Designing Exponentially Weighted Moving Average Control Charts under Failure Censoring Reliability Tests

Document Type : Original Article

Authors

1 Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran

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

Abstract

One of the most important quality characteristics in a production process is the product lifetime. The production of highly reliable products is a concern of manufacturers. Since it is time-consuming and costly to measure lifetime data, designing a control chart seems difficult. To solve the problem, lifetime tests are employed. In the present study, one-sided and two-sided EWMA control charts are designed under a type II censoring (failure censoring) life test. Product lifetime is a quality characteristic dealt with in this study. It is assumed to follow the Weibull distribution with a fixed shape parameter and a variable scale parameter. In order to design a control chart, first, the control chart limits are calculated for different parameters, and then the Average Run Length (ARL) in the out-of-control state is used to evaluate the performance of the proposed control chart. Next, a comprehensive sensitivity analysis is performed for the different parameters involved. The computational results show that the one-sided control chart has better performance to detect the shift of lifetime data than the two-sided control chart. The average run length curve of the two-sided control chart is biased, while that of the one-sided control chart is unbiased. A very effective parameter that increases the performance of a control chart is found to be the number of failures in the failure censoring process. Finally, simulated and real examples are provided to show the performance of the proposed control chart.

Keywords


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    1. Tsekouras, K., Dimara, E. and Skuras, D., "Adoption of a quality assurance scheme and its effect on firm performance: A study of greek firms implementing iso 9000", Total quality management, Vol. 13, No. 6, (2002), 827-841, doi: 10.1080/0954412022000010163.
    2. Siraj, I. and Bharti, P.S., "Reliability analysis of a 3d printing process", Procedia Computer Science, Vol. 173, (2020), 191-200, doi: 10.1002/j.1538-7305.1926.tb00125.x.
    3. Montgomery, D.C., "Introduction to statistical quality control, John Wiley & Sons, (2020).
    4. Roberts, S., "Control chart tests based on geometric moving averages", Technometrics, Vol. 42, No. 1, (2000), 97-101, doi: 10.1080/00401706.2000.10485986.
    5. Barlow, R.E. and Proschan, F., Statistical theory of reliability and life testing: Probability models. 1975, Florida State Univ Tallahassee.
    6. Bayati, N. and Kabiri Naeini, M., "Pattern recognition in control chart using neural network based on a new statistical feature", International Journal of Engineering, Vol. 30, No. 9, (2017), 1372-1380, doi: 10.5829/idosi.ije.2017.30.09c.10.
    7. Fattahzadeh, M. and Saghaei, A., "A statistical method for sequential images–based process monitoring", International Journal of Engineering, Vol. 33, No. 7, (2020), 1285-1292, doi: 10.5829/IJE.2020.33.07A.15.
    8. Rasay, H., Fallahnezhad, M. and ZareMehrjardi, Y., "Application of multivariate control charts for condition based maintenance", International Journal of Engineering, Vol. 31, No. 4, (2018), 597-604, doi: 10.5829/ije.2018.31.04a.11.
    9. Sadeghi, H., Owlia, M.S., Doroudyan, M.H. and Amiri, A., "Monitoring financial processes with arma-garch model based on shewhart control chart (case study: Tehran stock exchange)", International Journal of Engineering, Vol. 30, No. 2, (2017), 270-280, doi: 10.5829/idosi.ije.2017.30.02b.14.
    10. Khan, N., Aslam, M., Raza, S.M.M. and Jun, C.H., "A new variable control chart under failureā€censored reliability tests for weibull distribution", Quality and Reliability Engineering International, Vol. 35, No. 2, (2019), 572-581, doi: 10.1002/qre.2422.
    11. Adeoti, O.A. and Ogundipe, P., "A control chart for the generalized exponential distribution under time truncated life test", Life Cycle Reliability and Safety Engineering, Vol. 10, No. 1, (2021), 53-59, doi: 10.1007/s41872-020-00146-9.
    12. Balamurali, S. and Jeyadurga, P., "An attribute np control chart for monitoring mean life using multiple deferred state sampling based on truncated life tests", International Journal of Reliability, Quality and Safety Engineering, Vol. 26, No. 01, (2019), 1950004, doi: 10.1142/S0218539319500049.
    13. Aslam, M., Raza, M.A., Sherwani, R.A.K., Farooq, M., Jeong, J.Y. and Jun, C.-H., "A mixed control chart for monitoring failure times under accelerated hybrid censoring", Journal of Applied Statistics, Vol. 48, No. 1, (2021), 138-153, doi: 10.1080/02664763.2020.1713060.
    14. Gadde, S.R., Fulment, A. and Josephat, P., "Attribute control charts for the dagum distribution under truncated life tests", Life Cycle Reliability and Safety Engineering, Vol. 8, No. 4, (2019), 329-335, doi: 10.1007/s41872-019-00090-3.
    15. Xu, S. and Jeske, D.R., "Weighted ewma charts for monitoring type i censored weibull lifetimes", Journal of Quality Technology, Vol. 50, No. 2, (2018), 220-230, doi: 10.1080/00224065.2018.1436830.
    16. Faraz, A., Saniga, E.M. and Heuchenne, C., "Shewhart control charts for monitoring reliability with weibull lifetimes", Quality and Reliability Engineering International, Vol. 31, No. 8, (2015), 1565-1574, doi: 10.1002/qre.1692.
    17. Rasay, H. and Arshad, H., "Designing variable control charts under failure censoring reliability tests with replacement", Transactions of the Institute of Measurement and Control, Vol. 42, No. 15, (2020), 3002-3011, doi: 10.1177/0142331220938206.
    18. Jun, C.-H., Lee, H., Lee, S.-H. and Balamurali, S., "A variables repetitive group sampling plan under failure-censored reliability tests for weibull distribution", Journal of Applied Statistics, Vol. 37, No. 3, (2010), 453-460, doi: 10.1080/02664760802715914.