scholarly journals A Study of Cumulative Quantity Control Chart for a Mixture of Rayleigh Model under a Bayesian Framework

2016 ◽  
Vol 39 (2) ◽  
pp. 185 ◽  
Author(s):  
Muhammad Aslam ◽  
Muhammad Riaz ◽  
Tabassum Naz Sindhu ◽  
Zaheer Ahmed

<p>This study deals with the cumulative charting technique based on a simple and a mixture of Rayleigh models. The respective charting schemes are referred as the SRCQC-chart and the MRCQC-chart. These are stimulated from existing statistical control charts in this direction i.e. the cumulative quantity control (CQC) chart, based on exponential and Weibull models, and the cumulative count control (CCC) chart, based on the simple geometricmodel. Another motivation for this study is the mixture cumulative count control (MCCC) chart based on the two component geometric model. The use of mixture cumulative quantity is an attractive approach for process monitoring. The design structure of the proposed control chart is derived by using the cumulative distribution function of simple, and two components of mixture distribution(s). We observed that the proposed charting structure is efficient in detecting the changes in process parameters. The application of the proposed scheme is illustrated using a real dataset.</p>

Author(s):  
Carrison K.S. Tong ◽  
Eric T.T. Wong

The present study advocates the application of statistical process control (SPC) as a performance monitoring tool for a PACS. The objective of statistical process control (SPC) differs significantly from the traditional QC/QA process. In the traditional process, the QC/QA tests are used to generate a datum point and this datum point is compared to a standard. If the point is out of specification, then action is taken on the product and action may be taken on the process. To move from the traditional QC/QA process to SPC, a process control plan should be developed, implemented, and followed. Implementing SPC in the PACS environment need not be a complex process. However, if the maximum effect is to be achieved and sustained, PACSSPC must be implemented in a systematic manner with the active involvement of all employees from line associates to executive management. SPC involves the use of mathematics, graphics, and statistical techniques, such as control charts, to analyze the PACS process and its output, so as to take appropriate actions to achieve and maintain a state of statistical control. While SPC is extensively used in the healthcare industry, especially in patient monitoring, it is rarely applied in the PACS environment. One may refer to a recent SPC application that Mercy Hospital (Alegent Health System) initiated after it implemented a PACS in November 2003 (Stockman & Krishnan, 2006). The anticipated benefits characteristic to PACS through the use of SPC include: • Reduced image retake and diagnostic expenditure associated with better process control. • Reduced operating costs by optimizing the maintenance and replacement of PACS equipment components. • Increased productivity by identification and elimination of variation and outof- control conditions in the imaging and retrieval processes. • Enhanced level of quality by controlled applications. SPC involves using statistical techniques to measure and analyze the variation in processes. Most often used for manufacturing processes, the intent of SPC is to monitor product quality and maintain processes to fixed targets. Hence besides the HSSH techniques, the proposed TQM approach would include the use of SPC. Although SPC will not improve the reliability of a poorly designed PACS, it can be used to maintain the consistency of how the individual process is provided and, therefore, of the entire PACS process. A primary tool used for SPC is the control chart, a graphical representation of certain descriptive statistics for specific quantitative measurements of the PACS process. These descriptive statistics are displayed in the control chart in comparison to their “in-control” sampling distributions. The comparison detects any unusual variation in the PACS delivery process, which could indicate a problem with the process. Several different descriptive statistics can be used in control charts and there are several different types of control charts that can test for different causes, such as how quickly major vs. minor shifts in process means are detected. These control charts are also used with service level measurements to analyze process capability and for continuous process improvement efforts.


2017 ◽  
Vol 40 (13) ◽  
pp. 3860-3871 ◽  
Author(s):  
Muhammad Abid ◽  
Hafiz Zafar Nazir ◽  
Muhammad Riaz ◽  
Zhengyan Lin

Control charts are widely used to monitor the process parameters. Proper design structure and implementation of a control chart requires its in-control robustness, otherwise, its performance cannot be fairly observed. It is important to know whether a chart is sensitive to disturbances to the model (e.g. normality under which it is developed) or not. This study, explores the robustness of Mixed EWMA-CUSUM (MEC) control chart for location parameter under different non-normal and contaminated environments and compares it with its counterparts. The robustness of the MEC scheme and counterparts is evaluated by using the run length distributions, and for better assessment not only is in-control average run length (ARL) used, but also standard deviation of run length (SDRL) and different percentiles – that is, 5th, 50th and 95th– are considered. A careful insight is necessary in selection and application of control charts in non-normal and contaminated environments. It is observed that the in-control robustness performance of the MEC scheme is quite good in the case of normal, non-normal and contaminated normal distributions as compared with its competitor’s schemes.


