scholarly journals Cumulative Sum Chart Modeled under the Presence of Outliers

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 269 ◽  
Author(s):  
Nasir Abbas ◽  
Mu’azu Ramat Abujiya ◽  
Muhammad Riaz ◽  
Tahir Mahmood
Keyword(s):  
Phase I ◽  
Phase Ii ◽  
Estimation Error ◽  
Signal Strength ◽  
Received Signal Strength ◽  
Cusum Chart ◽  
Cumulative Sum ◽  
Run Length ◽  
Design Structure ◽  
Control Limits

Cumulative sum control charts that are based on the estimated control limits are extensively used in practice. Such control limits are often characterized by a Phase I estimation error. The presence of these errors can cause a change in the location and/or width of control limits resulting in a deprived performance of the control chart. In this study, we introduce a non-parametric Tukey’s outlier detection model in the design structure of a two-sided cumulative sum (CUSUM) chart with estimated parameters for process monitoring. Using Monte Carlo simulations, we studied the estimation effect on the performance of the CUSUM chart in terms of the average run length and the standard deviation of the run length. We found the new design structure is more stable in the presence of outliers and requires fewer amounts of Phase I observations to stabilize the run-length performance. Finally, a numerical example and practical application of the proposed scheme are demonstrated using a dataset from healthcare surveillance where received signal strength of individuals’ movement is the variable of interest. The implementation of classical CUSUM shows that a shift detection in Phase II that received signal strength data is indeed masked/delayed if there are outliers in Phase I data. On the contrary, the proposed chart omits the Phase I outliers and gives a timely signal in Phase II.

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.

Effect of phase I estimation error on the monitoring of simple linear profiles in phase II

2015 ◽  
Author(s):  
R. Noorossana ◽  
Mozhdeh Aminmadani ◽  
Abbas Saghaei
Keyword(s):  
Phase I ◽  
Phase Ii ◽  
Estimation Error ◽  
Linear Profiles

scholarly journals Change Point Detection with Robust Control Chart

2011 ◽  
Vol 2011 ◽  
pp. 1-20
Author(s):  
Ng Kooi Huat ◽  
Habshah Midi
Keyword(s):  
Robust Control ◽  
Phase I ◽  
Control Chart ◽  
Phase Ii ◽  
Control Process ◽  
Change Point Detection ◽  
Process Data ◽  
To Come ◽  
Point Detection ◽  
Control Limits

Monitoring a process over time using a control chart allows quick detection of unusual states. In phase I, some historical process data, assumed to come from an in-control process, are used to construct the control limits. In Phase II, the process is monitored for an ongoing basis using control limits from Phase I. In Phase II, observations falling outside the control limits or unusual patterns of observations signal that the process has shifted from in-control process settings. Such signals trigger a search for assignable cause and, if the cause is found, corrective action will be implemented to prevent its recurrence. The purpose of this paper is to introduce a new methodology appropriate for constructing a robust control chart when a nonnormal or a contaminated data that may arise in phase I state. Through extensive Monte Carlo simulations, we examine the behaviors and performances of the proposed MM robust control chart when there is a process shift in mean.

THE EXACT RUN LENGTH DISTRIBUTION AND DESIGN OF THE S2 CHART WHEN THE IN-CONTROL VARIANCE IS ESTIMATED

2009 ◽  
Vol 16 (01) ◽  
pp. 23-38 ◽  
Author(s):  
PHILIPPE CASTAGLIOLA ◽  
GIOVANNI CELANO ◽  
GEMAI CHEN
Keyword(s):  
Phase I ◽  
Length Distribution ◽  
Control Process ◽  
Data Set ◽  
Run Length ◽  
Variance Formula ◽  
Process Standard Deviation ◽  
Run Length Distribution ◽  
Process Variance ◽  
Control Limits

When monitoring the process variability, it is a common practice that a Phase I data set is used to estimate the unknown in-control process standard deviation σ0 or variance [Formula: see text] to set up the control limits, then monitoring proceeds. Once the process is considered to be in-control, the estimated control limits are assumed as fixed. This practice ignores the effect of estimating the unknown in-control process variance [Formula: see text]. In this paper, we derive the exact run length distribution of the S2 control chart when the in-control process variance [Formula: see text] is estimated and find that m = 200 or more Phase I samples are needed to neglect the effect of using estimated control limits. New control limits when m is small are also derived.

