MLEs of the parameters are then derived by using the conditional moment generating function approach. Construction of confidence intervals for the model parameters are discussed by using the exact conditional distributions (when available), asymptotic distributions, and two parametric bootstrap methods. The performance of these four confidence intervals, in terms of coverage probabilities are then assessed through Monte Carlo simulation studies. Finally, some examples are presented to illustrate all the methods of inference developed here. In the case of Type-I and Type-II censored data, since there are no closed-form expressions for the MLEs, we present an iterative maximum likelihood estimation procedure for the determination of the MLEs of all the model parameters. We also carry out a Monte Carlo simulation study to examine the bias and variance of the MLEs. In the case of Type-II censored data, since the exact distributions of the MLEs depend on the data, we discuss the exact conditional confidence intervals and asymptotic confidence intervals for the unknown parameters by conditioning on the data observed.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.038 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".