2015 ◽  
Vol 18 (2) ◽  
pp. 54-56 ◽  
Author(s):  
Katarína Lestyánszka Škůrková ◽  
Jozefína Kudičová

Abstract Ensuring the process capability currently means the warranty that produced products will be in accordance with requirements, both on the company‘s as well as customer‘s side. This study focuses on the statistical control of injection process capability in serial production in a company focusing on products for healthcare. The injection process is evaluated by control charts, specifically by control chart for average and range ( x̄ , R). As the results showed, based on the chart for average and range, we are able to say that the injection process is under statistical control. The requirement for process capability was met; the indices of process capability Cp and Cpk are higher than the determined value 1.33. The normality of measured values was verified by histogram. The obtained values are: Cp = 1.85 and Cpk = 1.82. Therefore, we may consider the process as capable.


2018 ◽  
Vol 35 (2) ◽  
pp. 335-353 ◽  
Author(s):  
Damaris Serigatto Vicentin ◽  
Brena Bezerra Silva ◽  
Isabela Piccirillo ◽  
Fernanda Campos Bueno ◽  
Pedro Carlos Oprime

Purpose The purpose of this paper is to develop a monitoring multiple-stream processes control chart with a finite mixture of probability distributions in the manufacture industry. Design/methodology/approach Data were collected during production of a wheat-based dough in a food industry and the control charts were developed with these steps: to collect the master sample from different production batches; to verify, by graphical methods, the quantity and the characterization of the number of mixing probability distributions in the production batch; to adjust the theoretical model of probability distribution of each subpopulation in the production batch; to make a statistical model considering the mixture distribution of probability and assuming that the statistical parameters are unknown; to determine control limits; and to compare the mixture chart with traditional control chart. Findings A graph was developed for monitoring a multi-stream process composed by some parameters considered in its calculation with similar efficiency to the traditional control chart. Originality/value The control chart can be an efficient tool for customers that receive product batches continuously from a supplier and need to monitor statistically the critical quality parameters.


2019 ◽  
Vol 16 (1) ◽  
pp. 1-13
Author(s):  
Custodio Da Cunha Alves ◽  
Andréa Cristina Konrath ◽  
Elisa Henning ◽  
Olga Maria Formigoni Carvalho Walter ◽  
Edson Pacheco Paladini ◽  
...  

Goal: The objective is to conclude, based on a comparative study, if there is a significant difference in sensitivity between the application of MCE and the individual application of the CUSUM or EWMA chart, i.e., greater sensitivity particularly for cases of lesser magnitude of change. Design/Methodology/Approach: These are an applied research and statistical techniques such as statistical control charts are used for monitoring variability. Results: The results show that the MCE chart signals a process out of statistical control, while individual EWMA and CUSUM charts does not detect any situation out of statistical control for the data analyzed. Limitations: This article is dedicated to measurable variables and individual analysis of quality characteristics, without investing in attribute variables. The MCE chart was applied to items that are essential to the productive process development being analysed. Practical Implications: The practical implications of this study can contribute to: the correct choice of more sensitive control charts to detect mainly small changes in the location (mean) of processes; provide clear and accurate information about the fundamental procedures for the implementation of statistical quality control; and encourage the use of this quality improvement tool. Originality/Value: The MCE control chart is a great differential for the improvement of the quality process of the studied company because it goes beyond what CUSUM and EWMA control charts can identify in terms of variability.