Bewegungstherapie und körperliche Aktivität bei Patienten mit Herzinsuffizienz

Praxis ◽  
2018 ◽  
Vol 107 (17-18) ◽  
pp. 951-958 ◽  
Author(s):  
Matthias Wilhelm
Keyword(s):  
Phase I ◽  
Phase Ii ◽  
Körperliche Aktivität ◽  
Phase Iii

Zusammenfassung. Herzinsuffizienz ist ein klinisches Syndrom mit unterschiedlichen Ätiologien und Phänotypen. Die überwachte Bewegungstherapie und individuelle körperliche Aktivität ist bei allen Formen eine Klasse-IA-Empfehlung in aktuellen Leitlinien. Eine Bewegungstherapie kann unmittelbar nach Stabilisierung einer akuten Herzinsuffizienz im Spital begonnen werden (Phase I). Sie kann nach Entlassung in einem stationären oder ambulanten Präventions- und Rehabilitationsprogramm fortgesetzt werden (Phase II). Typische Elemente sind Ausdauer-, Kraft- und Atemtraining. Die Kosten werden von der Krankenversicherung für drei bis sechs Monate übernommen. In erfahrenen Zentren können auch Patienten mit implantierten Defibrillatoren oder linksventrikulären Unterstützungssystemen trainieren. Wichtiges Ziel der Phase II ist neben muskulärer Rekonditionierung auch die Steigerung der Gesundheitskompetenz, um die Langzeit-Adhärenz bezüglich körperlicher Aktivität zu verbessern. In Phase III bieten Herzgruppen Unterstützung.

KAJIAN KEKUATAN SINYAL RADIO (RSSI) XBEE DALAM RANGKA PEMASANGAN LANDSLIDE EARLY WARNING SYSTEM (LEWS) DI KABUPATEN GARUT, TASIKMALAYA DAN MAJALENGKA

2019 ◽  
Vol 3 (2) ◽  
pp. 88
Author(s):  
Riski Fitriani
Keyword(s):  
Early Warning ◽  
Early Warning System ◽  
Warning System ◽  
Signal Strength ◽  
Received Signal Strength ◽  
Received Signal Strength Indicator ◽  
Landslide Early Warning ◽  
Point To Point

Salah satu inovasi untuk menanggulangi longsor adalah dengan melakukan pemasangan Landslide Early Warning System (LEWS). Media transmisi data dari LEWS yang dikembangkan menggunakan sinyal radio Xbee. Sehingga sebelum dilakukan pemasangan LEWS, perlu dilakukan kajian kekuatan sinyal tersebut di lokasi yang akan terpasang yaitu Garut, Tasikmalaya, dan Majalengka. Kajian dilakukan menggunakan 2 jenis Xbee yaitu Xbee Pro S2B 2,4 GHz dan Xbee Pro S5 868 MHz. Setelah dilakukan kajian, Xbee 2,4 GHz tidak dapat digunakan di lokasi pengujian Garut dan Majalengka karena jarak modul induk dan anak cukup jauh serta terlalu banyak obstacle. Topologi yang digunakan yaitu topologi pair/point to point, dengan mengukur nilai RSSI menggunakan software XCTU. Semakin kecil nilai Received Signal Strength Indicator (RSSI) dari nilai receive sensitivity Xbee maka kualitas sinyal semakin baik. Pengukuran dilakukan dengan meninggikan antena Xbee dengan beberapa variasi ketinggian untuk mendapatkan kualitas sinyal yang lebih baik. Hasilnya diperoleh beberapa rekomendasi tinggi minimal antena Xbee yang terpasang di tiap lokasi modul anak pada 3 kabupaten.

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