EXACT EXPRESSION OF AVERAGE RUN LENGTH FOR TWO-SIDED EXPONENTIAL CUSUM PROCEDURE

2016 ◽  
Vol 48 (6) ◽  
pp. 429-444
Author(s):  
Saowanit Sukparungsee ◽  
Sophana Somran ◽  
Yupaporn Areepong
Keyword(s):  
Average Run Length ◽  
Exact Expression ◽  
Run Length ◽  
Cusum Procedure

scholarly journals Water Particles Monitoring in the Atacama Desert: SPC Approach Based on Proportional Data

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 154
Author(s):  
Anderson Fonseca ◽  
Paulo Henrique Ferreira ◽  
Diego Carvalho do Nascimento ◽  
Rosemeire Fiaccone ◽  
Christopher Ulloa-Correa ◽  
...  
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Atacama Desert ◽  
Real Data ◽  
Interval Data ◽  
Total Quality ◽  
Statistical Process ◽  
Monte Carlo Simulation Study ◽  
Run Length ◽  
Study Results

Statistical monitoring tools are well established in the literature, creating organizational cultures such as Six Sigma or Total Quality Management. Nevertheless, most of this literature is based on the normality assumption, e.g., based on the law of large numbers, and brings limitations towards truncated processes as open questions in this field. This work was motivated by the register of elements related to the water particles monitoring (relative humidity), an important source of moisture for the Copiapó watershed, and the Atacama region of Chile (the Atacama Desert), and presenting high asymmetry for rates and proportions data. This paper proposes a new control chart for interval data about rates and proportions (symbolic interval data) when they are not results of a Bernoulli process. The unit-Lindley distribution has many interesting properties, such as having only one parameter, from which we develop the unit-Lindley chart for both classical and symbolic data. The performance of the proposed control chart is analyzed using the average run length (ARL), median run length (MRL), and standard deviation of the run length (SDRL) metrics calculated through an extensive Monte Carlo simulation study. Results from the real data applications reveal the tool’s potential to be adopted to estimate the control limits in a Statistical Process Control (SPC) framework.

scholarly journals Multivariate Statistical Quality Control Based on Ranked Set Sampling

2017 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Hakan Eygü ◽  
M. Suphi Özçomak
Keyword(s):  
Control Charts ◽  
Sampling Methods ◽  
Average Run Length ◽  
Ranked Set Sampling ◽  
Multivariate Statistical ◽  
Run Length ◽  
Hotelling's T2 ◽  
Median Ranked Set Sampling ◽  
Hotelling’S T2 ◽  
T2 Control Chart

The sample of the study was formed using simple random sampling, ranked set sampling, extreme ranked set sampling and median ranked set sampling. At the end of this process, the researcher created Hotelling’s T2 control charts, a multivariate statistical process control method. The performances of SRS, RSS, ERSS and MRSS sampling methods were compared to one another using these control charts. A simulation was performed to see the average run-length values for Hotelling’s T2 control charts, and these findings were also used for the comparison of the sampling performances.At the end of the study, the researcher formed a sample using median ranked set sampling and created the Hotelling’s T2 control chart. As a result of this operation, the researcher found that there was an out-of-control signal in the process, while there was no such signal in other sampling methods. When the average run-length values obtained from Hotelling’s T2 control charts were compared, it was seen that a shift in the process was detected by the ranked set sampling earlier, when compared to other sampling methods. This paper it can be said that the methods used are unique to the literature because they are applied to multivariate data.

scholarly journals Monitoring multinomial processes based on a weighted chi-square control chart

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Achouri Ali ◽  
Emira Khedhiri ◽  
Ramzi Talmoudi ◽  
Hassen Taleb
Keyword(s):  
Quality Improvement ◽  
Control Chart ◽  
Process Improvement ◽  
Average Run Length ◽  
The Other ◽  
Statistical Control ◽  
Chi Square ◽  
Crucial Step ◽  
Run Length ◽  
Control Situation

Abstract: Interpreting an out-of-control signal is a crucial step in monitoring categorical processes. For the Chi-Square Control Chart (CSCC), an out-of control situation does not specify if it was a process deterioration or a process improvement. For this reason, a weighted chi-square statistical control chart WSCC is proposed with different weighting categories in order to enable an accelerated disclosure of a control situation after a shift due to a deterioration of quality and on the other hand, decelerate an out of control situation after a shift due to a quality improvement. Furthermore, in comparison with Marcucci’s method, the new procedure provides an accurate and easier way to interpret several signals. In other words, the WSCC allows a faster detection of an out-of control situation in the case of a quality deterioration, however, an out-of control situation is not quickly detected in the case of a quality improvement. Indeed, comparative studies have been performed to find the best control chart for each combination. Concluding remarks with comments and recommendations are given based on Average Run Length (ARL) and standard deviation run length (SDRL).

scholarly journals PERBANDINGAN KINERJA PETA KENDALI CUMULATIVE SUM DAN PETA KENDALI EXPONENTIALLY WEIGHTED MOVING AVERAGE

