A robust $$ \overline {\hbox{X}} $$ control chart based on M-estimators in presence of outliers

Maddahi, Alireza; Shahriari, Hamid; Shokouhi, Amir H.

doi:10.1007/s00170-011-3226-5

Cited by 7 publications

(6 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This estimator was often used for smoothing the nonlinear response surface [61] , [62] . It was reported that bisquare estimator could be adapted to process noisy data with outliers [63] .…”

Section: Discussionmentioning

confidence: 99%

BP-ANN for Fitting the Temperature-Germination Model and Its Application in Predicting Sowing Time and Region for Bermudagrass

Mantri

Ngai

et al. 2013

PLoS ONE

View full text Add to dashboard Cite

Temperature is one of the most significant environmental factors that affects germination of grass seeds. Reliable prediction of the optimal temperature for seed germination is crucial for determining the suitable regions and favorable sowing timing for turf grass cultivation. In this study, a back-propagation-artificial-neural-network-aided dual quintic equation (BP-ANN-QE) model was developed to improve the prediction of the optimal temperature for seed germination. This BP-ANN-QE model was used to determine optimal sowing times and suitable regions for three Cynodon dactylon cultivars (C. dactylon, ‘Savannah’ and ‘Princess VII’). Prediction of the optimal temperature for these seeds was based on comprehensive germination tests using 36 day/night (high/low) temperature regimes (both ranging from 5/5 to 40/40°C with 5°C increments). Seed germination data from these temperature regimes were used to construct temperature-germination correlation models for estimating germination percentage with confidence intervals. Our tests revealed that the optimal high/low temperature regimes required for all the three bermudagrass cultivars are 30/5, 30/10, 35/5, 35/10, 35/15, 35/20, 40/15 and 40/20°C; constant temperatures ranging from 5 to 40°C inhibited the germination of all three cultivars. While comparing different simulating methods, including DQEM, Bisquare ANN-QE, and BP-ANN-QE in establishing temperature based germination percentage rules, we found that the R2 values of germination prediction function could be significantly improved from about 0.6940–0.8177 (DQEM approach) to 0.9439–0.9813 (BP-ANN-QE). These results indicated that our BP-ANN-QE model has better performance than the rests of the compared models. Furthermore, data of the national temperature grids generated from monthly-average temperature for 25 years were fit into these functions and we were able to map the germination percentage of these C. dactylon cultivars in the national scale of China, and suggested the optimum sowing regions and times for them.

show abstract

Section: Discussionmentioning

confidence: 99%

BP-ANN for Fitting the Temperature-Germination Model and Its Application in Predicting Sowing Time and Region for Bermudagrass

Mantri

Ngai

et al. 2013

PLoS ONE

View full text Add to dashboard Cite

show abstract

“…Ebadi and Shahriari 40 use the M estimator to estimate the parameters of a simple linear profile. The M estimator is used to construct an

\overset{X}{true}

control chart to monitor the mean of a process in presence of outliers in other work 41 …”

Section: Robust Estimatorsmentioning

confidence: 99%

“…The M estimator is used to construct an � X control chart to monitor the mean of a process in presence of outliers in other work. 41…”

Section: The M Estimators Of the Mean Vector And The Variance-covarmentioning

confidence: 99%

Robust T² control chart using median‐based estimators

Maleki

Mehri

Aghaie

et al. 2020

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

One of the most widely used multivariate control charts is the Hotelling T 2. In order to construct a Hotelling T 2 control chart, the mean vector (μ) and the variance-covariance matrix (Σ) must be first estimated. The classical estimators of μ and Σ are usually used to design Hotelling T 2 control chart. The classical estimators are sensitive to the presence of outliers. One way to deal with outliers is to use robust estimators. In this study, a robust T 2 control chart is proposed. The mean vector is obtained from the sample median. The median absolute deviation and the comedian are used as the estimates of the elements of the variance-covariance matrix. The proposed robust estimators of the mean vector and the variance-covariance matrix are compared with the sample mean vector and the sample variance-covariance matrix, and the M estimator of these parameters, through efficiency and robustness measures. The performances of the proposed robust T 2 control chart and the classical and the M estimators are also compared by means of average run length. Simulation results reveal that the proposed robust T 2 control chart has much better performance than the traditional Hotelling T 2 and similar performance to the M estimator in detecting shifts in process mean vector. Use of other robust estimators to estimate the process parameters is an area for further research.

show abstract

“…Robust estimators for the mean as well as for the standard deviation of a process were introduced by Maddahi et al . for constructing a reliable

\overset{X}{true}

chart in the presence of outliers.…”

Section: Shewhart Control Chartsmentioning

confidence: 99%

“…However, when the pooled standard deviation is considered, the biased estimatorσ 10 ¼ c 4 S pooled is more efficient than the unbiased one (and generally used)σ 7 ¼ S c4 . Robust estimators for the mean as well as for the standard deviation of a process were introduced by Maddahi et al 8 for constructing a reliable X chart in the presence of outliers. The proposed estimators can be obtained from the following equations:…”

Section: Shewhart Control Chartsmentioning

confidence: 99%

Some Recent Developments on the Effects of Parameter Estimation on Control Charts

Psarakis

Vyniou

Castagliola

2013

Quality & Reliability Eng

153

View full text Add to dashboard Cite

show abstract

A robust $$ \overline {\hbox{X}} $$ control chart based on M-estimators in presence of outliers

Cited by 7 publications

References 14 publications

BP-ANN for Fitting the Temperature-Germination Model and Its Application in Predicting Sowing Time and Region for Bermudagrass

BP-ANN for Fitting the Temperature-Germination Model and Its Application in Predicting Sowing Time and Region for Bermudagrass

Robust T² control chart using median‐based estimators

Some Recent Developments on the Effects of Parameter Estimation on Control Charts

Contact Info

Product

Resources

About

A robust $$ \overline {\hbox{X}} $$ control chart based on M-estimators in presence of outliers

Cited by 7 publications

References 14 publications

BP-ANN for Fitting the Temperature-Germination Model and Its Application in Predicting Sowing Time and Region for Bermudagrass

BP-ANN for Fitting the Temperature-Germination Model and Its Application in Predicting Sowing Time and Region for Bermudagrass

Robust T2 control chart using median‐based estimators

Some Recent Developments on the Effects of Parameter Estimation on Control Charts

Contact Info

Product

Resources

About

Robust T² control chart using median‐based estimators