Exact Determination of the Run Length Distribution of a One-Sided CUSUM Procedure Applied on an Ordinary Poisson Process

2004 ◽  
Vol 23 (2) ◽  
pp. 159-178 ◽  
Author(s):  
S. Zacks
Keyword(s):  
Poisson Process ◽  
Length Distribution ◽  
Run Length ◽  
Exact Determination ◽  
Cusum Procedure ◽  
Run Length Distribution

Combined effect of autocorrelation and measurement errors on the adaptive X¯ monitoring schemes

2020 ◽  
pp. 014233122093529 ◽  
Author(s):  
Sandile Charles Shongwe ◽  
Jean-Claude Malela-Majika
Keyword(s):  
Measurement Errors ◽  
Length Distribution ◽  
Real Life ◽  
Adaptive Designs ◽  
Combined Effect ◽  
Sampling Strategies ◽  
Run Length ◽  
Variable Sampling ◽  
Negative Effect ◽  
Run Length Distribution

For independent and identically distributed observations, and those with measurement errors only, the adaptive designs (i.e. variable sampling sizes (VSS), variable sampling intervals (VSI) and the latter two combined to form VSSI) have been thoroughly discussed. However, no research exists for processes under the combined effect of autocorrelation and measurement errors; thus, such adaptive Shewhart [Formula: see text] schemes are proposed. The Markov chain approach for adaptive designs are used to evaluate the run-length distribution properties with two special sampling strategies (i.e. s-skip and multiple measurements) incorporated to reduce the combined negative effect of autocorrelation and measurement inaccuracy. Using numerous run-length metrics, it is shown that the combination of the two sampling strategies with the VSSI design reduces this negative effect considerably and improves the detection ability of the [Formula: see text] scheme by a significant margin as compared with using the fixed sample size and sampling interval (FSSI), VSS and VSI designs. Autocorrelation level has a higher negative effect as compared with the measurement inaccuracy level. For high levels of autocorrelation ([Formula: see text]0.8), the s-skip strategy has little influence in reducing the negative effect; but the VSSI design maintains better performance than the other designs. Finally, a real-life example is used to illustrate its implementation.

scholarly journals Run length distribution of dimerized kinesin-3 molecular motors: comparison with dimeric kinesin-1

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Si-Kao Guo ◽  
Xiao-Xuan Shi ◽  
Peng-Ye Wang ◽  
Ping Xie
Keyword(s):  
Molecular Motors ◽  
Average Run Length ◽  
Length Distribution ◽  
Dissociation Rate ◽  
Run Length ◽  
Proposed Model ◽  
Run Length Distribution ◽  
Run Lengths ◽  
Kinesin Superfamily ◽  
Single Exponential

AbstractKinesin-3 and kinesin-1 molecular motors are two families of the kinesin superfamily. It has been experimentally revealed that in monomeric state kinesin-3 is inactive in motility and cargo-mediated dimerization results in superprocessive motion, with an average run length being more than 10-fold longer than that of kinesin-1. In contrast to kinesin-1 showing normally single-exponential distribution of run lengths, dimerized kinesin-3 shows puzzlingly Gaussian distribution of run lengths. Here, based on our proposed model, we studied computationally the dynamics of kinesin-3 and compared with that of kinesin-1, explaining quantitatively the available experimental data and revealing the origin of superprocessivity and Gaussian run length distribution of kinesin-3. Moreover, predicted results are provided on ATP-concentration dependence of run length distribution and force dependence of mean run length and dissociation rate of kinesin-3.

OPTIMAL STATISTICAL DESIGNS OF A MULTIVARIATE CUSUM CHART BASED ON ARL AND MRL

2006 ◽  
Vol 13 (05) ◽  
pp. 479-497 ◽  
Author(s):  
M. H. LEE ◽  
MICHAEL B. C. KHOO
Keyword(s):  
Average Run Length ◽  
Length Distribution ◽  
Statistical Design ◽  
Reference Value ◽  
Cusum Chart ◽  
Run Length ◽  
Cusum Charts ◽  
Potential Alternative ◽  
Run Length Distribution ◽  
Statistical Designs

Optimal statistical designs of the multivariate CUSUM (MCUSUM) chart for multivariate individual observations based on ARL and MRL are proposed. Statistical design procedures refer to choices of the reference value, k and the control limit, H to ensure that the MCUSUM chart's performance meets certain statistical criteria. The primary criterion is the average run length (ARL) which is the most commonly used measure of a control chart's performance, while the median run length (MRL) which is the 50th percentage point of the run length distribution is suggested to be used as a potential alternative to the ARL or as a secondary criterion in the evaluation of the performance of the MCUSUM control chart. Although the MRL is used in the optimal design of the univariate EWMA and univariate CUSUM charts but the design of an optimal multivariate CUSUM chart based on MRL is not yet given in any literature. This paper also suggests a systematic approach of designing an optimal MCUSUM chart based on the average run length (ARL). The MRL profiles are considered as supplements to the ARL profiles for the control scheme. Examples of optimal designs of the MCUSUM chart based on both MRL and ARL are also presented. Tables are provided to determine the optimal chart parameters for the design of the chart based on both ARL and MRL.

scholarly journals A synthetic exponentially weighted moving average control chart to monitor process median based on ranked set sampling

2021 ◽  
Vol 36 ◽  
pp. 01002
Author(s):  
Jing Wen Ng ◽  
Voon Hee Wong ◽  
Sook Theng Pang
Keyword(s):  
Control Chart ◽  
Moving Average ◽  
Length Distribution ◽  
Ranked Set Sampling ◽  
Exponentially Weighted Moving Average ◽  
Process Mean ◽  
Run Length ◽  
Ewma Chart ◽  
Run Length Distribution ◽  
Weighted Moving Average

Exponentially Weighted Moving Average (EWMA) control charts yield insights into data in a way more comprehensible to the practitioners and researchers because of its capability in discovering small to moderate process mean shifts. EWMA control chart is incorporated with conforming run length (CRL) chart, named synthetic EWMA chart, to enhance the performance of the chart in detecting the out-of-control signal. Synthetic EWMA chart based on ranked set sampling (RSS) for monitoring process mean has been proposed as it advanced the detection of chart over a series of mean shifts. With the situation that normality assumption is scarcely attain in practice, we proposed synthetic EWMA median chart based on RSS. Rather than select average run length (ARL) as sole performance evaluating tool, the median and percentiles of run-length distribution are used to examine the performance of the proposed chart as it provides more information on the entire run-length distribution. Near-optimal parameters of the proposed chart will be acquired by setting the incontrol ARL at a designated value. The run length performances of the proposed chart are then compared with the existing charts such as EWMA median chart based on RSS.

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