Average Run Length Performance of Shewhart Control Charts with Interpretation Rules

2006 ◽  
Author(s):  
Abdul Jamali ◽  
Li JinLin ◽  
Muhammad Durad
Keyword(s):  
Control Charts ◽  
Average Run Length ◽  
Run Length ◽  
Shewhart Control Charts ◽  
Shewhart Control

scholarly journals Outliers Detection Models in Shewhart Control Charts; an Application in Photolithography: A Semiconductor Manufacturing Industry

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 857 ◽  
Author(s):  
Ishaq Adeyanju Raji ◽  
Muhammad Hisyam Lee ◽  
Muhammad Riaz ◽  
Mu’azu Ramat Abujiya ◽  
Nasir Abbas
Keyword(s):  
Phase I ◽  
Outlier Detection ◽  
Control Charts ◽  
Semiconductor Manufacturing ◽  
Manufacturing Industry ◽  
Estimation Errors ◽  
Run Length ◽  
Shewhart Control Charts ◽  
Shewhart Control ◽  
Control Limits

Shewhart control charts with estimated control limits are widely used in practice. However, the estimated control limits are often affected by phase-I estimation errors. These estimation errors arise due to variation in the practitioner’s choice of sample size as well as the presence of outlying errors in phase-I. The unnecessary variation, due to outlying errors, disturbs the control limits implying a less efficient control chart in phase-II. In this study, we propose models based on Tukey and median absolute deviation outlier detectors for detecting the errors in phase-I. These two outlier detection models are as efficient and robust as they are distribution free. Using the Monte-Carlo simulation method, we study the estimation effect via the proposed outlier detection models on the Shewhart chart in the normal as well as non-normal environments. The performance evaluation is done through studying the run length properties namely average run length and standard deviation run length. The findings of the study show that the proposed design structures are more stable in the presence of outlier detectors and require less phase-I observation to stabilize the run-length properties. Finally, we implement the findings of the current study in the semiconductor manufacturing industry, where a real dataset is extracted from a photolithography process.

On Shewhart Control Charts for Zero-Truncated Negative Binomial Distributions

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Anwer Khurshid ◽  
Ashit B Chakraborty
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Control Charts ◽  
Negative Binomial ◽  
Average Run Length ◽  
Shewhart Control Charts ◽  
Binomial Distributions ◽  
Shewhart Control ◽  
Cusum Charts ◽  
Number Of Individuals

<p><span>The negative binomial distribution (NBD) is extensively used for the<br /><span>description of data too heterogeneous to be fitted by Poisson<br /><span>distribution. Observed samples, however may be truncated, in the<br /><span>sense that the number of individuals falling into zero class cannot be<br /><span>determined, or the observational apparatus becomes active when at<br /><span>least one event occurs. Chakraborty and Kakoty (1987) and<br /><span>Chakraborty and Singh (1990) have constructed CUSUM and<br /><span>Shewhart charts for zero-truncated Poisson distribution respectively.<br /><span>Recently, Chakraborty and Khurshid (2011 a, b) have constructed<br /><span>CUSUM charts for zero-truncated binomial distribution and doubly<br /><span>truncated binomial distribution respectively. Apparently, very little<br /><span>work has specifically addressed control charts for the NBD (see, for<br /><span>example, Kaminsky et al., 1992; Ma and Zhang, 1995; Hoffman, 2003;<br /><span>Schwertman. 2005).<br /></span></span></span></span></span></span></span></span></span></span></span></span></span></span></p><p><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>The purpose of this paper is to construct Shewhart control charts<br /><span>for zero-truncated negative binomial distribution (ZTNBD). Formulae<br /><span>for the Average run length (ARL) of the charts are derived and studied<br /><span>for different values of the parameters of the distribution. OC curves<br /><span>are also drawn.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br /><br class="Apple-interchange-newline" /></span></p>

scholarly journals Design of a Control Chart Using Extended EWMA Statistic

Technologies ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 108 ◽  
Author(s):  
Muhammad Naveed ◽  
Muhamma Azam ◽  
Nasrullah Khan ◽  
Muhammad Aslam
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Shewhart Control Charts ◽  
Shewhart Control ◽  
Application Data ◽  
Mean And Variance ◽  
The Mean ◽  
Working Procedure

In the present paper, we propose a control chart based on extended exponentially weighted moving average (EEWMA) statistic to detect a quick shift in the mean. The mean and variance expression of the proposed EEWMA statistic are derived. The proposed EEWMA statistic is unbiased and simulation results show a smaller variance as compared to the traditional EWMA. The performance of the proposed control chart with the existing chart based on the EWMA statistic is evaluated in terms of average run length (ARL). Various tables were constructed for different values of parameters. The comparison of the EEWMA control chart with the traditional EWMA and Shewhart control charts illustrates that the proposed control chart performs better in terms of quick detection of the shift. The working procedure of the proposed control chart was also illustrated by simulated and application data.

