IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v216y2021ics0951832021004981.html
   My bibliography  Save this article

Estimation of renewal function under progressively censored data and its applications

Author

Listed:
  • AltındaÄŸ, Ömer
  • AydoÄŸdu, Halil

Abstract

Renewal function is an important tool used by researchers in the fields of applied probability such as reliability theory, risk analysis, inventory theory and warranty analysis etc. Estimation problem of this function under complete and right censored samples is well studied in the literature. However, there isn't any study dealing with the estimation problem of this function under progressive censoring which is used widely in survival and failure analyzes. In this study, estimation problem of renewal function as well as variance function of a renewal process under progressively censored data is considered. Some parametric plug-in estimators are proposed, and their statistical properties are investigated. Consistency and asymptotic unbiasedness of these estimators are established. Possible applications of the estimators in maintenance, warranty and spare parts analyzes are investigated. Numerical procedures are provided to compute renewal and variance functions and their plug-in estimators. Small sample performances of the estimators are evaluated by a simulation study. Finally, two real data sets are examined to exhibit applicability of the estimators in some reliability problems.

Suggested Citation

  • AltındaÄŸ, Ömer & AydoÄŸdu, Halil, 2021. "Estimation of renewal function under progressively censored data and its applications," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    • Handle: RePEc:eee:reensy:v:216:y:2021:i:c:s0951832021004981
    DOI: 10.1016/j.ress.2021.107988
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832021004981
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2021.107988?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Edward W. Frees, 1986. "Warranty analysis and renewal function estimation," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(3), pages 361-372, August.
    2. Richard M. Soland, 1968. "A Renewal Theoretic Approach to the Estimation of Future Demand for Replacement Parts," Operations Research, INFORMS, vol. 16(1), pages 36-51, February.
    3. Ng, H. K. T. & Chan, P. S. & Balakrishnan, N., 2002. "Estimation of parameters from progressively censored data using EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 371-386, June.
    4. Chew, E. P. & Johnson, L. A., 1996. "Service level approximations for multiechelon inventory systems," European Journal of Operational Research, Elsevier, vol. 91(3), pages 440-455, June.
    5. Hongzhou Wang & Hoang Pham, 2006. "Reliability and Optimal Maintenance," Springer Series in Reliability Engineering, Springer, number 978-1-84628-325-3, January.
    6. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, January.
    7. Parsa, Hossein & Jin, Mingzhou, 2013. "An improved approximation for the renewal function and its integral with an application in two-echelon inventory management," International Journal of Production Economics, Elsevier, vol. 146(1), pages 142-152.
    8. Jiang, R., 2020. "A novel two-fold sectional approximation of renewal function and its applications," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    9. Helmut Schneider & Bin‐Shan Lin & Colm O'Cinneide, 1990. "Comparison of Nonparametric Estimators for the Renewal Function," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(1), pages 55-61, March.
    10. Liu, Bin & Wu, Jun & Xie, Min, 2015. "Cost analysis for multi-component system with failure interaction under renewing free-replacement warranty," European Journal of Operational Research, Elsevier, vol. 243(3), pages 874-882.
    11. Sarah Marshall & Richard Arnold & Stefanka Chukova & Yu Hayakawa, 2018. "Warranty cost analysis: Increasing warranty repair times," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(4), pages 544-561, July.
    12. Rezapour, Shabnam & Allen, Janet K. & Mistree, Farrokh, 2016. "Reliable product-service supply chains for repairable products," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 95(C), pages 299-321.
    13. Musleh, Rola M. & Helu, Amal, 2014. "Estimation of the inverse Weibull distribution based on progressively censored data: Comparative study," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 216-227.
    14. Wallace R. Blischke & Ernest M. Scheuer, 1981. "Applications of renewal theory in analysis of the free‐replacement warranty," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(2), pages 193-205, June.
