An attribute control chart for compound Weibull distribution based on median

Öz

This study proposes an attribute control chart for the compound Weibull distribution based on a single sampling plan under a time-truncated life test to monitor failure rates. To provide a more reliable representation of process deterioration in right-skewed lifetime distributions, process shifts are defined in terms of the median lifetime. The performance of the proposed attribute control chart is evaluated under different in-control average run length values, process shift magnitudes, and sample sizes. In addition, the performance of the chart is assessed by calculating the expected average run length and expected quadratic loss values. Design tables are constructed and interpreted by considering different combinations of the compound Weibull distribution shape parameters, sample sizes, average run length values, and process shift magnitudes. Finally, data generated from the compound Weibull distribution are used to demonstrate the effectiveness of the proposed np attribute control chart in detecting changes in the median lifetime and monitoring product quality under a time-truncated life test, and the proposed approach is illustrated through representative example scenarios. Overall, the results demonstrate that the proposed attribute control chart is applicable to processes in which product lifetimes follow the Compound Weibull distribution and provides an effective tool for monitoring process shifts.

Anahtar Kelimeler

• Average run length
• Compound Weibull distribution
• expected average run length
• expected quadratic loss
• Monte Carlo simulation
• standard deviation of the run length
• time-truncated life test.

Destekleyen Kurum

The authors received no specific funding for this research.

Etik Beyan

This study is a theoretical and simulation-based methodological study. It does not involve human participants, animals, or identifiable personal data. Therefore, ethics committee approval was not required.

Teşekkür

The authors would like to thank the anonymous reviewers and the Associate Editor for their valuable comments and constructive suggestions, which helped improve the quality and presentation of this manuscript.

Bileşik Weibull dağılımı için medyan yaşam süresine dayalı niteliksel kontrol kartı

Öz

Bu çalışmada, tek örnekleme planına dayalı ve zaman kısıtlı yaşam testi altında arıza oranlarını izlemek amacıyla bileşik Weibull dağılımı için nitelik kontrol kartı ele alınmıştır. Süreç kaymaları, sağa çarpık yaşam süresi dağılımlarında süreç bozulmasını daha güvenilir biçimde yansıtabilmek amacıyla, medyan yaşam süresi üzerinden tanımlanmıştır. Önerilen nitelik kontrol kartının performansı, farklı kontol içi ortalama işletim uzunluğu değerleri, kayma parametreleri ve örneklem büyüklükleri altında incelenmiştir. Ayrıca, beklenen ortalama işletim uzunluğu, karesel kayıp fonksiyonu değerleri de hesaplanarak kartın performansı değerlendirilmiştir. Bileşik Weibull dağılımı şekil parametreleri, örneklem büyüklükleri, ortalama işletim uzunluğu ve süreç kayma büyüklüklerine ilişkin farklı kombiansyonlar ele alınarak tasarım tabloları hazırlanmış ve yorumlanmıştır. Niteliksel np kontrol kartının medyan yaşam süresindeki değişimleri belirlemede ve zaman kısıtlı yaşam testi altında ürün kalitesini izlemede etkili olduğunu göstermek için bileşik Weibull verisi türetilmiş, örnek senaryolar verilerek açıklanmıştır. Genel olarak, elde edilen bulgular önerilen nitelik kontrol kartının yaşam sürelerinin bileşik Weibull dağılımını izlediği süreçlerde uygulanabilir olduğunu ortaya koymakta ve süreç kaymalarının izlenmesinde etkili bir araç sunduğunu göstermektedir.

Anahtar Kelimeler

• Ortalama işletim uzunluğu
• bileşik Weibull dağılımı
• beklenen ortalama işletim uzunluğu
• beklenen karesel kayıp
• Monte Carlo simülasyonu
• işletim uzunluğunun standart sapması
• zaman kısıtlı yaşam testi

Destekleyen Kurum

Bu çalışma herhangi bir kurum veya kuruluş tarafından desteklenmemiştir.

