scholarly journals Performance of Synthetic Double Sampling Chart with Estimated Parameters Based on Expected Average Run Length

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Huay Woon You
Keyword(s):  
Standard Deviation ◽  
Phase I ◽  
Process Parameters ◽  
Average Run Length ◽  
Performance Measure ◽  
Double Sampling ◽  
Control Phase ◽  
Run Length ◽  
Estimated Parameters ◽  
The Common

A synthetic double sampling (SDS) chart is commonly evaluated based on the assumption that process parameters (namely, mean and standard deviation) are known. However, the process parameters are usually unknown and must be estimated from an in-control Phase-I dataset. This will lead to deterioration in the performance of a control chart. The average run length (ARL) has been implemented as the common performance measure in process monitoring of the SDS chart. Computation of ARL requires practitioners to determine shift size in advance. However, this requirement is too restricted as practitioners may not have the experience to specify the shift size in advance. Thus, the expected average run length (EARL) is introduced to assess the performance of the SDS chart when the shift size is random. In this paper, the SDS chart, with known and estimated process parameters, was evaluated based on EARL and compared with the performance measure, ARL.

scholarly journals The Expected Average Run Length of the EWMA Median Chart with Estimated Process Parameters

2020 ◽  
Vol 49 (3) ◽  
pp. 19-24
Author(s):  
Huay Woon You ◽  
Michael Khoo Boon Chong ◽  
Chong Zhi Lin ◽  
Teoh Wei Lin
Keyword(s):  
Phase I ◽  
Control Chart ◽  
Process Parameters ◽  
Average Run Length ◽  
Moving Average ◽  
Background Knowledge ◽  
Exponentially Weighted Moving Average ◽  
Control Phase ◽  
Run Length ◽  
Weighted Moving Average

The performance of a control chart is commonly investigated based on the assumption of known process parameters. Nevertheless, in most manufacturing and service applications, the process parameters are usually unknown to practitioners. Hence, they are estimated from an in-control Phase-I samples. As such, the performance of the control chart with estimated process parameters will behave differently from the corresponding chart with known process parameters. To study this issue, the exponentially weighted moving average (EWMA) median chart is examined in this article. The EWMA median chart is traditionally investigated based on the average run length (ARL). The limitation of the ARL is that it requires practitioners to specify the shift size in advance. This phenomenon is not ideal for practitioners who do not have background knowledge of the process. In view of this, the EWMA median chart with known and estimated process parameters is studied based on the ARL and expected average run length (EARL). The results indicate that as long as the particular shift size is within the range of shifts, the performance of the chart is almost the same, for the EWMA median chart with known and estimated process parameters.

scholarly journals Variable sampling interval run sum X‾ chart with estimated process parameters

2018 ◽  
Vol 192 ◽  
pp. 01012
Author(s):  
Sajal Saha ◽  
Michael Boon Chong Khoo ◽  
Peh Sang Ng ◽  
Mahfuza Khatun
Keyword(s):  
Standard Deviation ◽  
Phase I ◽  
Process Parameters ◽  
Sampling Interval ◽  
Performance Measure ◽  
Performance Gap ◽  
Average Time To Signal ◽  
Variable Sampling Interval ◽  
Variable Sampling ◽  
Parameter Case

The X‾ type control chart is often evaluated by assuming the process parameters are known. However, the exact values of process parameters are hardly known and thus Phase-I dataset is needed to estimate them. In this paper, the performance of the variable sampling interval run sum X‾ chart with estimated process parameters is evaluated by using the performance measure of the average of the average time to signal (AATS) and the optimal design of the proposed chart in minimizing the out-of-control AATS is developed. The performance measure of the standard deviation of the average time to signal (SDATS) is then used to identify the number of Phase-I samples (w) needed to have an in-control AATS performance close to its known process parameter case. Results show that large w is needed to minimize the performance gap between known and unknown process parameters cases of the VSI RS X‾ chart.

scholarly journals Nonparametric Double EWMA Control Chart for Process Monitoring

2016 ◽  
Vol 39 (2) ◽  
pp. 167 ◽  
Author(s):  
Muhammad Riaza ◽  
Saddam Akber Abbasib
Keyword(s):  
Standard Deviation ◽  
Control Chart ◽  
Average Run Length ◽  
Location Parameter ◽  
Quality Characteristic ◽  
Quadratic Loss ◽  
Run Length ◽  
Ewma Control Chart ◽  
Monitoring Process ◽  
Nonparametric Techniques

<p>In monitoring process parameters, we assume normality of the quality characteristic of interest, which is an ideal assumption. In many practical sit- uations, we may not know the distributional behavior of the data, and hence, the need arises use nonparametric techniques. In this study, a nonparametric double EWMA control chart, namely the NPDEWMA chart, is proposed to ensure efficient monitoring of the location parameter. The performance of the proposed chart is evaluated in terms of different run length properties, such as average, standard deviation and percentiles. The proposed scheme is compared with its recent existing counterparts, namely the nonparametric EWMA and the nonparametric CUSUM schemes. The performance mea- sures used are the average run length (ARL), standard deviation of the run length (SDRL) and extra quadratic loss (EQL). We observed that the pro- posed chart outperforms the said existing schemes to detect shifts in the process mean level. We also provide an illustrative example for practical considerations.</p>

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.

scholarly journals AEWMA t Control Chart for Short Production Runs

2016 ◽  
Vol 4 (5) ◽  
pp. 444-459 ◽  
Author(s):  
Zhiyuan Chang ◽  
Jinsheng Sun
Keyword(s):  
Standard Deviation ◽  
Phase I ◽  
Control Chart ◽  
Average Run Length ◽  
Statistical Design ◽  
Joint Effect ◽  
Process Mean ◽  
Short Run ◽  
Better Than ◽  
Correct Estimate

AbstractOwing to the limited number of inspections during a short run process, it is impossible to get the correct estimate of the population mean and standard deviation during Phase I implementation of control chart. Thetcontrol chart proposed recently can overcome this problem. The EWMAtcontrol chart has been proposed to monitor the process mean, but a single EWMAtcontrol chart cannot perform well for small and large shifts simultaneously, which is known as the “inertia problem”. The adaptive varying smoothing parameter EWMA (AEWMA) control chart can overcome the inertia problem. In this paper, the AEWMAtcontrol chart for short run process is proposed. The truncated average run length and the probability of trigger a signal are adopted to test the performance of short run AEWMAtchart. Based on the investigation of the joint effect of control chart parameters on the performance of AEWMAtchart, a new optimization algorithm is proposed for statistical design of the AEWMA control chart. Simulations are performed for perfect and imperfect setup conditions, the results show that the AEWMAtcontrol chart performs better than the EWMAtcontrol chart.

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.

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