Conditional median run length performance of the synthetic X¯ chart with unknown process parameters

2020 ◽  
Vol 36 (3) ◽  
pp. 1111-1131 ◽  
Author(s):  
XueLong Hu ◽  
Philippe Castagliola ◽  
AnAn Tang ◽  
XiaoJian Zhou ◽  
PanPan Zhou
Keyword(s):  
Process Parameters ◽  
Run Length ◽  
Conditional Median

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 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.

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