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id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="24346199" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/24346199/The_Modified_r_Out_of_m_Control_Chart">The Modified r Out of m Control Chart</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="46942583" href="https://piraeus.academia.edu/DemetriosAntzoulakos">Demetrios Antzoulakos</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Communications in Statistics - Simulation and Computation, 2008</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline 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ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/35818841/Alarm_rates_for_quality_control_charts">Alarm rates for quality control charts</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="75765081" href="https://independent.academia.edu/VanessaGail">Vanessa Gail</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Alarm rates for quality control charts","attachmentId":55695831,"attachmentType":"pdf","work_url":"https://www.academia.edu/35818841/Alarm_rates_for_quality_control_charts","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/35818841/Alarm_rates_for_quality_control_charts"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="27002273" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/27002273/COMPARATIVE_ANALYSIS_OF_DIFFERENT_APPROACHES_TO_ESTIMATE_THE_RISK_IN_NP_CONTROL_CHARTS">COMPARATIVE ANALYSIS OF DIFFERENT APPROACHES TO ESTIMATE THE RISK IN NP CONTROL CHARTS</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="26183260" href="https://upv.academia.edu/AndresCarrion">Andres Carrion</a></div><p class="ds-related-work--abstract ds2-5-body-sm">One of the tools widely used in modern industry are control charts, of which are the p and np. Conventionally these charts have been constructed using the normal approximation of binomial data, but due to the asymmetry in the exact distribution, this suffers an inaccuracy when the true proportion of nonconforming is small or the sample size is not large enough. This paper shows a comparative review between the different approaches to estimate the probability of the type I error (α) and the probability of the type II error (β) presented in these charts analysis, from a preset alpha value to generates chart design. A detailed comparison of the effect of such approaches to the alpha risk and likewise for the beta risk was performed. Finally, a review was done with respect to the suitability of each approach according to adjustment with the established design.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"COMPARATIVE ANALYSIS OF DIFFERENT APPROACHES TO ESTIMATE THE RISK IN NP CONTROL CHARTS","attachmentId":47262679,"attachmentType":"pdf","work_url":"https://www.academia.edu/27002273/COMPARATIVE_ANALYSIS_OF_DIFFERENT_APPROACHES_TO_ESTIMATE_THE_RISK_IN_NP_CONTROL_CHARTS","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/27002273/COMPARATIVE_ANALYSIS_OF_DIFFERENT_APPROACHES_TO_ESTIMATE_THE_RISK_IN_NP_CONTROL_CHARTS"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="9718668" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/9718668/SAFETY_DATA_SHEET_according_to_Regulation_EC">SAFETY DATA SHEET according to Regulation (EC</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="23308666" href="https://theopage.academia.edu/jakartavanaroma">jakarta van aroma</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"SAFETY DATA SHEET according to Regulation (EC","attachmentId":35905970,"attachmentType":"pdf","work_url":"https://www.academia.edu/9718668/SAFETY_DATA_SHEET_according_to_Regulation_EC","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/9718668/SAFETY_DATA_SHEET_according_to_Regulation_EC"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="36336757" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/36336757/ijircst_2_1_006_33_39_pdf">ijircst-2-1-006-33-39.pdf</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="17130648" href="https://independent.academia.edu/IJIRCSTI">IJIRCST I</a></div><p class="ds-related-work--abstract ds2-5-body-sm">— Various control charts are already developed for the problem of detecting any shift in the mean/median of a sequence of observations from a specified control value taken from some process. Some of them for detecting small shift(s) from the target values are Cumulative Sum (CUSUM), Cumulative Score (CuScore) and recently developed nonparametric charts. Various authors have already worked on CUSUM control charts and found suitable results. Another chart is Cuscore chart, which is also suitable for this situation. Another test is nonparametricCUSUM charts based on nonparametric test statistic. One of the efficient procedure is the Cumulative Sum Control chart (CSCC) originally introduced by Page [1]. The properties of CSCC procedure are usually derived under the assumption that the observations are independent and identically distributed normal random variables, another control chart based on