scholarly journals X bar control chart for non-normal symmetric distributions

2016 ◽  
Vol 13 (2) ◽  
Author(s):  
Kristina Veljkovic
Keyword(s):  
Control Chart ◽  
Goodness Of Fit ◽  
Theoretical Distribution ◽  
Quality Characteristic ◽  
Statistical Quality Control ◽  
Symmetric Distributions ◽  
Sample Mean ◽  
Uniform Distributions ◽  
Pearson Type ◽  
Control Limits

In statistical quality control, X bar control chart is extensively used to monitor a change in the process mean. In this paper, X bar control chart for non-normal symmetric distributions is proposed. For chosen Student, Laplace, logistic and uniform distributions of quality characteristic, we calculated theoretical distribution of standardized sample mean and fitted Pearson type II or type VII distributions. Width of control limits and power of the X bar control chart were established, giving evidence of the goodness of fit of the corresponding Pearson distribution to the theoretical distribution of standardized sample mean. For implementation of X bar control chart in practice, numerical example of construction of a proposed chart is given.

scholarly journals Economic statistical design of X bar control chart for non-normal symmetric distribution of quality characteristic

Filomat ◽  
2015 ◽  
Vol 29 (10) ◽  
pp. 2325-2338 ◽  
Author(s):  
Kristina Veljkovic ◽  
Halima Elfaghihe ◽  
Vesna Jevremovic
Keyword(s):  
Control Chart ◽  
Loss Function ◽  
Statistical Design ◽  
Economic Loss ◽  
Theoretical Distribution ◽  
Quality Characteristic ◽  
Symmetric Distribution ◽  
Logistic Distribution ◽  
False Alarms ◽  
Sample Mean

In economic statistical design of a control chart, the economic-loss function is minimized subject to a constrained minimum value of power, maximum value of probability of false alarms and average time to signal an expected shift. This paper is concerned with the optimum economic statistical design of the X bar chart when quality characteristic has non-normal symmetric distribution. We considered three types of distributions: Student distribution, standard Laplace distribution and logistic distribution. For each of these distributions, we calculated theoretical distribution of standardized sample mean (or its best approximation) and approximated it with normal, Pearson VII and Johnson SU distributions. For considered example, constrained minimization of expected loss function was done using genetic algorithm in statistical software R. We compared results of economic statistical design of X-bar chart for theoretical distribution of standardized sample mean with the results for normal, Pearson and Johnson distributions. We found that, for all chosen distributions of quality characteristic, Pearson VII distribution and Johnson SU distribution give results very close to results based on theoretical distribution of standardized sample mean, while normal distribution gives much worse fit.

scholarly journals Penerapan Peta Kendali Neutrosophic Exponentially Weighted Moving Average (NEWMA) X dalam Monitoring Rata-Rata Proses Ketebalan Kaca

2022 ◽  
Vol 4 (1) ◽  
Author(s):  
Wibawati Wibawati ◽  
Widya Amalia Rahma ◽  
Muhammad Ahsan ◽  
Wilda Melia Udiatami
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Moving Average ◽  
Quality Characteristic ◽  
Average Process ◽  
Exponentially Weighted Moving Average ◽  
Ewma Control Chart ◽  
Control Limits ◽  
Weighted Moving Average ◽  
Exponentially Weighted

In the industrial sector, the measurement results of a quality characteristic often involve an uncertainty interval (interval indeterminacy). This causes the classical control chart to be less suitable for monitoring quality. Currently, a control chart with a neutrosophic approach has been developed. The neutrosophic control chart was developed based on the concept of neutrosophic numbers with control charts. One of the control charts that have been developed to monitor the mean process is the Neutrosophic Exponentially Weighted Moving Average (NEWMA) X control chart. This control chart is a combination of neutrosophic with classical EWMA control chart.  The neutrosophic control chart consists of two control charts, namely lower and upper, each of which consists of upper and lower control limits. Therefore, NEWMA X is more sensitive to detect out-of-control observations. In this research, the NEWMA X control chart will be used to monitor the average process of the thickness of the panasap dark grey 5mm glass produced by a glass industry. Through the analysis in this research, it was found that by using weighting λN [0, 10; 0, 10] and constant value kN [2, 565; 2, 675], the average process of the thickness of panasap dark grey 5mm glass has not beet controlled statistically because 21 observations were identified that were outside the control limits (out of control). When compared with the classical EWMA control chart with the same weighting λ, 17 observations were detected out of control. This proves that the NEWMA X control chart is more sensitive in detecting observations that are out of control because the determination of the in-control state is based on two values, lower and upper, both at the lower and upper control limits.

