Proposed Control Charts For Monitoring Cumulative Counts Of Conforming Items And Ratio Of Two Variables

This research provides a derivation of the analytical formulae to compute the average time to signal (ATS) value of the exponentially weighted moving average (EWMA) cumulative count of conforming (CCC) chart using the Markov chain technique. In the current literature, this chart is evaluated using simulation. Additionally, the variable sampling interval (VSI) EWMA CCC chart is also proposed to increase the sensitivity of the basic EWMA CCC chart in detecting process shifts. The optimal designs of the VSI EWMA CCC chart are obtained based on the Markov chain procedure by minimizing the expected delay time in detecting a process shift. The optimal parameters that minimize the average time to signal (ATS) criterion are provided and can be directly used in practice. Four charts, i.e. the basic CCC, VSI CCC, EWMA CCC and VSI EWMA CCC charts are considered in the numerical comparison using the ATS criterion. The VSI EWMA CCC chart has an impressive performance in comparison to the basic CCC, VSI CCC and EWMA CCC charts. An illustrative example via real data from an injection moulding process producing an array of micro-prism of an optical element is given to demonstrate the implementation of the VSI EWMA CCC chart in practice. In addition, this research proposes a two-sided run sum ratio chart to monitor the ratio of two normal variables. A Markov chain procedure is applied to evaluate the statistical performance of the chart based on the average run length (ARL) and expected average run length (EARL) criteria. Numerical comparisons with the Shewhart ratio and synthetic ratio charts based on the zero state analysis reveal that the run sum ratio chart has a better sensitivity in most cases

Modeling and designing control chart for monitoring time-between events data

Ph.DDOCTOR OF PHILOSOPH

Cumulative sum quality control charts design and applications

Includes bibliographical references (pages 165-169).Classical Statistical Process Control Charts are essential in Statistical Control exercises and thus constantly obtained attention for quality improvements. However, the establishment of control charts requires large-sample data (say, no less than I 000 data points). On the other hand, we notice that the small-sample based Grey System Theory Approach is well-established and applied in many areas: social, economic, industrial, military and scientific research fields. In this research, the short time trend curve in terms of GM( I, I) model will be merged into Shewhart and CU SUM two-sided version control charts and establish Grey Predictive Shewhart Control chart and Grey Predictive CUSUM control chart. On the other hand the GM(2, I) model is briefly checked its of how accurate it could be as compared to GM( I, 1) model in control charts. Industrial process data collected from TBF Packaging Machine Company in Taiwan was analyzed in terms of these new developments as an illustrative example for grey quality control charts

New Variable Sampling Interval Run Sum Standard Deviation And Run Sum Multivariate Coefficient Of Variation Charts

In Statistical Process Control (SPC), the control charting technique is an effective method to solve quality issues in manufacturing and service industries. The R and S charts are commonly used to monitor the process variance in industries due to the charts’ simplicity and high sensitivity toward large shifts. However, these charts are not sensitive toward small and moderate shifts in the process variance. On the other hand, the more sophisticated charts, such as the exponentially weighted moving average (EWMA) S chart and the cumulative sum (CUSUM) S chart are very effective in detecting small changes in the process variance. However, most quality practitioners do not adopt these charts in real applications due to their design complexity. In view of this setback, the variable sampling interval (VSI) approach is incorporated into the run sum (RS) S chart, in order to suggest an effective, yet a simple chart, for detecting small, moderate and large shifts in the process variance. Apart from that, the coefficient of variation (CV) is an important quality characteristic to take into account when the process mean and standard deviation are not constant, even though the process is in-control

Computational applications in stochastic operations research

Several computational applications in stochastic operations research are presented, where, for each application, a computational engine is used to achieve results that are otherwise overly tedious by hand calculations, or in some cases mathematically intractable. Algorithms and code are developed and implemented with specific emphasis placed on achieving exact results and substantiated via Monte Carlo simulation. The code for each application is provided in the software language utilized and algorithms are available for coding in another environment. The topics include univariate and bivariate nonparametric random variate generation using a piecewise-linear cumulative distribution, deriving exact statistical process control chart constants for non-normal sampling, testing probability distribution conformance to Benford\u27s law, and transient analysis of M/M/s queueing systems. The nonparametric random variate generation chapters provide the modeler with a method of generating univariate and bivariate samples when only observed data is available. The method is completely nonparametric and is capable of mimicking multimodal joint distributions. The algorithm is black-box, where no decisions are required from the modeler in generating variates for simulation. The statistical process control chart constant chapter develops constants for select non-normal distributions, and provides tabulated results for researchers who have identified a given process as non-normal The constants derived are bias correction factors for the sample range and sample standard deviation. The Benford conformance testing chapter offers the Kolmogorov-Smirnov test as an alternative to the standard chi-square goodness-of-fit test when testing whether leading digits of a data set are distributed according to Benford\u27s law. The alternative test has the advantage of being an exact test for all sample sizes, removing the usual sample size restriction involved with the chi-square goodness-of-fit test. The transient queueing analysis chapter develops and automates the construction of the sojourn time distribution for the nth customer in an M/M/s queue with k customers initially present at time 0 (k ≥ 0) without the usual limit on traffic intensity, rho \u3c 1, providing an avenue to conduct transient analysis on various measures of performance for a given initial number of customers in the system. It also develops and automates the construction of the sojourn time joint probability distribution function for pairs of customers, allowing the calculation of the exact covariance between customer sojourn times

A systematic study on time between events control charts

Ph.DDOCTOR OF PHILOSOPH

A study of advanced control charts for complex time-between-events data

Ph.DDOCTOR OF PHILOSOPH

A Quality Systems Economic-Risk Design Theoretical Framework

Quality systems, including control charts theory and sampling plans, have become essential tools to develop business processes. Since 1928, research has been conducted in developing the economic-risk designs for specific types of control charts or sampling plans. However, there has been no theoretical or applied research attempts to combine these related theories into a synthesized theoretical framework of quality systems economic-risk design. This research proposes to develop a theoretical framework of quality systems economic-risk design from qualitative research synthesis of the economic-risk design of sampling plan models and control charts models. This theoretical framework will be useful in guiding future research into economic risk quality systems design theory and application