scholarly journals SAMPLE STANDARD DEVIATION(s) CHART UNDER THE ASSUMPTION OF MODERATENESS AND ITS PERFORMANCE ANALYSIS

2017 ◽  
Vol 5 (6) ◽  
pp. 368-377
Author(s):  
Kalpesh S. Tailor
Keyword(s):  
Standard Deviation ◽  
Performance Analysis ◽  
Normal Distribution ◽  
Control Chart ◽  
Control Charts ◽  
Curve Analysis ◽  
Mean Deviation ◽  
Sample Standard Deviation ◽  
Underlying Distribution ◽  
Control Limits

Moderate distribution proposed by Naik V.D and Desai J.M., is a sound alternative of normal distribution, which has mean and mean deviation as pivotal parameters and which has properties similar to normal distribution. Mean deviation (δ) is a very good alternative of standard deviation (σ) as mean deviation is considered to be the most intuitively and rationally defined measure of dispersion. This fact can be very useful in the field of quality control to construct the control limits of the control charts. On the basis of this fact Naik V.D. and Tailor K.S. have proposed 3δ control limits. In 3δ control limits, the upper and lower control limits are set at 3δ distance from the central line where δ is the mean deviation of sampling distribution of the statistic being used for constructing the control chart. In this paper assuming that the underlying distribution of the variable of interest follows moderate distribution proposed by Naik V.D and Desai J.M, 3δ control limits of sample standard deviation(s) chart are derived. Also the performance analysis of the control chart is carried out with the help of OC curve analysis and ARL curve analysis.

scholarly journals Construction of Fuzzy Mean using Standard Deviation ( X  S  ) Control Chart with Process Capability

2019 ◽  
Vol 8 (4) ◽  
pp. 5390-5396
Keyword(s):  
Quality Control ◽  
Standard Deviation ◽  
Set Theory ◽  
Control Chart ◽  
Control Charts ◽  
Total Quality ◽  
Statistical Process ◽  
Research Article ◽  
Fuzzy Mean ◽  
Control Limits

The Quality has established over a number of points such as inspection, quality control, quality assurance, and total quality control and the effects produced by the above phases are used to check and develop the production/service procedure. Statistical process control (SPC) is a powerful collection of problem solving tools valuable in attaining process steadiness and enlightening capability through the decline of variability. Fuzzy set theory is a utilitarian tool to succeed the uncertainty environmental circumstances and the Fuzzy control limits provide a more accurate and flexible rating than the traditional control charts. The purpose of this research article is to construct the fuzzy mean using standard deviation ( X S   ) control chart with the assistance of process capabilityThe Quality has established over a number of points such as inspection, quality control, quality assurance, and total quality control and the effects produced by the above phases are used to check and develop the production/service procedure. Statistical process control (SPC) is a powerful collection of problem solving tools valuable in attaining process steadiness and enlightening capability through the decline of variability. Fuzzy set theory is a utilitarian tool to succeed the uncertainty environmental circumstances and the Fuzzy control limits provide a more accurate and flexible rating than the traditional control charts. The purpose of this research article is to construct the fuzzy mean using standard deviation ( X S   ) control chart with the assistance of process capability

scholarly journals Performance of Moving Average (MA) Chart Under Three Delta Control Limits and Six Delta Initiatives

2019 ◽  
Vol 7 (2) ◽  
pp. 157-160
Author(s):  
Kalpesh S Tailor
Keyword(s):  
Quality Control ◽  
Normal Distribution ◽  
Six Sigma ◽  
Control Charts ◽  
Moving Average ◽  
Mean Deviation ◽  
Telephone Company ◽  
Graphical Tool ◽  
Control Limits

An SQC chart is a graphical tool for representation of the data for knowing the extent of variations from the expected standard. This technique was first suggested by W.A. Shewhart of Bell Telephone Company based on 3σ limits. M. Harry, the engineer of Motorola has introduced the concept of six sigma in 1980. In 6σ limits, it is presumed to attain 3.4 or less number of defects per million of opportunities. Naik V.D and Desai J.M proposed an alternative of normal distribution, which is named as moderate distribution. The parameters of this distribution are mean and mean deviation. Naik V.D and Tailor K.S. have suggested the concept of 3-delta control limits and developed various control charts based on this distribution. Using these concepts, control limits based on 6-delta is suggested in this paper. Also the moving average chart is studied by using 6-delta methodology. A ready available table for mean deviation is prepared for the quality control experts for taking fast actions. 

scholarly journals Exponentially Weighted Moving Average (EWMA) Chart Based on Six Delta Initiatives

2018 ◽  
Vol 6 (2) ◽  
pp. 127-135
Author(s):  
Kalpesh S. Tailor
Keyword(s):  
Normal Distribution ◽  
Control Chart ◽  
Six Sigma ◽  
Control Charts ◽  
Moving Average ◽  
Mean Deviation ◽  
Exponentially Weighted Moving Average ◽  
Ewma Chart ◽  
Weighted Moving Average ◽  
Exponentially Weighted

A control chart is a graphical device for representation of the data for knowing the extent of variations from the expected standard. The technique of control chart was suggested by W.A. Shewhart of Bell Telephone Company based on three sigma limits. M. Harry, the engineer of Motorola has introduced the concept of six sigma in 1980. In six sigma initiatives, it is expected to produce 3.4 or less number of defects per million of opportunities. Moderate distribution proposed by Naik and Desai is a sound alternative of normal distribution, which has mean and mean deviation as pivotal parameters and which has properties similar to normal distribution. Naik and Tailor have developed various control charts based on this distribution. In this paper an attempt is made to construct a control chart based on six delta initiatives for exponentially weighted moving average chart. Suitable Table for mean deviation is also constructed and presented for the engineers for making quick decisions.