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.

SIMULATED SHEWHART CONTROL CHART FOR MONITORING VARIANCE COMPONENTS

2009 ◽  
Vol 16 (01) ◽  
pp. 1-22 ◽  
Author(s):  
TZONG-RU TSAI ◽  
YI-WEI HSIEH
Keyword(s):  
Variance Components ◽  
Control Charts ◽  
Average Run Length ◽  
Random Effect ◽  
Random Effect Model ◽  
Simulation Method ◽  
Shewhart Control Charts ◽  
Effect Model ◽  
Shewhart Control ◽  
Simulation Results

Shewhart control charts based on the simulation method are proposed for monitoring separate variance components of the single-factor random effect model. Monte Carlo simulation results show that the proposed control charts have competitive performance relative to the approximate Shewhart regression control charts (ARSCCs) proposed by Chang and Gan2 in terms of the average run length (ARL). Compared with the ARSCCs, our control charts can be constructed easily with less sample resources. The application of our proposed method is illustrated with two examples.

SHEWHART CHARTS FOR THE DETECTION OF LINEAR TRENDS AND OF SHIFTS IN AN AUTOREGRESSION MODEL

2000 ◽  
Vol 07 (04) ◽  
pp. 309-330 ◽  
Author(s):  
RAINER GÖB
Keyword(s):  
Control Charts ◽  
Linear Trend ◽  
Average Run Length ◽  
Model Parameters ◽  
Adjustment Policy ◽  
Shewhart Control Charts ◽  
Shewhart Control ◽  
Autoregression Model ◽  
The Mean ◽  
Biased Estimates

The paper considers a univariate characteristic of a manufacturing process which is measured at discrete time points. The characteristic exhibits a linear trend under an AR(1) disturbance. If the slope of the linear trend and the autoregression coefficient are known, the process characteristic can be adjusted to vary as white noise around its target. However, the adjustment policy is very sensitive to departures from model assumptions and fails to achieve its objective in case of shifted model parameters, e.g., in case of biased estimates or external assignable causes which change the parameters. A discussion of the behaviour of the adjusted process shows that parameter shifts can have harmful consequences. As a protection against parameter shifts, additional statistical monitoring of the process is indispensable. The paper introduces various Shewhart control charts for the detection of shifts in the mean, the trend parameter, or the autoregression parameter. The performance of the charts is analyzed by the average run length criterion.

The Enhanced EWMA Control Chart with Autocorrelation

2014 ◽  
Vol 71 (5) ◽  
Author(s):  
Abbas Umar Farouk ◽  
Ismail Mohamad
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Independence Assumption ◽  
Shewhart Control Charts ◽  
Ewma Chart ◽  
Ewma Control Chart ◽  
Shewhart Control ◽  
Autocorrelated Data ◽  
The Given

Control charts are effective tool with regard to improving process quality and productivity, Shewhart control charts are efficiently good at detecting large shifts in a given process but very slow in detecting small and moderate shifts, such problem could be tackled through design of sensitizing rules. It has been observed that autocorrelation has an advert effect on the control charts developed under the independence assumption [1]. In this article a new EWMA control chart has been introduced with autocorrelation and some run rule schemes were introduced to enhanced the performance of the EWMA control chart when autocorrelated. The three-out-of three EWMA scheme and three-out-of- four EWMA schemes were introduced and the generated data with induced autocorrelation were used to construct the EWMA chart to sensitize the shifts presence.  Simulation of autocorrelated data were carried out for the proposed schemes which detects the shifts as soon as it occurs in the given process, the performance were evaluated using the ARL (average run length) and the results were compared with the published results of Steiner (1991) and the Saccucci (1990) which were designed for large, small and moderate shift. The results indicates that the proposed schemes are more sensitive to the shifts at ARL0=500, 300 and 200 with autocorrelation of 0.2, 0.5 and 0.9 considered in the study.

Sign in / Sign up

Export Citation Format

Share Document