    15. Park, Minjae & Mun Jung, Ki & Park, Dong Ho, 2013. "Optimal post-warranty maintenance policy with repair time threshold for minimal repair," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 147-153.
    16. Stefanka Chukova & Yu Hayakawa, 2004. "Warranty cost analysis: non‐zero repair time," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 20(1), pages 59-71, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ji Hwan Cha & Maxim Finkelstein, 2020. "On optimal life extension for degrading systems," Journal of Risk and Reliability, , vol. 234(3), pages 487-495, June.
    2. Maxim Finkelstein & Ji Hwan Cha, 2022. "Reducing degradation and age of items in imperfect repair modeling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1058-1081, December.
    3. Chengye Ma & Yongjun Du & Lijun Shang & Li Yang & Kaiye Gao, 2023. "Random Maintenance Strategy Modeling of Warranted Products with Reliability Heterogeneity," Sustainability, MDPI, vol. 15(18), pages 1-19, September.
    4. Wang, Xiaolin & Li, Lishuai & Xie, Min, 2020. "An unpunctual preventive maintenance policy under two-dimensional warranty," European Journal of Operational Research, Elsevier, vol. 282(1), pages 304-318.
    5. Ait Mokhtar, El Hassene & Laggoune, Radouane & Chateauneuf, Alaa, 2023. "Imperfect maintenance modeling and assessment of repairable multi-component systems," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    6. Wang, Guan Jun & Zhang, Yuan Lin, 2013. "Optimal repair–replacement policies for a system with two types of failures," European Journal of Operational Research, Elsevier, vol. 226(3), pages 500-506.
    7. Finkelstein, Maxim & Cha, Ji Hwan & Bedford, Tim, 2023. "Optimal preventive maintenance strategy for populations of systems that generate outputs," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    8. Hashemi, M. & Asadi, M. & Tavangar, M., 2022. "Optimal maintenance strategies for coherent systems: A warranty dependent approach," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    9. Jiang, R., 2020. "A novel two-fold sectional approximation of renewal function and its applications," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    10. Ji Hwan Cha & Maxim Finkelstein, 2019. "Optimal preventive maintenance for systems having a continuous output and operating in a random environment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 327-350, July.
    11. Shang, Lijun & Liu, Baoliang & Qiu, Qingan & Yang, Li & Du, Yongjun, 2023. "Designing warranty and maintenance policies for products subject to random working cycles," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    12. Maxim Finkelstein & Mahmood Shafiee, 2017. "Preventive maintenance for systems with repairable minor failures," Journal of Risk and Reliability, , vol. 231(2), pages 101-108, April.
    13. Ji Hwan Cha & Maxim Finkelstein & Gregory Levitin, 2017. "Bivariate preventive maintenance for repairable systems subject to random shocks," Journal of Risk and Reliability, , vol. 231(6), pages 643-653, December.
    14. Maxim Finkelstein & Ji Hwan Cha, 2021. "On degradation-based imperfect repair and induced generalized renewal processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 1026-1045, December.
    15. Asadi, Majid, 2023. "On a parametric model for the mean number of system repairs with applications," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    16. Yongjun Du & Lijun Shang & Qingan Qiu & Li Yang, 2022. "Optimum Post-Warranty Maintenance Policies for Products with Random Working Cycles," Mathematics, MDPI, vol. 10(10), pages 1-16, May.
    17. Maxim Finkelstein & Gregory Levitin & Oleg A Stepanov, 2019. "On operation termination for degrading systems with two types of failures," Journal of Risk and Reliability, , vol. 233(3), pages 419-426, June.
    18. Maxim Finkelstein & Ji Hwan Cha & Amy Langston, 2023. "Termination versus operation extension for degrading systems," Journal of Risk and Reliability, , vol. 237(6), pages 1175-1185, December.
    19. Kumar Gupta, Sanjib & De, Soumen & Chatterjee, Aditya, 2017. "Some reliability issues for incomplete two-dimensional warranty claims data," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 64-77.
    20. Shafiee, Mahmood & Finkelstein, Maxim, 2015. "An optimal age-based group maintenance policy for multi-unit degrading systems," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 230-238.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:216:y:2021:i:c:s0951832021004981. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.