ARL1 of the Attribute c Control Chart with Estimated Parameter

2015 ◽  
Vol 22 (02) ◽  
pp. 1550009 ◽  
Author(s):  
Teodor Tiplica
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Computational Results ◽  
Run Length ◽  
Estimated Parameters ◽  
Starting Point ◽  
Polynomial Expression ◽  
Discrete Nature ◽  
Good Starting Point

In this paper, the out of control average run length (ARL1) of the c control chart with estimated parameter is computed for various shifts in the average number of nonconformities. In spite of the discrete nature of this chart, it is proved that a target in-control average run length (ARL0) can be obtained when the average number of nonconformities is estimated. This is a good starting point for comparing the performances of the c control chart with those of other attribute control charts with estimated parameters. Based on the computational results obtained, it is showed that the ARL1 of the c control chart with estimated parameter can be approximated by using a polynomial expression.

In-control robustness comparison of different control charts

2017 ◽  
Vol 40 (13) ◽  
pp. 3860-3871 ◽  
Author(s):  
Muhammad Abid ◽  
Hafiz Zafar Nazir ◽  
Muhammad Riaz ◽  
Zhengyan Lin
Keyword(s):  
Standard Deviation ◽  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Location Parameter ◽  
Normal Distributions ◽  
Run Length ◽  
Design Structure ◽  
Control Robustness ◽  
Proper Design

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.

Average Run Lengths in Shewhart Type Charts for 2-Order Autoregressive Process

2010 ◽  
Vol 139-141 ◽  
pp. 1860-1863
Author(s):  
Qiu Xia Sun ◽  
Jian Li Zhao ◽  
Qi Sheng Gao
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Correlation Coefficients ◽  
Autoregressive Process ◽  
Run Length ◽  
Shewhart Control ◽  
Control Schemes ◽  
Run Lengths ◽  
Residual Control

In this paper the average run length is adopted as the tool to describe the performance of control charts. The respective methods for calculating the average run length of the modified Shewhart control chart and the Shewhart residual control chart for 2-order autoregressive process are derived and shown in detail. By the proposed approach some numerical results of average run lengths of both Shewhart type charts are formulated and discussed. We analyze and compare that the influence of the correlation coefficients of the 2-order autoregressive process on the performance of both charts based on the estimated data. Several clear and main points of the issue are summed up. Lastly, we give some recommendations for the choice of both Shewhart type control schemes.

scholarly journals New Control Charts for a Multivariate Gamma Distribution

2021 ◽  
pp. 607-614
Author(s):  
Hamzeh Torabi ◽  
Shohreh Enami ◽  
STA Niaki
Keyword(s):  
Control Chart ◽  
Gamma Distribution ◽  
Control Charts ◽  
Normal Approximation ◽  
Average Run Length ◽  
Exact Distribution ◽  
Run Length ◽  
Multivariate Gamma Distribution ◽  
Satterthwaite Approximation

In this study, a multivariate gamma distribution is first introduced. Then, by defining a new statistic, three control charts called the MG charts, are proposed for this distribution. The first control chart is based on the exact distribution of this statistic, the second control chart is based on the Satterthwaite approximation, and the last is based on the normal approximation. Efficiency of the proposed control charts is evaluated by average run length (ARL) criterion.

scholarly journals Moving Average control charts for Burr X and Inverse Gaussian distributions

2020 ◽  
Vol 30 (4) ◽  
Author(s):  
Ambreen Shafqat ◽  
Muhammad Aslam ◽  
Mohammed Albassam
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Inverse Gaussian ◽  
Life Test ◽  
Run Length ◽  
Truncated Life Test ◽  
Average Control ◽  
Better Than

The Burr X and Inverse Gaussian (IG) distributions are considered in this paper to design an attribute control chart for time truncated life test with Moving Average (MA) scheme w. The presentation of the MA control chart is estimated in terms of average run length (ARL) by using the Monte Carlo simulation. The ARL is decided for different values of sample sizes, MA statistics size, parameters’ values, and specified average run length. The performance of this new MA attribute control chart is compared with the usual time truncated control chart for Burr X and IG distributions. The performance of a new control chart is better than the existing control chart.

scholarly journals A New Generalized Range Control Chart for the Weibull Distribution

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Osama H. Arif ◽  
Muhammad Aslam
Keyword(s):  
Weibull Distribution ◽  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Comparison Study ◽  
Exponentially Weighted Moving Average ◽  
Run Length ◽  
Weighted Moving Average ◽  
Exponentially Weighted

In this study, a generalized range control chart is designed for the Weibull distribution using generally weighted moving average statistics. The proposed chart is based on minimum generally weighted moving average statistic and maximum generally weighted moving average statistics. We utilize the inverse erf function to transform the Weibull data to normal data. The necessary measures are given to assess the performance of the proposed control chart. The comparison study shows that the proposed control chart outperforms the existing control charts based on exponentially weighted moving average statistic in terms of the average run length. A real example is given for applying the proposed chart in the industry.

scholarly journals Multiple Dependent State Repetitive Sampling-Based Control Chart for Birnbaum–Saunders Distribution

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Muhammad Aslam ◽  
Ambreen Shafqat ◽  
G. Srinivasa Rao ◽  
Jean-Claude Malela-Majika ◽  
Sandile C. Shongwe
Keyword(s):  
Control Chart ◽  
Simulation Study ◽  
Control Charts ◽  
Average Run Length ◽  
Real Life ◽  
Detection Ability ◽  
Run Length ◽  
Comprehensive Comparison ◽  
Shift Detection ◽  
Dependent State