Cumulative Scores developed by Munford [2]. The ARL of this scheme are simpler to compute than those of CSCC. Recently a new control chart is developed based on the nonparametric chart which is preferable from the robustness point of view. Few of the workers on nonparametric CSCC are Parent [3], Reynolds [4, 5], Mcgilchrist and Woodyer [6], Bakir and Reynolds [7] etc. In this paper we want to study the performance of CSCC, CuScore and Nonparametric CUSUM control Chart in detecting the mean/median shift from the specified (target) values. For this purpose we computed the ARL by the simulation method for both in control and under control situations of the process. Results obtained are displayed in various tables using different shift parameters and under different distributions. Results are also shown in graph for easy visual comparison.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"ijircst-2-1-006-33-39.pdf","attachmentId":56244707,"attachmentType":"pdf","work_url":"https://www.academia.edu/36336757/ijircst_2_1_006_33_39_pdf","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/36336757/ijircst_2_1_006_33_39_pdf"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="57014637" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/57014637/On_Statistical_Design_of_the_S_2_Control_Chart">On Statistical Design of the S 2 Control Chart</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="37743105" href="https://independent.academia.edu/CLai4">C. Lai</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Communications in Statistics - Theory and Methods, 2005</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On Statistical Design of the S 2 Control Chart","attachmentId":72117823,"attachmentType":"pdf","work_url":"https://www.academia.edu/57014637/On_Statistical_Design_of_the_S_2_Control_Chart","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/57014637/On_Statistical_Design_of_the_S_2_Control_Chart"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="37472623" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/37472623/SAFETY_DATA_SHEET">SAFETY DATA SHEET</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="93566784" href="https://brawijaya.academia.edu/udiekwidhianto">udiek widhianto</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"SAFETY DATA SHEET","attachmentId":57441517,"attachmentType":"pdf","work_url":"https://www.academia.edu/37472623/SAFETY_DATA_SHEET","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/37472623/SAFETY_DATA_SHEET"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="35690266" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/35690266/The_Effect_of_Level_of_Significance_%CE%B1_on_the_Performance_of_Hotelling_T_2_Control_Chart">The Effect of Level of Significance (α) on the Performance of Hotelling-T 2 Control Chart</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="74666405" href="https://fedpolel.academia.edu/JustusADEMUYIWA">Justus ADEMUYIWA</a></div><p class="ds-related-work--abstract ds2-5-body-sm">Multivariate statistical process control methods are applicable when several process variables are simultaneously monitored. These methods use the relationship between variables to generate powerful control algorithms which are sensitive to assignable causes that are poorly detected by univariate control charts on individual observations. This study looks at the effect of level of significance () on the performance of Hotelling-control chart. The levels of significance were varied from 0.001-0.10. It is however observed that the higher the alpha level, the more sensitive the control chart. 1. INTRODUCTION: The control chart is one of the primary techniques of statistical process control (SPC). A subtle approach towards monitoring and improving quality is statistical process control that aims at quality improvement through reduction of variation.In many quality control settings, the process under examination have two or more correlated quality characteristics (variables), hence an appropriate approach is needed to monitor all these characteristics simultaneously. This leads to the multivariate quality control problem which is the subject of research for many quality control experts. Jackson and Morris (1957) mentioned that multivariate control charts should possess three important properties, namely, they should produce answers to (i) whether the process is in-control (ii) whether the specified probability of type-I error has been maintained and (iii) whether the relationship between the variables is taken into account. As the objective of performing multivariate statistical process control is to monitor the process over time, in order to detect any unusual events that allow quality and process improvement, it is essential to track the cause of an out-of-control signal. However, as opposed to univariate control charts and the complexity of multivariate control charts and the cross correlation among those variables makes the analysis of assignable causes of out-of-control signals difficult.This