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 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>

scholarly journals Economic Design of EWMA Control Charts with Variable Sampling Intervals for Monitoring the Mean and Standard Deviation under Preventive Maintenance and Taguchi’s Loss Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Li Xue ◽  
Zhen He
Keyword(s):  
Standard Deviation ◽  
Control Chart ◽  
Economic Model ◽  
Preventive Maintenance ◽  
Control Charts ◽  
Loss Functions ◽  
Variable Sampling ◽  
Sampling Intervals ◽  
Optimal Values ◽  
The Mean

The control chart and the maintenance management need to control process quality and reduce out-of-control cost. They are two key tools in the production process; however, they have usually been analyzed separately in the literature. Moreover, the existing studies integrating these two concepts suffer from three significant drawbacks as follows: (1) using control charts with fixed parameters to monitor the process, so that the small and middle shifts are detected slowly; (2) monitoring the mean and standard deviation separately, whereas, in real condition, the mean and standard deviation should be monitored simultaneously; (3) quality loss function is not usually used to design economic model, which leads to a large social quality loss in the monitoring process of control chart. To eliminate these weaknesses, the economic design of the exponential weighted moving average (EWMA) control chart with variable sampling intervals (VSI) for monitoring the mean and standard deviation under preventive maintenance and Taguchi’s loss functions is proposed. The optimal values of the parameters are determined to minimize the loss-per-item in an average cycle process. In addition, a genetic algorithm is used in a numerical example to search for the optimal values of the parameters. According to the sensitivity analysis, the effect of the model parameters on the solution of the economic model is obtained. Finally, the comparison study shows that the VSI EWMA control charts designed by the joint economic model are expected to reduce loss.

Comparison Between the Economic-Statistical Design of Double and Triple Sampling X ¯ \bar{X} Control Charts

2017 ◽  
Vol 32 (1) ◽  
Author(s):  
Azamsadat Iziy ◽  
Bahram Sadeghpour Gildeh ◽  
Ehsan Monabbati
Keyword(s):  
Optimal Control ◽  
Quality Control ◽  
Control Chart ◽  
Control Charts ◽  
Statistical Design ◽  
Sampling Interval ◽  
Point Of View ◽  
Double Sampling ◽  
Control Limits

AbstractControl charts have been established as major tools for quality control and improvement in industry. Therefore, it is always required to consider an appropriate design of a control chart from an economical point of view before using the chart. The economic design of a control chart refers to the determination of three optimal control chart parameters: sample size, the sampling interval, and the control limits coefficient. In this article, the double sampling (DS)

SKEW NORMAL DISTRIBUTION AND THE DESIGN OF CONTROL CHARTS FOR AVERAGES

2007 ◽  
Vol 14 (01) ◽  
pp. 49-63 ◽  
Author(s):  
TZONG-RU TSAI
Keyword(s):  
Normal Distribution ◽  
Simulation Study ◽  
Control Charts ◽  
Process Capability ◽  
Considerable Improvement ◽  
Quality Characteristic ◽  
Skew Normal Distribution ◽  
Underlying Distribution ◽  
Simulation Results ◽  
Skew Normal

The paper develops two new control charts and process capability ratios based on the skew normal distribution to monitor the process average and evaluate the process capability of non-normal data. Both control charts reduce to Shewhart-type control charts when the underlying distribution of quality characteristic is symmetric. A simulation study is conducted to compare the performances of the proposed control charts with those of existing control charts. Simulation results indicate that considerable improvement over those of existing control charts can be achieved when the proposed control charts are used to monitor the process average of non-normal data. Two examples are presented for illustration.

SHORT RUNS MULTIVARIATE CONTROL CHART FOR PROCESS DISPERSION

2005 ◽  
Vol 12 (02) ◽  
pp. 127-147 ◽  
Author(s):  
MICHAEL B. C. KHOO ◽  
S. H. QUAH ◽  
H. C. LOW ◽  
C. K. CH'NG
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Job Shops ◽  
Data Set ◽  
Control Charting ◽  
Standard Scale ◽  
Production Run ◽  
Process Dispersion ◽  
Manufacturing Techniques ◽  
Control Limits

The multivariate Hotelling's T2 control chart is designed to be used in a mass production for processes where data to estimate the mean vector and covariance matrix as well as the computation of control limits are available before a production run. Recent years have seen a trend in manufacturing industries to produce smaller lot sizes, a.k.a., low volume production which is a result of increased importance given to just-in-time (JIT) manufacturing techniques, synchronous manufacturing and the reduction of in-process inventory and costs. This new manufacturing environment is also referred to as short runs production or short runs. In a short runs environment, it is difficult or perhaps impossible to establish a reliable historical data set in setting valid control limits and in estimating process parameters due to the availability of insufficient data for a particular process because production runs are usually short and change frequently from one process to another. There is also a need to start charting at or very near the beginning of the run in such a case. Another problem encountered in a short runs production such as in job shops is that there are many different types of measurements so that many different control charts are needed. Standardized control charts that allow different statistics to be plotted on the same chart are extremely useful in short runs. Control charts with standard scale simplify the control charting process in a short runs environment. In this paper, we address the multivariate short runs problems for process dispersion based on individual measurements by presenting the required formulas so that the chart can be used from the start of production, whether or not prior information for estimating the chart's limit and its parameter is available. The proposed chart plots standardized statistics for multiple parts on the same chart. This paper extends the work of the authors in Ref. 13.

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