scholarly journals Estimasi Parameter Distribusi Weibull Dan Aplikasinya pada Pengendalian Mutu Dengan Memanfaatkan Kuantil

2019 ◽  
Vol 5 (01) ◽  
pp. 9-15
Author(s):  
Cecilia Novianti Salsinha
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Control Charts ◽  
Probability Distributions ◽  
Likelihood Estimation ◽  
Control Limit ◽  
Statistical Process ◽  
Shewhart Control Charts ◽  
Shewhart Control ◽  
Distribution Parameters

Abstract. Weibull distribution is one of the continuous probability distributions. As the other distributions, Weibull distribution is also characterized by Mean, Variance and Moment Generation Function. The advantage of this distribution compared to other distributions is its flexibility, that is, this distribution can change to another distribution such as an exponential distribution depending on the value of the selected distribution parameters, namely scale parameters and form parameters. From the distribution graph, it can be shown that, the flexibility will appear very clear. One application of the Weibull distribution is in statistical process control. Because not all data is normally distributed, the Shewhart control chart cannot be used. One way to solve this problem is that the data is analyzed with Weibull control charts by utilizing quantiles, namely 0.00135, 0.5 and 0.99865. Quantile 0.00135 is the bottom quintile used to form the Lower Control Limit, the Middle Line is the median of the data, which is 0.5 which replaces the average and the last to form the Upper Control Limit the top quintile is 0.99865. By generating 200 data with Weibull distribution, if the data is analyzed by Shewhart control charts then there is a lot of data that is outside the control limit so it will be concluded that the graph is out of control. Therefore, if the data is not from a Normal distribution, the use of Shewhart control charts is not recommended.  Keywords: Weibull Distribution, Maximum Likelihood Estimation (MLE), Quality Control, Weibull Control Charts   Abstrak. Distribusi Weibull merupakan salah satu distribusi probabilitas kontinu. Sama halnya dengan distribusi lainnya, distribusi Weibull pun dicirikan dengan Mean, Variansi dan Fungsi Pembangkit Momen. Kelebihan distribusi ini dibandingkan dengan distribusi lainnya adalah fleksibilitasnya, yaitu distribusi ini dapat berubah menjadi distribusi lain seperti distribusi eksponensial tergantung pada nilai parameter distribusi yang dipilih yaitu parameter skala dan parameter bentuk. Jika dilihat dari grafik distribusinya maka akan tampak sangat jelas fleksibilitas tersebut. Salah satu aplikasi dari distribusi Weibull yaitu dalam pengendalian proses statistik. Oleh karena tidak semua data berdistribusi normal maka grafik pengendali Shewhart tidak dapat digunakan. Salah satu cara menyelesaikan masalah tersebut adalah data dianalisis dengan grafik pengendali Weibull dengan memanfaatkan kuantil-kuantil yaitu 0,00135, 0,5 dan 0,99865. Kuantil 0,00135 adalah kuantil bawah yang digunakan untuk membentuk Batas Pengendali Bawah, Garis Tengah adalah median dari data yaitu 0,5 yang  menggantikan rata-rata dan untuk membentuk Batas Pengendali Atas digunakan kuantil atas yaitu 0,99865. Dengan membangkitkan data sebanyak 200 data berdistribusi Weibull, jika data tersebut dianalisis dengan grafik pengendali Shewhart maka terdapat banyak data yang berada diluar batas pengendali sehingga akan disimpulkan bahwa grafik tak terkendali. Oleh karena itu, jika data bukan berasal dari distribusi Normal, penggunaan grafik pengendali Shewhart tidak disarankan.  Kata Kunci: Distribusi Weibull, Estimasi Maximum Likelihood, Pengendalian Mutu, Grafik Pengendali Weibull

Utilizarea teoriei valorilor extreme în climatologie

2019 ◽  
Author(s):  
Valentin Raileanu ◽  
Keyword(s):  
Maximum Likelihood ◽  
Extreme Values ◽  
Probability Distributions ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
R Software ◽  
Data Set ◽  
Data Format ◽  
Generalized Pareto ◽  
Distribution Parameters

The article briefly describes the history and fields of application of the theory of extreme values, including climatology. The data format, the Generalized Extreme Value (GEV) probability distributions with Bock Maxima, the Generalized Pareto (GP) distributions with Point of Threshold (POT) and the analysis methods are presented. Estimating the distribution parameters is done using the Maximum Likelihood Estimation (MLE) method. Free R software installation, the minimum set of required commands and the GUI in2extRemes graphical package are described. As an example, the results of the GEV analysis of a simulated data set in in2extRemes are presented.

scholarly journals Application of Special Cause Control Charts to Green Sand Process

2015 ◽  
Vol 15 (4) ◽  
pp. 55-60 ◽  
Author(s):  
M. Perzyk ◽  
A. Rodziewicz
Keyword(s):  
Control Charts ◽  
Manufacturing Industry ◽  
Processing System ◽  
Original Data ◽  
Green Sand ◽  
Statistical Process ◽  
Shewhart Control Charts ◽  
Shewhart Control ◽  
Iron Foundry ◽  
Almost All

