Monitoring Lifetime Data for a Failure Censoring Reliability Test with Replacement Using Shewhart Type and Exponentially Weighted Moving Average Control Charts

Document Type : Article

Author

Department of Industrial Engineering, Kermanshah University of Technology, Kermanshah, Iran

Abstract

Lifetime data has two distinguishing features: they are usually censored and have non-normal distributions. Generally speaking, censoring schemes can be classified into (i) censoring schemes with replacement and (ii) censoring schemes without replacement. Replacement during a life testing means that once observing a failure item, it is replaced by a new one. While there is a relatively large body of literature regarding control charts under censoring schemes without replacement, i.e., the second type schemes, designing control charts for the first type schemes has not yet received considerable attention. In this paper, two types of control charts are developed to monitor the lifetime data of an exponentially distributed item. To obtain the information of the lifetime data, failure censoring is conducted: n items are randomly selected and put on the test simultaneously. The test continues until observing r (r≤n) failures. During the test, once observing a failure time, it is replaced by a new one. Development of Shewhart type and exponentially weighted moving average control charts under failure censoring with replacement is the main novelty of the current study. Comparative and simulation studies are conducted. ARL curves are also derived with respect to different parameters of the process.

Keywords

References

  1. References

    1. Rasay H, Naderkhani F, Golmohammadi AM. Designing variable sampling plans based on lifetime performance index under failure censoring reliability tests. Qual Eng. 2020;32(3):354-370. doi:10.1080/08982112.2020.1754426
    2. Xie M, Goh TN, Ranjan P. Some effective control chart procedures for reliability monitoring. Reliab Eng Syst Saf. 2002;77(1):143-150.
    3. Haq A, Abidin ZU. An enhanced CUSUM- t chart for process mean. Qual Reliab Eng Int. 2019;(March):1-14. doi:10.1002/qre.2490
    4. Santiago E, Smith J. Control Charts Based on the Exponential Distribution: Adapting Runs Rules for the t Chart. Qual Eng. 2013;25(1):85-96. doi:10.1080/08982112.2012.740646
    5. Dickinson RM, Roberts DAO, Driscoll AR, Woodall H, Vining GG. CUSUM Charts for Monitoring the Characteristic Life of Censored Weibull Lifetimes CUSUM Charts for Monitoring the Characteristic Life of Censored Weibull Lifetimes. J Qual Technol. 2014;46(4):340-358. doi:10.1080/00224065.2014.11917976
    6. Khan N, Aslam M. A new variable control chart under failure ‐ censored reliability tests for Weibull distribution. Qual Reliab Eng Int. 2019;35(2):572-581. doi:10.1002/qre.2422
    7. Xu S, Jeske DR. Weighted EWMA charts for monitoring type I censored Weibull lifetimes Weighted EWMA charts for monitoring type I censored Weibull lifetimes. J Qual Technol. 2018;50(2):220-230. doi:10.1080/00224065.2018.1436830
    8. Faraz A, Saniga EM, Heuchenne C. Shewhart Control Charts for Monitoring Reliability with Weibull Lifetimes. Qual Reliab Eng Int. 2015;31(8):1565-1574. doi:10.1002/qre.1692
    9. Jeyadurga P, Balamurali S. Evaluation of an np control chart under truncated life test using quick switching sampling system. Trans Inst Meas Control. 2018;40(12):1-8. doi:10.1177/0142331217721314
    10. Aslam M, Khan N, Jun C. A control chart for time truncated life tests using Pareto distribution of second kind. J Stat Comput Simul. 2016;86(11):2113-2122. doi:10.1080/00949655.2015.1103737
    11. Montgomery D. Introduction to Statistical Quality Control. John Wiley & Sons Inc.; 2009. doi:10.1002/1521-3773(20010316)40:6<9823::AID-ANIE9823>3.3.CO;2-C
    12. Rasay H, Arshad H. Designing variable control charts under failure censoring reliability tests with replacement. Trans Inst Meas Control. 2020;42(15):3002-3011. doi:10.1177/0142331220938206
    13. He Y, Wang L, He Z, Wei Y. Product Reliability Oriented Design Scheme of Control Chart Based on the Convergent CEV for Censored Characteristics. Math Probl Eng. 2015;2015. doi:10.1109/ICRSE.2015.7366495
    14. Rasay H, Naderkhani F. Designing a Reliability Quick Switching Sampling Plan based on the Lifetime Performance Index. In: 2020 IEEE International Conference of Prognastic and Health Management. ; 2020:1-7.
    15. Albazli AO, Aslam M, Dobbah SA. A Control Chart for Exponentially Distributed Characteristics Using Modified Multiple Dependent State Sampling. Math Probl Eng. 2020;2020. doi:10.1155/2020/5682587
    16. Shafqat A, Huang Z, Aslam M. Design of X-bar control chart based on Inverse Rayleigh Distribution under repetitive group sampling. Ain Shams Eng J. 2021;12(1):943-953. doi:10.1016/j.asej.2020.06.001
    17. Yousaf R, Ali S, Aslam M. On the Bayesian analysis of two-component mixture of transmuted Weibull distribution. Sci Iran. 2021;28(3):1711-1735. doi:10.24200/SCI.2019.51090.1997
    18. Adeoti OA. On control chart for monitoring exponentially distributed quality characteristic. Trans Inst Meas Control. 2020;42(2). doi:10.1177/0142331219868595
    19. Caballero Morales SO. Economic Statistical Design of Integrated X-bar-S Control Chart with Preventive Maintenance and General Failure Distribution. Reliab Eng Syst Saf. 2013;8(3):80-87. doi:10.1371/journal.pone.0059039
    20. Qiao Y, HU X, SUN J, XU AQ. Optimal Design of One-Sided Exponential EWMA Charts With Estimated Parameters Based on the Median Run Length. IEEE Access. 2019;7:76645-76658. doi:10.1109/ACCESS.2019.2921427
    21. Balamurali S, Jeyadurga P. Economic design of an attribute control chart for monitoring mean life based on multiple deferred state sampling. Appl Stoch Model Bus Ind. 2018;35(3):893-907. doi:10.1002/asmb.2419
    22. Goodarzi A, Amiri A, Asadzadeh S. Monitoring the censored lognormal reliability data in a three-stage process using AFT model. J Ind Eng Int. 2017;13(1):67-80. doi:10.1007/s40092-016-0168-4
    23. Guo B, Wang BX, Xie M. ARL-unbiased control charts for the monitoring of exponentially distributed characteristics based on type-II censored samples. J ofStatistical Comput Simul. 2014;84(12):2734-2747. doi:10.1080/00949655.2014.898766
    24. Aslam M, Jun C-H. Attribute Control Charts for the Weibull Distribution under Truncated Life Tests. Qual Eng. 2015;27(3):283-288. doi:10.1080/08982112.2015.1017649.
Scientia Iranica

Articles in Press, Accepted Manuscript
Available Online from 27 October 2021

Files

Share

How to cite

Statistics