Etik Beyan

Bu çalışma teorik ve simülasyona dayalı metodolojik bir çalışmadır. Çalışmada insan katılımcılar, deney hayvanları veya kişisel veriler kullanılmadığından etik kurul onayı gerekmemektedir.

Teşekkür

Yazarlar, makalenin kalitesinin ve sunumunun geliştirilmesine katkı sağlayan değerli görüş ve yapıcı önerileri için anonim hakemlere ve Alan Editörüne teşekkür eder.

Kaynakça

1. [1] D. C. Montgomery, 2009, Introduction to Statistical Quality Control, (6th ed) ed. New York: John Wiley & Sons, Inc; 2009.
2. [2] A. Shafqat et al., 2018, Attribute control chart for some popular distributions, Communications in Statistics-Theory and Methods, 47(8), 1978-1988. doi: 10.1080/03610926.2017.1335414
3. [3] O. A. Adeoti, G. S. Rao, M. Ahsan, 2022, Attribute control chart for Rayleigh distribution using repetitive sampling under truncated life test, Journal of Probability and Statistics, 2022(1). doi: 10.1155/2022/8763091
4. [4] T. Kavitha, M. Gunasekaran, 2025, Designing an attribute control chart based on exponential-Rayleigh distribution under hybrid censoring, Reliability: Theory & Applications, 20(2 (84))), 824–833. doi: 10.1080/03610918.2025.2458570
5. [5] N. S. Kolli, G. S. Rao, K. Rosaiah, 2025, A time truncated attribute control chart to monitor urgent physiological investigations turnaround times. Scientific Reports, 15(1), 7556. doi: 10.1038/s41598-024-78106-x
6. [6] C. Nanthakumar, T. Kavitha, 2017, Design of attribute control chart based on Inverse Rayleigh distribution under type-i censoring, International Journal of Scientific Research in Mathematical and Statistical Sciences, 4(6), 17-22. doi:10.26438/ijsrmss/v4i6.1722
7. [7] M. Saha et al., 2023, Time truncated attribute control chart for the Rayleigh distribution quality characteristics and beyond, International Journal of Quality & Reliability Management, 41(8). doi:10.1108/IJQRM-02-2023-0049
8. [8] E. M. Abd Elrazik, 2020, Attribute control charts for the new Weibull Pareto distribution under truncated life tests. Journal of Statistics Applications & Probability, 9(1), 43–49. doi: 10.18576/jsap/090105

