A Time Truncated Moving Average Chart for the Weibull Distribution

A control chart of monitoring the number of failures is proposed with a moving average scheme, when the life of an item follows a Weibull distribution. A specified number of items are put on a time truncated life test and the number of failures is observed. The proposed control chart has been evaluated by the average run lengths (ARLs) under different parameter settings. The control constant and the test time multiplier are to be determined by considering the in-control ARL. It is observed that the proposed control chart is more efficient in detecting a shift in the process as compared with the existing time truncated control chart. ? 2013 IEEE.11Ysciescopu

A semi-empirical Bayesian chart to monitor Weibull percentiles

This paper develops a Bayesian control chart for the percentiles of the Weibull distribution, when both its in-control and out-of-control parameters are unknown. The Bayesian approach enhances parameter estimates for small sample sizes that occur when monitoring rare events as in high-reliability applications or genetic mutations. The chart monitors the parameters of the Weibull distribution directly, instead of transforming the data as most Weibull-based charts do in order to comply with their normality assumption. The chart uses the whole accumulated knowledge resulting from the likelihood of the current sample combined with the information given by both the initial prior knowledge and all the past samples. The chart is adapting since its control limits change (e.g. narrow) during the Phase I. An example is presented and good Average Run Length properties are demonstrated. In addition, the paper gives insights into the nature of monitoring Weibull processes by highlighting the relationship between distribution and process parameters.Comment: 21 pages, 3 figures, 5 table

The viability of Weibull analysis of small samples in process manufacturing

This research deals with some Statistical Quality Control (SQC) methods, which are used in quality testing. It investigates the problem encountered with statistical process control (SPC) tools when small sample sizes are used. Small sample size testing is a new area of concern especially when using expensive (or large) products, which are produced in small batches (low volume production). Critical literature review and analysis of current technologies and methods in SPC with small samples testing failed to show a conformance with conventional SPC techniques, as the confidence limits for averages and standard deviation are too wide. Therefore, using such sizes will provide unsecured results with a lack in accuracy. The current research demonstrates such problems in manufacturing by using examples, in order to show the lack and the difficulties faced with conventional SPC tools (control charts). Weibull distribution has always shown a clear and acceptable prediction of failure and life behaviour with small sample size batches. Using such distribution enables the accuracy needed with small sample size to be obtained. With small sample control charts generate inaccurate confidence limits, which are low. On the contrary, Weibull theory suggests that using small samples enable achievement of accurate confidence limits. This research highlights these two aspects and explains their features in more depth. An outline of the overall problem and solution point out success of Weibull analysis when Weibull distribution is modified to overcome the problems encountered when small sample sizes are used. This work shows the viability of Weibull distribution to be used as a quality tool and construct new control charts, which will provide accurate result and detect nonconformance and variability with the use of small sample sizes. Therefore, the new proposed Weibull deduction control charts shows a successful replacement of the conventional control chart, and these new charts will compensate the errors in quality testing when using small size samples

Univariate And Multivariate Synthetic Control Charts For Monitoring The Process Mean Of Skewed Distributions

Alat yang paling berkuasa dalam Kawalan Kualiti Berstatistik (SQC) ialah carta kawalan. The most powerful tool in Statistical Quality Control (SQC) is the control chart. Control charts are now widely accepted and used in industries

A New Control Chart for Monitoring Reliability Using Sudden Death Testing Under Weibull Distribution

In this paper, a new control chart using sudden death testing is designed by assuming that the lifetime/failure time of the product follows the Weibull distribution. The structure of the proposed chart is presented. The control chart coefficient is determined using some specified average run length for the in control process and the shifted process. Simulation study is given for the illustration purpose.11Ysciescopu

Modelo de apoio à decisão para a manutenção condicionada de equipamentos produtivos

