×

CEV-hybrid DEWMA charts for censored data using Weibull distribution. (English) Zbl 1489.62385

Summary: In this article, a conditionally expected value (CEV) hybrid double exponentially weighted moving average (DEWMA) (named as CEVHDEWMA) control chart for monitoring the mean of Weibull distribution assuming type-I censored data is introduced. The average run length (ARL) is used as the performance assessment criterion for the new proposal. In addition to proposing CEVHDEWMA chart, we also compare its performance to simple hybrid DEWMA chart for censored data and show that the new proposal is more efficient for the detection of an out-of-control situation under different censoring rates. Effect of estimation on the in-control and out-of-control ARL is also studied in this article. To show the application of the proposal in practice, two real-life examples are also a part of this study.

MSC:

62P30 Applications of statistics in engineering and industry; control charts
62N05 Reliability and life testing
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ali, S., Time-between-events control charts for an exponentiated class of distributions of the renewal process, Quality and Reliability Engineering International, 33, 8, 2625-51 (2017) · doi:10.1002/qre.2223
[2] Aslam, M.; Khan, N.; Chi-Hyuck, J., Transactions of Institute of Measurement and Control (2018) · doi:10.1177/0142331216659920
[3] Azam, M.; Aslam, M.; Jun, C.-H., Designing of a hybrid exponentially weighted moving average control chart using repetitive sampling, The International Journal of Advanced Manufacturing Technology, 77, 9-12, 1927-33 (2015) · doi:10.1007/s00170-014-6585-x
[4] Guo, B.; Wang, B. X., Control charts for monitoring the Weibull shape parameter based on type II censored sample, Quality and Reliability Engineering International, 30, 1, 13-24 (2014) · doi:10.1002/qre.1473
[5] Huang, S.; Yang, J.; Xie, M., A study of control chart for monitoring exponentially distributed characteristics based on type II censored samples, Quality and Reliability Engineering International, 33, 7 (2017)
[6] Lawless, J. F., Statistical models and methods for lifetime data (2002), New York: John Wiley and Sons, New York · Zbl 0541.62081
[7] Li, Z.; Kong, Z., A generalized procedure for monitoring right censored failure time data, Quality and Reliability Engineering International, 31, 4, 695-705 (2015) · doi:10.1002/qre.1629
[8] Lu, W., and Tsai, T. R.. 2008. Exponentially Weighted Moving Average Control Chart for Gamma Distribution With Type I Censoring. The 3rd international conference on innovative computing information and control (ICICIC ’08).
[9] Montgomery, D. C., Introduction to statistical quality control (2009), New York: John Wiley & Sons, New York · Zbl 1274.62015
[10] Pascual, F.; Li, S., Monitoring the Weibull shape parameter by control charts for the sample range of type II censored data, Quality and Reliability Engineering International, 28, 2, 233-46 (2012) · doi:10.1002/qre.1239
[11] Polunchenko, A. S.; Sokolov, G.; Tartakovsky, A. G., Optimal design and analysis of the exponentially weighted moving average chart for exponential data, Sri Lankan Journal of Applied Statistics, 15, 2, 55-82 (2013)
[12] Raza, S. M.; Riaz, M.; Ali, S., On the performance of EWMA and DEWMA control charts for censored data, Journal of the Chinese Institute of Engineers, 38, 6, 714-22 (2015) · doi:10.1080/02533839.2015.1016877
[13] Raza, S. M. M.; Riaz, M.; Ali, S., EWMA control chart for poisson-exponential lifetime distribution under type I censoring, Quality and Reliability Engineering International, 32, 3, 995-1005 (2016) · doi:10.1002/qre.1809
[14] Raza, S. M. M.; Siddiqi, A. F., EWMA and DEWMA control charts for poisson‐Exponential distribution: Conditional median approach for censored data, Quality and Reliability Engineering International, 33, 2, 387-99 (2017) · doi:10.1002/qre.2015
[15] Roberts, S. W., Control chart tests based on geometric moving averages, Technometrics, 1, 3, 239-50 (1959) · doi:10.2307/1266443
[16] Steiner, S. H.; Mackay, J., Monitoring process with highly censored data, Journal of Quality Technology, 32, 3, 199-208 (2000) · doi:10.1080/00224065.2000.11979996
[17] Steiner, S. H.; Mackay, J., Detecting changes in the mean from censored lifetime data, Frontiers in Statistical Quality Control, 6, 275-89 (2001)
[18] Steiner, S. H.; Mackay, J., Monitoring process with data censored owing to competing risks by using exponentially weighted moving average control charts, Journal of the Royal Statistical Society: Series C (Applied Statistics), 50, 293-302 (2001) · Zbl 1112.62309 · doi:10.1111/1467-9876.00234
[19] Tsai, T. R.; Lin, C. C., The design of EWMA control chart for average with type-I censored data, International Journal of Quality & Reliability Management, 26, 397-405 (2009) · doi:10.1108/02656710910950379
[20] Zhang, L.; Chen, G., EWMA charts for monitoring the mean of censored Weibull lifetimes, Journal of Quality Technology, 36, 3, 321-5 (2004) · doi:10.1080/00224065.2004.11980277
[21] Zhang, C.; Tsung, F.; Xiang, D., Monitoring censored lifetime data with a weighted‐likelihood scheme, Naval Research Logistics (NRL), 63, 8, 631-46 (2016) · Zbl 1411.90133 · doi:10.1002/nav.21724
[22] Zhang, L.; Govindaraju, K.; Lai, C. D.; Bebbington, M. S., Poisson DEWMA control chart, Communications in Statistics-Simulation and Computation, 32, 4, 1265-83 (2003) · Zbl 1100.62635 · doi:10.1081/SAC-120023889
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.