scholarly journals Monitoring The Level Of Students GPA's Over Time

2010 ◽  
Vol 3 (6) ◽  
pp. 43-50
Author(s):  
Saad T. Bakir ◽  
Bob McNeal
Keyword(s):  
False Alarm ◽  
Normal Distribution ◽  
False Alarm Rate ◽  
Control Chart ◽  
Average Run Length ◽  
Statistical Quality Control ◽  
Grade Point ◽  
Run Length ◽  
College Of Business ◽  
Over Time

A nonparametric (or distribution-free) statistical quality control chart is used to monitor the cumulative grade point averages (GPAs) of students over time. The chart is designed to detect any statistically significant positive or negative shifts in student GPAs from a desired target level. This nonparametric control chart is based on the signed-ranks of the GPAs of the sampled students. The exact false alarm rate and the in-control average run length of the proposed chart can be computed exactly and are independent of the underlying probability distribution of GPAs. The traditional Shewhart X-bar control chart for monitoring the mean of a process is based on the assumption that data follows a normal distribution. However, student GPAs may differ significantly from the normal distribution. As a result, using a traditional control chart to monitor the GPAs of students may lead to incorrectly specifying the control limits and the average run length and/or the false alarm rate of the chart. A test study was conducted at the College of Business Administration at Alabama State University. The study monitored the median cumulative GPAs of management majors during the period Spring 2005 through Spring 2009. The study revealed that the GPAs of students were stable at a median level of 2.6 over the period of the study.

scholarly journals Precision Analysis of Poisson Control Chart Based on Sample Size

2020 ◽  
Vol 16 (3) ◽  
pp. 325
Author(s):  
Elsa Resa Sari
Keyword(s):  
Quality Control ◽  
Sample Size ◽  
Control Chart ◽  
Average Run Length ◽  
Statistical Quality Control ◽  
Sample Sizes ◽  
Precision Analysis ◽  
Run Length ◽  
Statistical Quality ◽  
Result Show

One technique used in performing statistical quality control is by poisson control chart. Poisson control chart used in data that have the same mean and varians for monitoring the number of defects in the study. In some cases, the different sample sizes influence the control chart performance. The control chart performance can be measured using average run length (ARL). The smaller ARL’s value, the better type of control chart. In this study, we used different sample sizes  that is  and mean . The result show the best performance of control chart is when  and m = 200, because its has a smaller ARL’s value.                            

scholarly journals A Nonparametric Shewhart-Type Quality Control Chart for Monitoring Broad Changes in a Process Distribution

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Saad T. Bakir
Keyword(s):  
Quality Control ◽  
Control Chart ◽  
Control Charts ◽  
Probability Distributions ◽  
Average Run Length ◽  
Training Sample ◽  
Statistical Quality Control ◽  
Test Statistic ◽  
Run Length ◽  
Quality Control Chart

This paper develops a distribution-free (or nonparametric) Shewhart-type statistical quality control chart for detecting a broad change in the probability distribution of a process. The proposed chart is designed for grouped observations, and it requires the availability of a reference (or training) sample of observations taken when the process was operating in-control. The charting statistic is a modified version of the two-sample Kolmogorov-Smirnov test statistic that allows the exact calculation of the conditional average run length using the binomial distribution. Unlike the traditional distribution-based control charts (such as the Shewhart X-Bar), the proposed chart maintains the same control limits and the in-control average run length over the class of all (symmetric or asymmetric) continuous probability distributions. The proposed chart aims at monitoring a broad, rather than a one-parameter, change in a process distribution. Simulation studies show that the chart is more robust against increased skewness and/or outliers in the process output. Further, the proposed chart is shown to be more efficient than the Shewhart X-Bar chart when the underlying process distribution has tails heavier than those of the normal distribution.

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 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).

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.

An EWMA control chart based on the Wilcoxon rank-sum statistic using repetitive sampling

2018 ◽  
Vol 35 (3) ◽  
pp. 711-728 ◽  
Author(s):  
Jean-Claude Malela-Majika ◽  
Olatunde Adebayo Adeoti ◽  
Eeva Rapoo
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Moving Average ◽  
Location Parameter ◽  
Process Mean ◽  
Content Type ◽  
Underlying Process ◽  
Run Length ◽  
Design And Implementation ◽  
Ewma Control Chart

Purpose The purpose of this paper is to develop an exponentially weighted moving average (EWMA) control chart based on the Wilcoxon rank-sum (WRS) statistic using repetitive sampling to improve the sensitivity of the EWMA control chart to process mean shifts regardless of the prior knowledge of the underlying process distribution. Design/methodology/approach The proposed chart is developed without any distributional assumption of the underlying quality process for monitoring the location parameter. The authors developed formulae as well as algorithms to facilitate the design and implementation of the proposed chart. The performance of the proposed chart is investigated in terms of the average run-length, standard deviation of the run-length (RL), average sample size and percentiles of the RL distribution. Numerical examples are given as illustration of the design and implementation of the proposed chart. Findings The proposed control chart presents very attractive RL properties and outperforms the existing nonparametric EWMA control chart based on the WRS in the detection of the mean process shifts in many situations. However, the performance of the proposed chart relatively deteriorates for small phase I sample sizes. Originality/value This study develops a new control chart for monitoring the process mean using a two-sample test regardless of the nature of the underlying process distribution. The proposed control chart does not require any assumption on the type (or nature) of the process distribution. It requires a small number of subgroups in order to reach stability in the phase II performance.

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