9. [9] A. H. Al-Marshadi et al., Performance of a new time-truncated control xhart for Weibull distribution under uncertainty, 2021, International Journal of Computational Intelligence Systems, 14(1), 1256-1262. doi: 10.2991/ijcis.d.210331.00
10. [10] M. Aslam, O. H. Arif, C. H. Jun, An attribute control chart for a Weibull distribution under accelerated hybrid censoring, PLoS ONE, 12, e0173406.
11. [11] M. Aslam, C. H. Jun, 2015, Attribute control charts for the Weibull distribution under truncated life tests, Qual Eng., 27 (3), 283–288. doi:10.1080/08982112.2015.1017649
12. [12] A. Baklizi, S. A. Ghannam, 2022, An attribute control chart for the inverse Weibull distribution under truncated life tests, Heliyon, 8, 12. doi: 10.1016/j.heliyon.2022.e11976
13. [13] N. Khan et.al., 2018, A variable control chart under the truncated life test for Weibull distribution, Technologies, 6(2), 2-10. doi: 10.3390/technologies6020055
14. [14] N. Khan et.al., 2017, A mixed control chart adapted to the truncated life test based on the Weibull distribution. Operations Research and Decisions, 27, 43–55. doi: 10.5277/ord170103
15. [15] M. S. Aldosari, M. Aslam, C. H. Jun, 2017, A new attribute control chart using multiple dependent state repetitive sampling, IEEE Access, 5(3), 6192–6197. doi:10.1109/access.2017.2687523
16. [16] M. Aslam, O. H. Arif, C. H. Jun, 2016, An Attribute Control Chart Based on the Birnbaum-Saunders Distribution Using Repetitive Sampling. In IEEE Access; IEEE:Washington, DC, USA.
17. [17] S. Balamurali, P. Jeyadurga, 2019, 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, 26(01), 1950004. doi: 10.1142/S0218539319500049
18. [18] B. Gokila, A. Sheik Abdullah, 2025, An attribute control chart approach for life testing using Exponential-Poisson distribution, Reliability: Theory & Applications, 20(2 (84)), 727–735. doi:10.24412/1932-2321-2025-489-370-380
19. [19] B. Gokila, A. Sheik Abdullah, 2025, Reliability based an attribute control chart using exponentiated exonential Poisson distribution under hybrid censoring. Reliability: Theory & Applications, 20(3 (86)), 829-840.
20. [20] M. Gunasekaran, 2024, A new attribute control chart based on exponentiated exponential distribution under accelerated life test with hybrid censoring, Reliability: Theory & Applications,4:80(19): 850–860.
21. [21] B. S. Rao, M. R. Reddy, K. Rosaiah, 2023, An attribute control chart for time truncated life tests using exponentiated inverse Kumaraswamy distribution. Reliability: Theory & Applications,3(74), 206-217.
22. [22] T. Kavitha, M. Gunasekaran, 2020, Construction of control chart based on exponentiated exponential distribution, Journal of Engineering Sciences,11(4), 979- 985.
23. [23] R. Nagaraju, M. Palanivel, G. V. Sriramachandran, 2025, Development of an attribute control chart based on the Inverse Kumaraswamy distribution, Reliability: Theory & Applications, 2, 84(20), 372 – 381.
24. [24] G. S. Rao, 2018, A control chart for time truncated life tests using exponentiated half logistic distribution, Applied Mathematics Information Sciences, 12(1), 125-131. doi: 10.18576/amis/120111
25. [25] K. Rosaiah, G. S. Rao, M. S. Babu, 2018, MS. An attribute control chart under truncated life tests for the exponentiated Fréchet distribution, Quality Access to Success, 19(163), 47-51.
26. [26] K. Rosaiah et al., 2021, A control chart for time truncated life tests using Type-II generalized log-logistic distribution, Biometrics and Biostatistics International Journal, 10(4), 138–143. doi: 10.15406/bbij.2021.10.00340
27. [27] G. S. Rao, M. E. Paul, 2020, Time truncated control chart using loglogistic distribution, Biometrics and Biostatistics International Journal, 9, 76- 82. doi: 10.15406/BBIJ.2020.09.00303
28. [28] G. S. Rao, A. K. Fulment, P. K. Josephat, 2019, Attribute control chart for the Dagum distribution under truncated life tests. Life Cycle Reliability and Safety Engineering, 8, 329– 33. doi:10.1007/s41872-019-00090-3
29. [29] H. Tripathi, M. Saha, J. Tushaveera, 2022, Time truncated attribute control chart for generalized half normal distribution and its application, Life Cycle Reliab Safety Eng, 11(3), 229–235. doi: 10.1007/s41872-022-00195-2
30. [30] M. Aslam, N. Khan, C. H. Jun, 2016, A control chart for time truncated life tests using Pareto distribution of second kind, Journal of Statistical Computation and Simulation, 86 (11), 2113-2122. doi: 10.1080/00949655.2015.1103737
31. [31] A. Hag, H.W. Woodall, H. S. Steiner, 2025, A study of attribute control charts for censored lifetime data. Quality Engineering, 37(2):247-256. doi: 10.1080/08982112.2024.2375612
32. [32] N. S. Qutb, E. Rajhi, 2016, Estimation of the parameters of compound Weibull distribution, Journal of Mathematics, 12(4), 11-18. doi:10.9790/5728-1204021118
33. [33] R Core Team. (2025). R: A language and environment for statistical computing (Version 4.5.0). R Foundation for Statistical Computing. Vienna, Austria. https://www.R-project.org/