Abstract Statistical Process Control (SPC) based on the well known Shewhart control charts, is widely used in contemporary manufacturing industry, including many foundries. However, the classic SPC methods require that the measured quantities, e.g. process or product parameters, are not auto-correlated, i.e. their current values do not depend on the preceding ones. For the processes which do not obey this assumption the Special Cause Control (SCC) charts were proposed, utilizing the residual data obtained from the time-series analysis. In the present paper the results of application of SCC charts to a green sand processing system are presented. The tests, made on real industrial data collected in a big iron foundry, were aimed at the comparison of occurrences of out-of-control signals detected in the original data with those appeared in the residual data. It was found that application of the SCC charts reduces numbers of the signals in almost all cases It is concluded that it can be helpful in avoiding false signals, i.e. resulting from predictable factors.

scholarly journals "Evaluation of Some Methods for Estimating the Weibull Distribution Parameters"

2017 ◽  
Vol 4 (2) ◽  
pp. 8-14
Author(s):  
J. A. Labban ◽  
H. H. Depheal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Mean Square Error ◽  
Random Sample ◽  
Likelihood Estimation ◽  
Mean Square ◽  
Distribution Parameters

"This paper some of different methods to estimate the parameters of the 2-Paramaters Weibull distribution such as (Maximum likelihood Estimation, Moments, Least Squares, Term Omission). Mean square error will be considered to compare methods fits in case to select the best one. There by simulation will be implemented to generate different random sample of the 2-parameters Weibull distribution, those contain (n=10, 50, 100, 200) iteration each 1000 times."

STATISTICAL PROCESS CONTROL FOR LOW NONCONFORMITY PROCESSES

1995 ◽  
Vol 02 (01) ◽  
pp. 15-22 ◽  
Author(s):  
T.N. GOH ◽  
M. XIE
Keyword(s):  
Process Control ◽  
Statistical Process Control ◽  
Control Charts ◽  
Exact Probability ◽  
Statistical Process ◽  
Shewhart Control Charts ◽  
Shewhart Control ◽  
Cumulative Count ◽  
Pattern Recognition Approach ◽  
Control Limits

Statistical process control of high quality products is an important issue in modern quality control applications because of the success of continuous improvement efforts worldwide. The conventional Shewhart control charts based on 3-sigma control limits tend to encounter certain practical and theoretical problems as “zero-defect” is approached. In this paper, we describe some general approaches to solving this problem, focusing on the control charts for nonconformities or defects. We suggest that for a moderate nonconformity process, the exact probability limits should be used. For a lower non-conformity process, a “pattern recognition” approach can be applied. Finally, for a near-zero nonconformity process, a modified approach based on the cumulative count of nonconformities can be used.

scholarly journals The Use of Statistical Process Control Tools for Analysing Financial Statements

2017 ◽  
Vol 17 (1) ◽  
pp. 129-137
Author(s):  
Janusz Niezgoda
Keyword(s):  
Process Control ◽  
Statistical Process Control ◽  
Control Chart ◽  
Control Charts ◽  
Financial Statements ◽  
Arithmetic Mean ◽  
Statistical Process ◽  
Shewhart Control Charts ◽  
Shewhart Control ◽  
Financial Analyses

Abstract This article presents the proposed application of one type of the modified Shewhart control charts in the monitoring of changes in the aggregated level of financial ratios. The control chart x̅ has been used as a basis of analysis. The examined variable from the sample in the mentioned chart is the arithmetic mean. The author proposes to substitute it with a synthetic measure that is determined and based on the selected ratios. As the ratios mentioned above, are expressed in different units and characters, the author applies standardisation. The results of selected comparative analyses have been presented for both bankrupts and non-bankrupts. They indicate the possibility of using control charts as an auxiliary tool in financial analyses.

scholarly journals Statistical Process Control as a Failure Removal Improvement Tool

2018 ◽  
Vol 21 (3) ◽  
pp. 124-129
Author(s):  
Michał Zasadzień ◽  
Katarzyna Midor
Keyword(s):  
Control Charts ◽  
Preventive Measures ◽  
Positive Impact ◽  
Quality Engineering ◽  
Small Company ◽  
Statistical Process ◽  
Shewhart Control Charts ◽  
Shewhart Control ◽  
Belt Conveyors ◽  
Maintenance Process

Abstract Continuous improvement should be a part of the strategy of every modern company that wishes to meet the requirements posed by the demanding, competitive market. The article presents a concept of applying a tool known from quality engineering, i.e. Shewhart control charts, for the improvement of the maintenance process in a small company providing services for the agricultural and construction industries. The improvement of the process included the reducing of the downtime of belt conveyors due to failures. Using control charts allowed the detection of interferences in the process and defining of their nature. Using other tools such as 5 WHY allowed the identification of the root causes of overly long downtimes and, consequently, formulation and implementation of improvements and preventive measures that were optimal for the organisation. The verification of actions taken has shown their positive impact on the process, which was reflected in the shortening of downtime and, subsequently, streamlining the failure removal process. The paper presents a possibility and validity of utilising quality engineering tools, such as Shewhart’s charts, 5 WHY or Ishikawa diagram, for improving the maintenance processes.

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