has been the basis for extensive research performed in the field of multivariate control chart since the 1940s. When Hotelling (1947) recognized that the quality of a product might depend on several correlated characteristics. However, because of computational complexity, researchers and practitioners did not pursue the multivariate quality control at that time. Today, the development of high speed computers, the technological advances in industrial control procedures and the availability of modern data acquisition equipment have alleviated this problem. Thus, many researchers have proposed several multivariate control charts, (Montgomery, 2005). Many control charts have been proposed for multivariate data with the most popular being Hotelling's T 2 and χ 2 (Chi-Square) charts, the multivariate exponentially weighted moving average (MEWMA) charts and the multivariate cumulative sum (MCUMSUM) charts. Lowry and Montgomery (1995) presented a review of these multivariate charts. Mason et al (1997)presented an assessment of many multivariate techniques. In their paper, they recommended when multivariate charts should be used.Hotelling's T 2 and χ 2 charts have been the subject of much research. Mason, Chou and Young (2001) applied the T 2 charts to batch processes. Jarret and Pan (2007) used the chart to monitor the</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The Effect of Level of Significance (α) on the Performance of Hotelling-T 2 Control Chart","attachmentId":55561294,"attachmentType":"pdf","work_url":"https://www.academia.edu/35690266/The_Effect_of_Level_of_Significance_%CE%B1_on_the_Performance_of_Hotelling_T_2_Control_Chart","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/35690266/The_Effect_of_Level_of_Significance_%CE%B1_on_the_Performance_of_Hotelling_T_2_Control_Chart"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="89401744" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/89401744/Rare_Events_F_Galetto_Control_Charts_for_TBE_and_Quality_Decisions">Rare Events F Galetto Control Charts for TBE and Quality Decisions</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="38714012" href="https://independent.academia.edu/FaustoGaletto">Fausto Galetto</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2022</p><p class="ds-related-work--abstract ds2-5-body-sm">We deal with Control Charts (CC) when the data are exponentially distributed. We will use the data taken from the book of D. C. Montgomery Introduction to Statistical Quality Control which is also an example of two papers dealing with CC based on a method “Box-plot” for Time Between Events (TBE). Since T Charts are claimed to be a good method for dealing with “rare events”, we consider, as well, the Minitab Software for “T Charts”. We will compare the two methods, “Box-plot” and “T Charts” with the Reliability Integral Theory (RIT) of Reliability Tests, for various cases found in the literature. In order to reduce the paper length we cannot provide the author’s ideas related to those of W. Shewhart about the Control Charts; the reader can appreciate the big difference between the Shewhart Control Charts and the TBE Control Charts by reading the author’s books. Doing that the future decisions of the Decision Makers will be sounder when the data are not normally distributed.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Rare Events F Galetto Control Charts for TBE and Quality Decisions","attachmentId":93212247,"attachmentType":"docx","work_url":"https://www.academia.edu/89401744/Rare_Events_F_Galetto_Control_Charts_for_TBE_and_Quality_Decisions","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/89401744/Rare_Events_F_Galetto_Control_Charts_for_TBE_and_Quality_Decisions"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="51429176" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/51429176/Specific_activities_and_DOE_STD_1027_92_hazard_Category_2_thresholds_LANL_fact_sheet">Specific activities and DOE-STD-1027-92 hazard Category 2 thresholds, LANL fact sheet</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="50416684" href="https://independent.academia.edu/GuthrieMiller">Guthrie Miller</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1994</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Specific activities and DOE-STD-1027-92 hazard Category 2 thresholds, LANL fact sheet","attachmentId":69158440,"attachmentType":"pdf","work_url":"https://www.academia.edu/51429176/Specific_activities_and_DOE_STD_1027_92_hazard_Category_2_thresholds_LANL_fact_sheet","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/51429176/Specific_activities_and_DOE_STD_1027_92_hazard_Category_2_thresholds_LANL_fact_sheet"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":50829347,"attachmentType":"doc","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":50829347,"attachmentType":"doc","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_50829347" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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