scholarly journals PENERAPAN DIAGRAM KENDALI MAXIMUM MULTIVARIATE CUMULATIVE SUM (MAX-MCUSUM) PADA PENGENDALIAN KUALITAS PRODUK KACANG (Studi Kasus: Produk Kacang Garing di PT XY)

2022 ◽  
Vol 10 (4) ◽  
pp. 573-582
Author(s):  
Sintia Rizki Aprilianti ◽  
Tatik Widiharih ◽  
Sudarno Sudarno
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Quality Standards ◽  
Quality Characteristic ◽  
Statistical Quality Control ◽  
Industry Data ◽  
Machine Material ◽  
Small Shift ◽  
Pareto Chart ◽  
Main Factor

Now, Statistical quality control be a particular concern to large companies.PT XY is one of the largest nut company in Indonesia that has implemented the quality standards of a product. Max-MCUSUM control chart becomes a tool that is graphically used to monitor and evaluate whether the process is under control or nut. Based on Cheng and Thaga (2005), Max-MCUSUM control chart takes precedence over detecting small shift based on average and variability in industry data. The quality characteristic of Kacang Garing will be variables, namely broken nut skin, bean seed 1, and foam nut skin. Max-MCUSUM control chart is controlled with the control limit (h) from ARL (Average Run Length) simulation of 370 is 429,69. ARL is an average of samples that need to be decribed before it goes out of control. The research continued with multivariate capability process with MCp worth 0,905 and MCpk worth 1,355. Those value indicates that Kacang Garing has met the quality specification stipulated by PT XY. Broken nut skin becomes the most dominant cause based on pareto chart and carried out analysis by using fishbone chart so that is known the main factor causing broken nut skin are machine, material, and method. 

scholarly journals On Performance of Two-Parameter Gompertz-Based X¯ Control Charts

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Johnson A. Adewara ◽  
Kayode S. Adekeye ◽  
Olubisi L. Aako
Keyword(s):  
Control Chart ◽  
Coverage Probability ◽  
Control Charts ◽  
Average Run Length ◽  
Real Life ◽  
Correction Method ◽  
Gompertz Distribution ◽  
Real Life Data ◽  
Control Limits ◽  
Two Parameter

In this paper, two methods of control chart were proposed to monitor the process based on the two-parameter Gompertz distribution. The proposed methods are the Gompertz Shewhart approach and Gompertz skewness correction method. A simulation study was conducted to compare the performance of the proposed chart with that of the skewness correction approach for various sample sizes. Furthermore, real-life data on thickness of paint on refrigerators which are nonnormal data that have attributes of a Gompertz distribution were used to illustrate the proposed control chart. The coverage probability (CP), control limit interval (CLI), and average run length (ARL) were used to measure the performance of the two methods. It was found that the Gompertz exact method where the control limits are calculated through the percentiles of the underline distribution has the highest coverage probability, while the Gompertz Shewhart approach and Gompertz skewness correction method have the least CLI and ARL. Hence, the two-parameter Gompertz-based methods would detect out-of-control faster for Gompertz-based X¯ charts.

scholarly journals A best-fit probability distribution for the estimation of rainfall in northern regions of Pakistan

2016 ◽  
Vol 11 (1) ◽  
pp. 432-440 ◽  
Author(s):  
M. T. Amin ◽  
M. Rizwan ◽  
A. A. Alazba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Future Research ◽  
Maximum Rainfall ◽  
Type Iii ◽  
Goodness Of Fit Tests ◽  
Pearson Type ◽  
Northern Regions ◽  
Best Fit

AbstractThis study was designed to find the best-fit probability distribution of annual maximum rainfall based on a twenty-four-hour sample in the northern regions of Pakistan using four probability distributions: normal, log-normal, log-Pearson type-III and Gumbel max. Based on the scores of goodness of fit tests, the normal distribution was found to be the best-fit probability distribution at the Mardan rainfall gauging station. The log-Pearson type-III distribution was found to be the best-fit probability distribution at the rest of the rainfall gauging stations. The maximum values of expected rainfall were calculated using the best-fit probability distributions and can be used by design engineers in future research.

