{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:45:49Z","timestamp":1760060749714,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T00:00:00Z","timestamp":1758499200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Project of the Education Department of Liaoning Province","award":["Grant Nos. JYTMS20230768","22YJC910009","62473183","JYTMS20230773","LJKQZ2021179"],"award-info":[{"award-number":["Grant Nos. JYTMS20230768","22YJC910009","62473183","JYTMS20230773","LJKQZ2021179"]}]},{"name":"Research on Humanities and Social Sciences of the Ministry of Education","award":["Grant Nos. JYTMS20230768","22YJC910009","62473183","JYTMS20230773","LJKQZ2021179"],"award-info":[{"award-number":["Grant Nos. JYTMS20230768","22YJC910009","62473183","JYTMS20230773","LJKQZ2021179"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Grant Nos. JYTMS20230768","22YJC910009","62473183","JYTMS20230773","LJKQZ2021179"],"award-info":[{"award-number":["Grant Nos. JYTMS20230768","22YJC910009","62473183","JYTMS20230773","LJKQZ2021179"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific Research Fund of Educational Department of Liaoning Province, China","award":["Grant Nos. JYTMS20230768","22YJC910009","62473183","JYTMS20230773","LJKQZ2021179"],"award-info":[{"award-number":["Grant Nos. JYTMS20230768","22YJC910009","62473183","JYTMS20230773","LJKQZ2021179"]}]},{"name":"The Education Department of Liaoning Province","award":["Grant Nos. JYTMS20230768","22YJC910009","62473183","JYTMS20230773","LJKQZ2021179"],"award-info":[{"award-number":["Grant Nos. JYTMS20230768","22YJC910009","62473183","JYTMS20230773","LJKQZ2021179"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes two process monitoring schemes, namely the Shiryaev\u2013Roberts (SR) procedure and the cumulative sum (CUSUM) procedure, to detect shifts in the shape and scale parameters of Type I right-censored Gamma-distributed lifetime data. The performance of the proposed schemes is compared with that of an exponentially weighted moving average (EWMA) control chart based on deep learning networks. The performance of the proposed schemes is evaluated under various censoring rates using Monte Carlo simulations, with the average run length (ARL) as the primary metric. Furthermore, the SR and CUSUM schemes are compared for both zero-state and steady-state shifts. Simulation results indicate that the SR and CUSUM procedures exhibit superior performance, with the SR scheme showing particular advantages when the actual shift is small, while the CUSUM chart proves more effective for identifying larger shifts. The shape parameter has a significant effect on the performance of the control charts such that a reduction in the shape parameter effectively improves the ability to capture early offsets. Increased censoring rates reduce detection sensitivity. To maintain ARL0= 370, control limits h adapt differentially. The SR and CUSUM charts with different censoring rates need to recalibrate the parameter to mitigate performance losses under higher censoring conditions. The monitoring performance of the SR and CUSUM chart is enhanced by an increase in sample size. Finally, a practical example is provided to illustrate the application of the proposed monitoring schemes.<\/jats:p>","DOI":"10.3390\/axioms14090713","type":"journal-article","created":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T12:08:03Z","timestamp":1758542883000},"page":"713","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Performance Evaluation of Shiryaev\u2013Roberts and Cumulative Sum Schemes for Monitoring Shape and Scale Parameters in Gamma-Distributed Data Under Type I Censoring"],"prefix":"10.3390","volume":"14","author":[{"given":"He","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China"}]},{"given":"Peile","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China"}]},{"given":"Ruicheng","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China"}]},{"given":"Jiujun","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,22]]},"reference":[{"key":"ref_1","unstructured":"Shewhart, W.A. (1931). Economic Control of Quality of Manufactured Product, Macmillan and Co., Ltd."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1093\/biomet\/41.1-2.100","article-title":"Continuous inspection schemes","volume":"41","author":"Page","year":"1954","journal-title":"Biometrika"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5649","DOI":"10.1080\/00207540701325082","article-title":"A control chart for the Gamma distribution as a model of time between events","volume":"45","author":"Zhang","year":"2007","journal-title":"Int. J. Prod. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2765","DOI":"10.1080\/03610918.2018.1532516","article-title":"A double exponentially weighted moving average chart for time between events","volume":"49","author":"Alevizakos","year":"2020","journal-title":"Commun. Stat.-Simul. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1002\/qre.1813","article-title":"Design of Gamma Charts Based on Average Time to Signal","volume":"32","author":"Yang","year":"2016","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"7790","DOI":"10.1080\/03610918.2016.1252397","article-title":"A generally weighted moving average chart for time between events","volume":"46","author":"Chakraborty","year":"2017","journal-title":"Commun. Stat.-Simul. Comput."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1002\/qre.2430","article-title":"Monitoring of time between events with a double generally weighted moving average control chart","volume":"35","author":"Alevizakos","year":"2019","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1002\/qre.2763","article-title":"Time between events control charts for gamma distribution","volume":"37","author":"Shah","year":"2021","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1002\/qre.2781","article-title":"A triple exponentially weighted moving average control chart for monitoring time between events","volume":"37","author":"Alevizakos","year":"2021","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"19595","DOI":"10.3934\/math.20231000","article-title":"Enhanced fault detection models with real-life applications","volume":"8","author":"Lone","year":"2023","journal-title":"AIMS Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1080\/00224065.2000.11979996","article-title":"Monitoring Processes with Highly Censored Data","volume":"32","author":"Steiner","year":"2000","journal-title":"J. Qual. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1080\/00224065.2014.11917976","article-title":"CUSUM Charts for Monitoring the Characteristic Life of Censored Weibull Lifetimes","volume":"46","author":"Dickinson","year":"2014","journal-title":"J. Qual. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"823","DOI":"10.5351\/KJAS.2016.29.5.823","article-title":"A binomial CUSUM chart for monitoring type I right-censored Weibull lifetimes","volume":"29","author":"Choi","year":"2016","journal-title":"Korean J. Appl. Stat."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1080\/00224065.2018.1436830","article-title":"Weighted EWMA charts for monitoring type I censored Weibull lifetimes","volume":"50","author":"Xu","year":"2018","journal-title":"J. Qual. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Yu, D., Jin, L., Li, J., Qin, X., Zhu, Z., and Zhang, J. (2023). Monitoring the Weibull Scale Parameter Based on Type I Censored Data Using a Modified EWMA Control Chart. Axioms, 12.","DOI":"10.3390\/axioms12050487"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"126797","DOI":"10.1016\/j.eswa.2025.126797","article-title":"Monitoring right censored Weibull distributed lifetime with weighted adaptive CUSUM charts based on dynamic probability limits","volume":"272","author":"Zhang","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2365","DOI":"10.1002\/qre.3347","article-title":"Memory-type control charts for censored reliability data","volume":"39","author":"Ali","year":"2023","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Lee, P.-H., and Liao, S.-L. (2024). Monitoring gamma type-I censored data using an exponentially weighted moving average control chart based on deep learning networks. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-56884-8"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1080\/00949655.2023.2273960","article-title":"Adaptive EWMA control chart for monitoring two-parameter exponential distribution with type-II right censored data","volume":"94","author":"Jiang","year":"2024","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1080\/16843703.2023.2193773","article-title":"Control charts for monitoring relative risk rate in the presence of Weibull competing risks with censored and masked data","volume":"21","author":"Nadi","year":"2024","journal-title":"Qual. Technol. Quant. Manag."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1971","DOI":"10.1002\/qre.3754","article-title":"Control Charts for the Percentiles of an Inverse Pareto Distribution Under Complete and Middle-Censored Data","volume":"41","author":"Chaturvedi","year":"2025","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_22","first-page":"795","article-title":"The problem of the most rapid detection of a disturbance in a stationary process","volume":"2","author":"Shiryaev","year":"1961","journal-title":"Sov.-Math.-Dokl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1214\/aos\/1176347990","article-title":"Sequential Detection of a Change in a Normal Mean when the Initial Value is Unknown","volume":"19","author":"Pollak","year":"1991","journal-title":"Ann. Stat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1080\/02664769624413","article-title":"Data-analytic aspects of the Shiryayev-Roberts control chart: Surveillance of a non-homogeneous Poisson process","volume":"23","author":"Kenett","year":"1996","journal-title":"J. Appl. Stat."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1214\/aos\/1176349142","article-title":"Comparison of EWMA, CUSUM and Shiryayev-Roberts Procedures for Detecting a Shift in the Mean","volume":"21","author":"Srivastava","year":"1993","journal-title":"Ann. Stat."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"728","DOI":"10.1080\/03610918.2011.552823","article-title":"A New Chart for Detecting the Process Mean and Variability","volume":"40","author":"Zhang","year":"2011","journal-title":"Commun. Stat.-Simul. Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1166","DOI":"10.1016\/j.cie.2011.07.006","article-title":"An adaptive Shiryaev-Roberts procedure for monitoring dispersion","volume":"61","author":"Zhang","year":"2011","journal-title":"Comput. Ind. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3225","DOI":"10.1080\/03610920902947774","article-title":"Numerical Comparison of CUSUM and Shiryaev\u2013Roberts Procedures for Detecting Changes in Distributions","volume":"38","author":"Moustakides","year":"2009","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1002\/qre.2945","article-title":"The Shiryaev\u2013Roberts control chart for Markovian count time series","volume":"38","author":"Ottenstreuer","year":"2022","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3379","DOI":"10.1002\/qre.3125","article-title":"Performance of the Shiryaev-Roberts-type scheme in comparison to the CUSUM and EWMA schemes in monitoring weibull scale parameter based on Type I censored data","volume":"38","author":"Yu","year":"2022","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_31","unstructured":"Meeker, W. (1998). Statistical Methods for Reliability Data, Wiley."},{"key":"ref_32","unstructured":"Montgomery, D.C. (2020). Introduction to Statistical Quality Control, Wiley."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/00224065.2019.1611354","article-title":"A Review of Some Sampling and Aggregation Strategies for Basic Statistical Process Monitoring","volume":"53","author":"Zwetsloot","year":"2021","journal-title":"J. Qual. Technol."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/9\/713\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:46:56Z","timestamp":1760035616000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/9\/713"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,22]]},"references-count":33,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["axioms14090713"],"URL":"https:\/\/doi.org\/10.3390\/axioms14090713","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,9,22]]}}}