Evaluation of an np control chart under truncated life test using quick switching sampling system

2017 ◽  
Vol 40 (12) ◽  
pp. 3407-3414 ◽  
Author(s):  
P Jeyadurga ◽  
S Balamurali
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Optimal Parameters ◽  
Life Test ◽  
Sampling System ◽  
Run Length ◽  
Truncated Life Test ◽  
Control Limits

In this paper, we propose a new attribute np control chart for monitoring Weibull distributed mean life of a product using a quick switching sampling system. The proposed control chart consists of two pairs of control limits, namely normal and tightened control limits. The optimal parameters of the proposed control chart, such as coefficients of control limits and experiment termination ratio, are determined so that the average run length (ARL) is close to the target in-control ARL. The ARL is calculated for various shift constants for the corresponding determined parameters. The performance of the proposed control chart is evaluated and compared with other existing charts in terms of ARL.

scholarly journals Moving Average control charts for Burr X and Inverse Gaussian distributions

2020 ◽  
Vol 30 (4) ◽  
Author(s):  
Ambreen Shafqat ◽  
Muhammad Aslam ◽  
Mohammed Albassam
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Inverse Gaussian ◽  
Life Test ◽  
Run Length ◽  
Truncated Life Test ◽  
Average Control ◽  
Better Than

The Burr X and Inverse Gaussian (IG) distributions are considered in this paper to design an attribute control chart for time truncated life test with Moving Average (MA) scheme w. The presentation of the MA control chart is estimated in terms of average run length (ARL) by using the Monte Carlo simulation. The ARL is decided for different values of sample sizes, MA statistics size, parameters’ values, and specified average run length. The performance of this new MA attribute control chart is compared with the usual time truncated control chart for Burr X and IG distributions. The performance of a new control chart is better than the existing control chart.

An Attribute np Control Chart for Monitoring Mean Life Using Multiple Deferred State Sampling Based on Truncated Life Tests

2019 ◽  
Vol 26 (01) ◽  
pp. 1950004
Author(s):  
S. Balamurali ◽  
P. Jeyadurga
Keyword(s):  
Control Chart ◽  
Pareto Distribution ◽  
Average Run Length ◽  
Run Length ◽  
Manufacturing Process Control ◽  
The Status ◽  
Truncated Life Test ◽  
Life Tests ◽  
The Mean ◽  
Run Lengths

In this paper, we design an attribute [Formula: see text] control chart for monitoring the mean life of the product where the lifetime follows the Pareto distribution of the second kind. The lifetime of the product is determined by time truncated life test and the multiple deferred state sampling is used to declare the status of the manufacturing process. Control limit coefficients and multiple deferred state sampling parameters such as sample size and number of successive subgroups required to declare the state of the process are determined such that the in-control average run length is as near as possible to the target average run length. Out-of-control average run lengths are calculated for the determined parameters using various shift constants. The performance of the chart is compared with other existing chart in terms of average run length.

scholarly journals Average Run Length on CUSUM Control Chart for Seasonal and Non-Seasonal Moving Average Processes with Exogenous Variables

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 173
Author(s):  
Rapin Sunthornwat ◽  
Yupaporn Areepong
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Moving Average ◽  
Optimal Parameters ◽  
Exogenous Variables ◽  
Explicit Formulas ◽  
Run Length ◽  
Ewma Control Chart ◽  
Cusum Control Chart ◽  
Moving Average Processes

The aim of this study was to derive explicit formulas of the average run length (ARL) of a cumulative sum (CUSUM) control chart for seasonal and non-seasonal moving average processes with exogenous variables, and then evaluate it against the numerical integral equation (NIE) method. Both methods had similarly excellent agreement, with an absolute percentage error of less than 0.50%. When compared to other methods, the explicit formula method is extremely useful for finding optimal parameters when other methods cannot. In this work, the procedure for obtaining optimal parameters—which are the reference value ( a ) and control limit ( h )—for designing a CUSUM chart with a minimum out-of-control ARL is presented. In addition, the explicit formulas for the CUSUM control chart were applied with the practical data of a stock price from the stock exchange of Thailand, and the resulting performance efficiency is compared with an exponentially weighted moving average (EWMA) control chart. This comparison showed that the CUSUM control chart efficiently detected a small shift size in the process, whereas the EWMA control chart was more efficient for moderate to large shift sizes.

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 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 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 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>

On the Estimation Error in Zero-Inflated Poisson Model for Process Control

2003 ◽  
Vol 10 (02) ◽  
pp. 159-169 ◽  
Author(s):  
B. He ◽  
M. Xie ◽  
T. N. Goh ◽  
P. Ranjan
Keyword(s):  
Sample Size ◽  
Poisson Distribution ◽  
Control Chart ◽  
Average Run Length ◽  
Estimation Error ◽  
Accurate Estimate ◽  
Minimum Size ◽  
High Quality ◽  
Run Length ◽  
Run Length Distribution

The control chart based on a Poisson distribution has often been used to monitor the number of defects in sampling units. However, many false alarms could be observed due to extra zero counts, especially for high-quality processes. Therefore, some alternatives have been developed to alleviate this problem, one of which is the control chart based on the zero-inflated Poisson distribution. This distribution takes into account the extra zeros present in the data, and yield more accurate results than the Poisson distribution. However, implementing a control chart is often based on the assumption that the parameters are either known or an accurate estimate is available. For a high quality process, an accurate estimate may require a very large sample size, which is seldom available. In this paper the effect of estimation error is investigated. An analytical approximation is derived to compute shift detection probability and run length distribution. The study shows that the false alarm rates are higher than the desirable level for smaller values of the sample size. This is further supported by smaller average run length. In general, the quantitative results from this paper can be utilized to select a minimum size of the initial sample for estimating the control limits so that certain average run length requirements are met.

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