This paper proposes a new control chart for the Birnbaum–Saunders distribution based on multiple dependent state repetitive sampling (MDSRS). The proposed control chart is a generalization of the control charts based on single sampling, repetitive sampling, and multiple dependent state sampling. Its sensitivity is evaluated in terms of the average run length (ARL) using both exact formulae and simulations. A comprehensive comparison between the Birnbaum–Saunders distribution control chart based on the MDSRS method and other existing competing methods is provided using a simulation study as well as a real-life illustration. The results reveal that the proposed chart outperforms the existing charts considered in this study by having better shift detection ability.

scholarly journals Statistical Design for Monitoring Process Mean of a Modified EWMA Control Chart based on Autocorrelated Data

2021 ◽  
Vol 18 (12) ◽  
Author(s):  
Yadpirun SUPHARAKONSAKUN
Keyword(s):  
Explicit Formula ◽  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Series Data ◽  
Run Length ◽  
Ewma Control Chart ◽  
Autocorrelated Observations ◽  
Normally Distributed

From the principles of statistical process control, the observations are assumed to be identically and independently normally distributed, although this assumption is frequently untrue in practice. Therefore, control charts have been developed for monitoring and detecting data which are autocorrelated. Recently, a modified exponentially weighted moving average (EWMA) control chart has been introduced that is a correction of the EWMA statistic and is very effective for detecting small and abrupt changes in independent normally distributed or autocorrelated observations. In this study, the performance of a modified EWMA chart is investigated by examining the 2 sides of the exact average run length based on an explicit formula when the observations are from a general-order moving average process with exponential white noise. A performance comparison of the EWMA and the modified EWMA control charts is also presented. In addition, the performance of the modified and EWMA control charts is contrasted using Dow Jones composite average from a real-life dataset. The findings suggest that the modified EWMA control chart is more sensitive than the EWMA control chart for almost every case of the studied smoothing parameter and constant values of the control chart. HIGHLIGHTS Autocorrelation data is frequency untrue of assumption practice in time series data Modified EWMA is a new control chart that is effective for detecting change in independent normal distribution and autocorrelated observations The efficiency of the control chart is measured by average run length Explicit formula is easy to derive and provides the exact value of the average run length

Explicit Formulas of ARL on Double Moving Average Control Chart for Monitoring Process Mean of ZIPINAR(1) Model with an Excessive Number of Zeros

2021 ◽  
Author(s):  
Kobkun Raweesawat ◽  
Saowanit Sukparungsee
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Mean Shift ◽  
Process Mean ◽  
Explicit Formulas ◽  
Run Length ◽  
Number Of Zeros ◽  
Excessive Number

Usually, the performance of control charts are widely measured by average run length (ARL). In this paper, the derivative explicit formulas of the ARL for double moving average (DMA) control chart are proposed for monitoring the process mean of zero-inflated Poisson integer-valued autoregressive first-order (ZIPINAR(1)) model. This model is fit when there are an excessive number of zeros in the count data. The performance of the DMA control chart is compared with the results of moving average and Shewhart control charts by considering from out of control average run length (ARL1). The numerical results found that the DMA control chart performed better than other control charts in order to detect mean shift in the process. In addition, the real-world application of the DMA control chart for ZIPINAR(1) process is addressed.

scholarly journals Multiatributte Double Sampling Control Chart

2014 ◽  
Vol 2 (1) ◽  
pp. 42-51
Author(s):  
Esmeralda Ramirez-Mendez ◽  
Mario Cantu-Sifuentes
Keyword(s):  
Control Chart ◽  
Comparative Studies ◽  
Control Charts ◽  
Average Run Length ◽  
Double Sampling ◽  
Manufacturing Processes ◽  
Run Length ◽  
Quality Issues

In recent years, multiattribute control charts have received an increasing attention. These charts are able to monitor two or more attributes in the same chart. In addition, there are many applications of multiatributte control charts in a wide variety of manufacturing processes and services. In this article, a multiattribute double sampling (DS D2) control chart is proposed. Double sampling is a methodology used to improve the efficiency of a control chart to detect quality issues without increase the sampling. Results of comparative studies via simulation indicate that the proposed control chart significantly outperforms in most of the supposed sceneries, in terms of the Average Run Length.

scholarly journals A Nonparametric Shewhart-Type Quality Control Chart for Monitoring Broad Changes in a Process Distribution

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Saad T. Bakir
Keyword(s):  
Quality Control ◽  
Control Chart ◽  
Control Charts ◽  
Probability Distributions ◽  
Average Run Length ◽  
Training Sample ◽  
Statistical Quality Control ◽  
Test Statistic ◽  
Run Length ◽  
Quality Control Chart

This paper develops a distribution-free (or nonparametric) Shewhart-type statistical quality control chart for detecting a broad change in the probability distribution of a process. The proposed chart is designed for grouped observations, and it requires the availability of a reference (or training) sample of observations taken when the process was operating in-control. The charting statistic is a modified version of the two-sample Kolmogorov-Smirnov test statistic that allows the exact calculation of the conditional average run length using the binomial distribution. Unlike the traditional distribution-based control charts (such as the Shewhart X-Bar), the proposed chart maintains the same control limits and the in-control average run length over the class of all (symmetric or asymmetric) continuous probability distributions. The proposed chart aims at monitoring a broad, rather than a one-parameter, change in a process distribution. Simulation studies show that the chart is more robust against increased skewness and/or outliers in the process output. Further, the proposed chart is shown to be more efficient than the Shewhart X-Bar chart when the underlying process distribution has tails heavier than those of the normal distribution.

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