2009 ◽  
Vol 52 (3) ◽  
pp. 272-283 ◽  
Author(s):  
J. Engler ◽  
K.-H. Tölle ◽  
H. H. Timm ◽  
E. Hohls ◽  
J. Krieter

Abstract. Statistical control charts are effective tools to reveal changes in a production process. The CUSUM (cumulative sum) and the EWMA (exponentially weighted moving average) control chart are used to detect small deviations in a process. Data from two sow herds, herd A and herd B, were collected from 1999 to 2004. Farm A had an average number of 530 breeding sows, Farm B had an average of 370 breeding sows. Both herds were diagnosed with Porcine Reproductive and Respiratory Syndrome (PRRS). The weekly means of the number of piglets weaned (NPW), the pre-weaning mortality (PWM) and return to service rate (RSR) were analysed with different settings of the CUSUM as well as the EWMA control chart to reveal a shift in the production process. For the pre-weaning mortality and the number of piglets weaned, the two charts detected a change in the process 4 weeks (Farm A) and 2 weeks before (Farm B) PRRS was diagnosed. The CUSUM and the EWMA chart revealed a shift in the return to service rate on Farm A 3.5 months before PRRS was detected. On Farm B, the signal occurred 6 weeks before the infection was detected. The CUSUM and the EWMA control charts were effective tools for detecting small deviations in sow herd data. Compared with EWMA, the use of the CUSUM chart is more straightforward and the settings are more easily handled. The CUSUM chart is therefore the preferred option for use in practice.


Author(s):  
L. Y. Chan ◽  
M. Xie ◽  
T. N. Goh

In this paper, a two-stage control chart for monitoring the defective rate of high-yield processes is proposed and studied. The Cumulative Count of Conforming control chart is generalized by using the number of items inspected until two defective items are observed. As this will increase the time to alarm, a two-stage approach combining both schemes is proposed. The occurrence of a defective within n1 items inspected in the first stage indicates that the process is out of control. If no defective occurs within n1 items inspected, the occurrence of two defectives within the next n2 - n1 in the second stage also indicates that the process is out of control. The probability of making a false alarm at the first and second stages are equal to α1 and α2, respectively. This procedure improves the sensitivity of the control chart in detecting shifting of the process defective rate p when p is at the parts-per-million order of magnitude.


2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Johnson A. Adewara ◽  
Kayode S. Adekeye ◽  
Olubisi L. Aako

In this paper, two methods of control chart were proposed to monitor the process based on the two-parameter Gompertz distribution. The proposed methods are the Gompertz Shewhart approach and Gompertz skewness correction method. A simulation study was conducted to compare the performance of the proposed chart with that of the skewness correction approach for various sample sizes. Furthermore, real-life data on thickness of paint on refrigerators which are nonnormal data that have attributes of a Gompertz distribution were used to illustrate the proposed control chart. The coverage probability (CP), control limit interval (CLI), and average run length (ARL) were used to measure the performance of the two methods. It was found that the Gompertz exact method where the control limits are calculated through the percentiles of the underline distribution has the highest coverage probability, while the Gompertz Shewhart approach and Gompertz skewness correction method have the least CLI and ARL. Hence, the two-parameter Gompertz-based methods would detect out-of-control faster for Gompertz-based X¯ charts.


2012 ◽  
Vol 12 (04) ◽  
pp. 1250083
Author(s):  
PERSHANG DOKOUHAKI ◽  
RASSOUL NOOROSSANA

In the field of statistical process control (SPC), usually two issues are addressed; the variables and the attribute quality characteristics control charting. Focusing on discrete data generated from a process to be monitored, attributes control charts would be useful. The discrete data could be classified into two categories; the independent and auto-correlated data. Regarding the independence in the sequence of discrete data, the typical Shewhart-based control charts, such as p-chart and np-chart would be effective enough to monitor the related process. But considering auto-correlation in the sequence of the data, such control charts would not workanymore. In this paper, considering the auto-correlated sequence of X1, X2,…, Xt,… as the sequence of zeros or ones, we have developed a control chart based on a two-state Markov model. This control chart is compared with the previously developed charts in terms of the average number of observations (ANOS) measure. In addition, a case study related to the diabetic people is investigated to demonstrate the applicability and high performance of the developed chart.


2014 ◽  
Vol 912-914 ◽  
pp. 1189-1192
Author(s):  
Hai Yu Wang

This article discusses robustness to non-normality of EWMA charts for dispersion. Comparison analysis of run length of four kinds of EWMA charts to monitoring process dispersion is provided to evaluate control charts performance and robustness. At last robust EWMA dispersion charts for non-normal processes are proposed by this way.


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