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Statistical Analysis from the Generalized Inverse Lindley Distribution with Adaptive Type-II Progressively Hybrid Censoring Scheme

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Abstract

The key assumption in accelerated life testing is that the mathematical model concerning the lifetime of the item and the stress is known or can be assumed. In several situations, such life-stress relationships are not known and cannot be assumed, i.e. accelerated life testing information cannot be extrapolated to use situation. So, in such cases, a partially accelerated life test is a more appropriate testing method to be executed for which tested objects are subjected to both normal and accelerated circumstances. Due to continual improvement in manufacturing design, it is more difficult to obtain information about the lifetime of products or materials with high reliability at the time of testing under normal conditions. An approach to accelerate failures is the step-stress partially accelerated life test which increases the load applied to the goods in a particular discrete sequence. In this study, the maximum likelihood estimators of inverse the generalized inverse Lindley distribution parameters and the acceleration factor are investigated in a step-stress partially accelerated life test model utilizing two various types of progressively hybrid censoring systems. Furthermore, the performance of the model parameter estimators with the two progressive hybrid censoring schemes is analyzed and compared in terms of biases and mean squared errors using a Monte Carlo simulation approach.

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Data Availability

The data used in the simulation study was self-generated.

Code availability

There are no real data or data codes used in the research.

References

  1. Epstein B (1954) Truncated life tests in exponential case. Ann Math Stat 25:555–564

    Article  Google Scholar 

  2. Balakrishnan N, Kannan N, Lin CT, Ng HKT (2003) Point and interval estimation for Gaussian distribution based on progressive type-II censored samples. IEEE Tran Reliab 52:90–95

    Article  Google Scholar 

  3. Balakrishnan N, Kannan N, Lin CT, Wu SJS (2004) Inference for the extreme value distribution under progressive type-II censoring. J Stat Comput Simul 74:25–45

    Article  Google Scholar 

  4. Nassr SG, Elharoun NM (2019) Inference for exponentiated Weibull distribution under constant stress partially accelerated life tests with multiple censored. Commun Stat Appl Methods 26(2):131–148

    Google Scholar 

  5. DeGroot MH, Goel PK (1979) Bayesian and optimal design in partially accelerated life testing. Naval Res Logist 16(2):223–235

    Article  Google Scholar 

  6. Bhattacharyya GK, Soejoeti Z (1989) A tampered failure rate model for step-stress accelerated life test. Commun Stat Theory Methods 18(5):1627–1643

    Article  Google Scholar 

  7. Bai DS, Chung SW (1992) Optimal design of partially accelerated life tests for the exponential distribution under Type-I censoring. IEEE Trans Reliab 41(3):400–406

    Article  Google Scholar 

  8. Bai DS, Chung SW, Chun YR (1993) Optimal design of partially accelerated life tests for the lognormal distribution under type-I censoring. Reliab Eng Syst Saf 40:85–92

    Article  Google Scholar 

  9. Abdel-Ghani MM (1998) Investigation of some lifetime models under partially accelerated life tests, Ph.D. Thesis, Department of Statistics. Faculty of Economics and Political Science, Cairo University, Egypt.

  10. Abdel-Ghani MM (2004) The estimation problem of the log-logistic parameters in step partially accelerated life tests using type-I censored data. Nat Rev Social Sci 41(2):1–19

    Google Scholar 

  11. Abd-Elfattah AM, Hassan AS, Nassr SG (2008) Estimation in step-stress partially accelerated life tests for the Burr type XII distribution using type I censoring. Stat Methodol 5(6):502–514

    Article  Google Scholar 

  12. Zhang C, Shi Y, Wu M (2016) Statistical inference for competing risks model in step-stress partially accelerated life tests with progressively type-I hybrid censored Weibull life data. J Comput Appl Math 297:65–74

    Article  Google Scholar 

  13. Bakoban R (2012) Estimation in step-stress partially accelerated life tests for the generalized inverted exponential distribution using type I censoring. Am J Sci Res 3:25–35

    Google Scholar 

  14. Ismail AA, Aly HM (2010) Optimal planning of failure-step stress partially accelerated life test under type II censoring. J Stat Comput Simul 80(12):1335–1348

    Article  Google Scholar 

  15. Ismail AA (2010) Bayes estimation of Gompertz distribution parameters and acceleration factor under partially accelerated life tests with type I censoring. J Stat Comput Simul 80(11):1253–1264

    Article  Google Scholar 

  16. Mohamed AER, Abu-Youssef SE, Ali NS, El-Raheem AA (2018) Inference on constant accelerated life testing based on geometric process for extension of the exponential distribution under type-II progressive censoring. Pak J Stat Oper Res 14(2):233–251

    Article  Google Scholar 

  17. Almarashi AM (2020) Parameters estimation for constant-stress partially accelerated life tests of generalized half-logistic distribution based on progressive type-II censoring. Revstat Stat J 18(4):437–452

    Google Scholar 

  18. Zheng D, Fang X (2017) Exact confidence limits for the acceleration factor under constant-stress partially accelerated life tests with type-I censoring. IEEE Trans Reliab 67(1):92–104

    Google Scholar 

  19. Alam I, Intezar MA, Ahmed A (2021) Costs of maintenance service policy: a new approach on constant stress partially accelerated life test for generalized inverted exponential distribution. Reliab Theory Appl 16(2):45–57