Doctoral Thesis for PhD degree in Industrial and Systems EngineeringIntroduction: This thesis describes a methodology to combine Bayesian control chart and CBM (Condition-Based Maintenance) for developing a new integrated model. In maintenance management, it is a challenging task for decision-maker to conduct an appropriate and accurate decision. Proper and well-performed CBM models are beneficial for maintenance decision making. The integration of Bayesian control chart and CBM is considered as an intelligent model and a suitable strategy for forecasting items failures as well as allow providing an effectiveness maintenance cost. CBM models provides lower inventory costs for spare parts, reduces unplanned outage, and minimize the risk of catastrophic failure, avoiding high penalties associated with losses of production or delays, increasing availability. However, CBM models need new aspects and the integration of new type of information in maintenance modeling that can improve the results. Objective: The thesis aims to develop a new methodology based on Bayesian control chart for predicting failures of item incorporating simultaneously two types of data: key quality control measurement and equipment condition parameters. In other words, the project research questions are directed to give the lower maintenance costs for real process control. Method: The mathematical approach carried out in this study for developing an optimal Condition Based Maintenance policy included the Weibull analysis for verifying the Markov property, Delay time concept used for deterioration modeling and PSO and Monte Carlo simulation. These models are used for finding the upper control limit and the interval monitoring that minimizes the (maintenance) cost function. Result: The main contribution of this thesis is that the proposed model performs better than previous models in which the hypothesis of using simultaneously data about condition equipment parameters and quality control measurements improve the effectiveness of integrated model Bayesian control chart for Condition Based Maintenance.Introdução: Esta tese descreve uma metodologia para combinar Bayesian control chart e CBM (Condition- Based Maintenance) para desenvolver um novo modelo integrado. Na gestão da manutenção, é importante que o decisor possa tomar decisões apropriadas e corretas. Modelos CBM bem concebidos serão muito benéficos nas tomadas de decisão sobre manutenção. A integração dos gráficos de controlo Bayesian e CBM é considerada um modelo inteligente e uma estratégica adequada para prever as falhas de componentes bem como produzir um controlo de custos de manutenção. Os modelos CBM conseguem definir custos de inventário mais baixos para as partes de substituição, reduzem interrupções não planeadas e minimizam o risco de falhas catastróficas, evitando elevadas penalizações associadas a perdas de produção ou atrasos, aumentando a disponibilidade. Contudo, os modelos CBM precisam de alterações e a integração de novos tipos de informação na modelação de manutenção que permitam melhorar os resultados.Objetivos: Esta tese pretende desenvolver uma nova metodologia baseada Bayesian control chart para prever as falhas de partes, incorporando dois tipos de dados: medições-chave de controlo de qualidade e parâmetros de condição do equipamento. Por outras palavras, as questões de investigação são direcionadas para diminuir custos de manutenção no processo de controlo.Métodos: Os modelos matemáticos implementados neste estudo para desenvolver uma política ótima de CBM incluíram a análise de Weibull para verificação da propriedade de Markov, conceito de atraso de tempo para a modelação da deterioração, PSO e simulação de Monte Carlo. Estes modelos são usados para encontrar o limite superior de controlo e o intervalo de monotorização para minimizar a função de custos de manutenção.Resultados: A principal contribuição desta tese é que o modelo proposto melhora os resultados dos modelos anteriores, baseando-se na hipótese de que, usando simultaneamente dados dos parâmetros dos equipamentos e medições de controlo de qualidade. Assim obtém-se uma melhoria a eficácia do modelo integrado de Bayesian control chart para a manutenção condicionada

A Neural Network Approach to Synthetic Control Chart for the Process Mean

In this project, a multivariate synthetic control chart for monitoring the process mean vector of skewed populations using weighted standard deviations has been proposed. The proposed chart incorporates the weighted standard deviation (WSD) method of Chang and Bai (2004) into the standard multivariate synthetic chart of Ghute and Shirke (2008)

A Robust One-Sided Variability Control Chart

A new control charting technique to monitor the variability of any distribution is proposed. The simulation study shows that the new method outperforms all the existing methods in controlling the Type I error rates and it also has good power performance for all distributions considered in the study

A Robust One-Sided Variability Control Chart

A new control charting technique to monitor the variability of any distribution is proposed. The simulation study shows that the new method outperforms all the existing methods in controlling the Type I error rates and it also has good power performance for all distributions considered in the study