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On the Problem of Maximizing the Probability of Successful Passing of a Time-Limited Test

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Abstract

The problem of finding the optimal sequence of performing a set of tasks in a time-limited test is considered. That is, a task group is allocated for mandatory initial execution in the test, the remaining tasks are performed during the remaining time until the end of the test. For each correctly completed task of the test, the subject is awarded a certain number of points. The proposed criterion is the probability that the total number of points scored for the test exceeds a certain level, which is a fixed parameter, while simultaneously fulfilling the time limit of the test. Random parameters are the user’s response time to each test task. The correctness of the user’s answer to the task is modeled by a random variable with a Bernoulli distribution. The resulting stochastic bilinear programming problem boils down to a deterministic integer problem of mathematical programming.

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REFERENCES

  1. Van der Linden, W.J., Scrams, D.J., Schnipke, D.L., et al., Using Response-Time Constraints to Control for Differential Speededness in Computerized Adaptive Testing, Apll. Psychol. Meas., 1999, vol. 23, no. 3, pp. 195–210.

    Article  Google Scholar 

  2. Rasch, G., Probabilistic Models for Some Intelligence and Attainment Tests, Chicago: The University of Chicago Press, 1980.

    Google Scholar 

  3. Kuravsky, L.S., Marmalyuk, P.A., Alkhimov, V.I., and Yuryev, G.A., A New Approach to the Construction of Intellectual and Competency Tests, Modelirovanie i Analiz Dannyh, 2013, no. 1, pp. 4–28.

  4. Kuravsky, L.S., Margolis, A.A., Marmalyuk, P.A., Panfilova, A.S., Yuryev, G.A., and Dumin, P.N., A Probabilistic Model of Adaptive Training, Appl. Math. Sci., 2016, vol. 10, no. 48, pp. 2369–2380.

    Google Scholar 

  5. Naumov, A.V. and Martyushova, Ya.G., Adapting a Distance Learning System Based on Statistical Processing of User Performance Results, Tr. MAI, no. 109, December 2019.

  6. Bosov, A.V., Martyushova, Ya.G., Naumov, A.V., and Sapunova, A.P., Bayesian Approach to Building an Individual Trajectory of a User in a Distance Learning System, Informatika i Ee Primeneniya, 2020, vol. 14, no. 3, pp. 86–93.

  7. Naumov, A.V., Dzhumurat, A.S., and Inozemtsev, A.O., The CLASS.NET System for Distance Learning of Mathematical Disciplines, Vestnik Komp’yuternykh i Informatsionnykh Tekhnologii, 2014, no. 10, pp. 36–40.

  8. MAI CLASS.NET Distance Learning System [Electronic resource], https://distance.kaf804.ru/. Accessed February 27, 2003.

  9. Bosov, A.V., Mkhitarian, G.A., Naumov, A.V., and Sapunova, A.P., Using the Gamma Distribution in the Task of Forming a Time-Limited Test, Informatika i Ee Primeneniya, 2019, vol. 13, no. 4, pp. 12–18.

  10. Naumov, A.V., Mkhitarian, G.A., and Cherygova, E.E., Stochastic Formulation of the Task of Forming a Test of a Given Level of Difficulty with Minimization of the Time of Completion Quantile, Vestnik Komp’yuternykh i Informatsionnykh Tekhnologii, 2019, no. 2, pp. 37–46.

  11. Kan, Yu.S. and Kibzun, A.I., Zadachi stokhasticheskogo programmirovaniya s veroyatnostnymi kriteriyami (Problems of Stochastic Programming with Probabilistic Criteria), Moscow: Fizmatlit, 2009.

    Google Scholar 

  12. Kibzun, A.I., Naumov, A.V., and Norkin, V.I., Reduction of a Quantile Optimization Problem with Discrete Distribution to a Mixed Integer Programming Problem, Autom. Remote Control, 2013, vol. 74, no. 6, pp. 951–967.

    Article  MathSciNet  Google Scholar 

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Funding

This work was supported by the Russian Science Foundation, project no. 23-21-00293.

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Authors and Affiliations

  1. Moscow Aviation Institute (National Research University), Moscow, Russia

    A. V. Naumov, A. E. Stepanov & A. E. Ustinov

Authors
  1. A. V. Naumov
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  2. A. E. Stepanov
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  3. A. E. Ustinov
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Correspondence to A. V. Naumov, A. E. Stepanov or A. E. Ustinov.

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This paper was recommended for publication by A.I. Kibzun, a member of the Editorial Board

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Naumov, A.V., Stepanov, A.E. & Ustinov, A.E. On the Problem of Maximizing the Probability of Successful Passing of a Time-Limited Test. Autom Remote Control 85, 60–67 (2024). https://doi.org/10.1134/S0005117924010053

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  • DOI: https://doi.org/10.1134/S0005117924010053

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