    Google Scholar 

  20. Alam I, Islam AU, Ahmed A (2019) Parametric estimation on constant stress partially accelerated life tests for the exponentiated exponential distribution using multiple censoring. Reliab Theory Appl. 14(4):20–32

    Google Scholar 

  21. Alam I, Ahmed A (2020) Parametric and interval estimation under step-stress partially accelerated life tests using adaptive type-II progressive hybrid censoring. Ann Data Sci. https://doi.org/10.1007/s40745-020-00249-1

    Article  Google Scholar 

  22. Ling L, Xu W, Li M (2009) Parametric inference for progressive type-I hybrid censored data on a simple step-stress accelerated life test model. Math Comput Simul 79(10):3110–3121

    Article  Google Scholar 

  23. Alam I, Anwar S, Sharma LK, Ahmed A (2022) Competing risk analysis in constant stress partially accelerated life tests under censored information. Ann Data Sci. https://doi.org/10.1007/s40745-022-00401-z

    Article  Google Scholar 

  24. Lone SA, Alam I, Rahman A (2022) Statistical analysis under geometric process in accelerated life testing plans for generalized exponential distribution. Ann Data Sci. https://doi.org/10.1007/s40745-022-00397-6

    Article  Google Scholar 

  25. Alam I, Ahmed A (2021) Inference on maintenance service policy under step-stress partially accelerated life tests using progressive censoring. J Stat Comput Simul 92(4):813–829

    Article  Google Scholar 

  26. Almalki SJ, Farghal AWA, Rastogi MK, Abd-Elmougod GA (2022) Partially constant-stress accelerated life tests model for parameters estimation of Kumaraswamy distribution under adaptive type-II progressive censoring. Alex Eng J 61(7):5133–5143

    Article  Google Scholar 

  27. Çetinkaya Ç (2021) Estimation in step-stress partially accelerated life tests for the power lindley distribution under progressive censoring. Gazi Univ J Sci 34(2):579–590

    Article  Google Scholar 

  28. Shi Y (2022) Advances in big data analytics: theory, algorithm and practice. Springer, Singapore

    Book  Google Scholar 

  29. Olson DL, Shi Y (2007) Introduction to business data mining. McGraw-Hill/Irwin, New York

    Google Scholar 

  30. Shi Y, Tian YJ, Kou G, Peng Y, Li JP (2011) Optimization based data mining: theory and applications. Springer, Berlin

    Book  Google Scholar 

  31. Tien JM (2017) Internet of things, real-time decision making, and artificial intelligence. Ann Data Sci 4(2):149–178

    Article  Google Scholar 

  32. Sharma V, Singh S, Singh U, Agiwal V (2015) The inverse Lindley distribution: a stress-strength reliability model with applications to head and neck cancer data. J Ind Prod Eng 32(3):162–173

    Google Scholar 

  33. Sharma VK, Singh SK, Singh U, Merovci F (2016) The generalized inverse Lindley distribution: a new inverse statistical model for the study of upside-down bathtub data. Commun Stat Theory Methods 45(19):5709–5729

    Article  Google Scholar 

  34. Alkarni SH (2015) Extended inverse Lindley distribution: properties and application. Springerplus 4(1):1–13

    Article  Google Scholar 

  35. Hassan AS, Nassr SG (2019) Power Lindley-G family of distributions. Ann Data Sci 6:189–210

    Article  Google Scholar 

  36. Kundu D, Joarder A (2006) Analysis of type-II progressively hybrid censored data. Comput Stat Data Anal 50:2509–2528

    Article  Google Scholar 

  37. Lin CT, Ng HKT, Chan PS (2009) Statistical inference of type-II progressively hybrid censored data with Weibull lifetimes. Commun Stat Theory Methods 38:1710–1729

    Article  Google Scholar 

  38. Ng HKT, Kundu D, Chan PS (2009) Statistical analysis of exponential lifetimes under an adaptive hybrid type-II progressive censoring scheme. Naval Res Logist 56:687–698

    Article  Google Scholar 

  39. Miller RC (1981) Survival analysis. Wiley, NewYork

    Google Scholar 

Download references

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The author received no specific funding for this study.

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Authors and Affiliations

  1. Department of Management, St. Andrews Institute of Technology & Management, Gurgaon, Delhi (NCR), India

    Intekhab Alam

  2. Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, India

    Murshid Kamal

  3. Department of Law and Management, GD Goenka University, Gurugram, Haryana, India

    Mohammad Tariq Intezar

  4. Department of Civil Engineering, Guru Nanak Dev Engineering College, Ludhiana, Punjab, India

    Saqib Showkat Wani

  5. Al-Barkat College of Graduate Studies, Aligarh, India

    Imran Alam

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  1. Intekhab Alam
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  2. Murshid Kamal
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  4. Saqib Showkat Wani
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  5. Imran Alam
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All authors equally contributed. They read and approved the manuscript.

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Alam, I., Kamal, M., Intezar, M.T. et al. Statistical Analysis from the Generalized Inverse Lindley Distribution with Adaptive Type-II Progressively Hybrid Censoring Scheme. Ann. Data. Sci. 11, 479–506 (2024). https://doi.org/10.1007/s40745-022-00453-1

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  • DOI: https://doi.org/10.1007/s40745-022-00453-1

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