scholarly journals MENENTUKAN DISTRIBUSI REPRESENTATIF FREQUENSI CURAHAN HUJAN HARIAN MAKSIMUM DENGAN METODEHISTOGRAM DAN METODE PARAMETIK DI PROVINSI SUMATERA BARAT

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Selpa Dewi
Keyword(s):  
Goodness Of Fit ◽  
Type Iii ◽  
Pearson Type ◽  
Chi Squared ◽  
Anderson Darling

Penelitian ini bertujuan untuk menentukan distribusi yang representatif frequensi curahan hujan harian maksimum di Provinsi Sumatera Barat. Data yang digunakan untuk penelitian ini diambil dari data hujan maksimum harian selama 20 sampai 40 tahunan, dengan 24 stasiun penakar hujan untuk provinsi Sumatera Barat. Data masing-masing stasiun kemudian disusun dalam dua jenis deret data, yaitu deret data annual maxima dan deret data annual exceedances. Dari hasil uji deret data ini diharapkan mengikuti satu atau beberapa dari distribusi yang umum dipakai dalam hidrologi rekayasa, yaitu distribusi normal, normal-log, Gumbel, Gama-II, Gama-III dan distribusi Log-Pearson Type III (LP-III). Dengan mengunakan uji kecocokan (goodness of fit), uji parametrik, Chi-Squared test, Kolmogorov-Smirnovtest dan Anderson-Darling test ditambah dengan metode histrogram (visual).Kata kunci:Intensitas hujan distribusi representative annual maxima, annual exceendances, goodness of fitprovinsi Sumatera Barat.

scholarly journals X̅ and R control charts based on marshall-olkin inverse log-logistic distribution for positive skewed data

2020 ◽  
Vol 1 (1) ◽  
pp. 9-16
Author(s):  
O. L. Aako ◽  
J. A. Adewara ◽  
K. S Adekeye ◽  
E. B. Nkemnole
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Logistic Distribution ◽  
Skewed Data ◽  
Process Data ◽  
And Performance ◽  
Set Up ◽  
Control Limits ◽  
Normally Distributed

The fundamental assumption of variable control charts is that the data are normally distributed and spread randomly about the mean. Process data are not always normally distributed, hence there is need to set up appropriate control charts that gives accurate control limits to monitor processes that are skewed. In this study Shewhart-type control charts for monitoring positively skewed data that are assumed to be from Marshall-Olkin Inverse Loglogistic Distribution (MOILLD) was developed. Average Run Length (ARL) and Control Limits Interval (CLI) were adopted to assess the stability and performance of the MOILLD control chart. The results obtained were compared with Classical Shewhart (CS) and Skewness Correction (SC) control charts using the ARL and CLI. It was discovered that the control charts based on MOILLD performed better and are more stable compare to CS and SC control charts. It is therefore recommended that for positively skewed data, a Marshall-Olkin Inverse Loglogistic Distribution based control chart will be more appropriate.

scholarly journals Evaluasi Kinerja Bagan Kendali Fm Pada Proses Short-Run

2018 ◽  
Vol 17 (1) ◽  
Author(s):  
Darmanto Darmanto
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Job Shop ◽  
Average Run Length ◽  
Just In Time ◽  
Multivariate Normal ◽  
Sensitivity Level ◽  
Short Run ◽  
Control Limits ◽  
Vector Shift

<p><em>The manufacturing production process that is currently trend is short-run. Short-run process is a job shop and a just in-time. These causes the process parameters to be unknown due to unavailability of data and generally a small amount of product. The control chart is one of the control charts which  designed for the short run. The procedure of the control chart follows the concept of succesive difference and under the assumption of the multivariate Normal distribution. The sensitivity level of a control chart is evaluated based on the average run length (ARL) value. In this study, the ARL value was calculated based on the shift simulation of the average vector by recording the first m-point out of the control limits. The average vector shift simulation of the target () is performed simultaneously with the properties of a positive shift (=+ δ). Variations of data size and many variables in this study were m = 20, 50 and p = 2, 4, 8, respectively. Each scheme (a combination of δ, m and p) is iterated 250,000 times. The simulation results show that for all schemes when both parameters are known ARL<sub>0 </sub>≈ 370. But, when parameters are unknown, ARL<sub>1</sub> turn to smaller. This conclusion also implied when the number of p and n are increased, it reduce the sensitivity of the control chart.</em></p>

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