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Dhea Trinandya Wijayanti, Helmi, Nurfitri Imro’ah
Keyword(s):  
Average Run Length ◽  
Moving Average ◽  
Exponentially Weighted Moving Average ◽  
Cumulative Sum ◽  
Run Length ◽  
Weighted Moving Average ◽  
Exponentially Weighted

 Pada umumnya peta kendali yang sering digunakan dalam pengendalian kualitas statistik adalah peta kendali Shewhart. Peta kendali ini bekerja hanya dengan menggunakan informasi yang terkandung dalam titik sampel terakhir dan mengabaikan informasi dari seluruh barisan titik sampel sebelumnya. Hal ini membuat peta kendali Shewhart kurang efektif dalam mendeteksi pergeseran rata-rata yang relatif kecil pada proses produksi. Sebagai alternatif, dikembangkan peta kendali Cumulative Sum (Cusum) dan peta kendali Exponentially Weighted Moving Average (EWMA). Penelitian ini menerapkan peta kendali Cusum dan peta kendali EWMA serta membandingkan kinerjanya dalam mendeteksi pergeseran rata-rata yang relatif kecil pada data produksi. Tahapan pengerjaan dimulai dari melakukan analisis peta kendali Cusum dan peta kendali EWMA dengan menghitung nilai statistik, batas kendali, dan membentuk grafik setiap peta kendali. Selanjutnya, dihitung nilai Average Run Length (ARL) sebagai acuan untuk membandingkan kinerja kedua peta kendali. Berdasarkan hasil penerapannya pada produksi wajan nomor 18 di CV. XYZ, pada peta kendali Cusum tidak terdapat titik-titik yang berada di luar batas kendali. Namun, pada peta kendali EWMA mampu mendeteksi adanya 9 titik yang berada di luar batas kendali sehingga proses produksi tidak terkendali secara statistik. Selain itu berdasarkan perolehan nilai ARL, diketahui nilai ARL peta kendali EWMA menunjukkan hasil yang lebih kecil yaitu sebesar 45,832 dibandingkan dengan nilai ARL peta kendali Cusum yang sebesar 69,108. Dari hasil analisis didapat kesimpulan bahwa peta kendali EWMA lebih efektif daripada peta kendali Cusum dalam mendeteksi adanya pergeseran rata-rata yang relatif kecil pada produksi wajan nomor 18 di CV. XYZ. Kata Kunci: Cusum, EWMA, ARL                                       

Oil and Gas Drill Bit Technology and Drilling Application Engineering Saves 77 Drilling Days on the World’s Deepest Engineered Geothermal Systems EGS Wells

2021 ◽  
Author(s):  
Jennifer Cardoe ◽  
Gunnar Nygaard ◽  
Christopher Lane ◽  
Tero Saarno ◽  
Marc Bird
Keyword(s):  
Oil And Gas ◽  
Average Run Length ◽  
Renewable Energy Sources ◽  
Pilot Project ◽  
Geothermal System ◽  
Drill Bit ◽  
Geothermal Systems ◽  
Geothermal Heat ◽  
Run Length ◽  
Run Lengths

Abstract An Engineered Geothermal System (EGS) pilot project was commissioned to prove the economic viability of an industrial scale geothermal heat plant in Finland. The project aims to generate 40 MW of emission free heat energy, supplying up to 10% of the city of Espoo’s district heating needs. Two wells of 6400 m MD and 6213 m MD (measured depth) were drilled through formations of hard, abrasive granitic gneiss with maximum measured 560 MPa UCS (unconfined compressive strength). Typical dull conditions of lost and worn cutting structure and gauge diameter wear of between 3/16-in to ¼-in contributed to excessive torque, stuck incidences, low rate of penetration (ROP) and difficulties achieving build rate. To address these drilling challenges, this paper explores the interplay between new cemented carbide compact technology, drill bit design, and drilling parameter road mapping. The directional section of the first well was drilled with an average ROP below 2 m/hr and run length averaging 56 m per bit. The well took 246 drilling days and 44 BHAs (bottom hole assemblies) to achieve TD (total depth). Between the first and second well an application specific drill bit design package and step-wise parameter program were implemented. Design enhancements included improved gauge protection, bit hydraulics for minimizing cone erosion and subsequent TCI (tungsten carbide insert) compact loss. Novel hybrid TCI materials technology was introduced having a 100% improvement in wear resistance and durability as compared with conventional grades, to drill these hard and abrasive granitic formations. New BHAs and drilling plan were selected based on the bit design selection to reduce wear on BHA components, improve directional control and reducing drilling dysfunctions. Once these factors were under control, a low risk approach to extending the bit revolution limits (krev) for the roller cone sealed bearings could be implemented based on downhole parameters and previous bit dulls, leading to longer run lengths. The combination of bit design and material enhancements with a properly selected BHA and drill plan increased run lengths and ROP. The second well’s 8.5-in directional section was drilled with a 13% increase in average ROP and a 69% increase in average run length without exceeding krev limits. Well on well, a 77 day reduction in AFE (authorization for expenditure) was realized. We demonstrated the combination of oil and gas bit and BHA design, drilling plan, and new cutting material capabilities can reduce EGS well construction costs in order to make these renewable energy sources economical.

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