This paper proposes a new combined npx−Xtrue¯ control chart for monitoring the mean of a process. A sample of size n is split into two sub‐samples of sizes n1 and n2 = n ‐ n1, determined by an optimization search. The units of the first sub‐sample are evaluated by attributes and plotted on an npx control chart. If this chart signals an out‐of‐control condition, then values of the quality characteristic of interest are collected from the units of the second sub‐sample, and the sample mean is calculated and plotted on an trueX¯ control chart. If both control charts signal, then the process is halted for adjustment. The possibility that all n items will not be inspected may lead to a reduction in both the cost and time spent on examining the sampled items. The performance of the proposed procedure is compared to that of two separate trueX¯ and npx control charts. The proposed procedure exhibits superior performance to the trueX¯ control chart for a variety of sample sizes, n, and shifts, δ, of the target mean. The average time to signal (ATS) for the combined control chart was lower than that calculated for a single trueX¯ or npx control chart, indicating that the combined control chart is an efficient tool for monitoring the process mean. Copyright © 2013 John Wiley & Sons, Ltd.
The aim of this paper is to propose a combined attribute-variable control chart, namely Max D T 2 , to monitor a vector of process means D OE 1 , : : : , q in a multivariate process control. The procedure consists of splitting a sample of size n into two sub-samples of sizes n 1 and n 2 (n D n 2 C n 2 ), determined by an optimized process. Units of the first sub-sample are evaluated by an attribute inspection. Using a device like a gauge ring, each unit of the first sub sample is considered approved related to the quality characteristic i if X i 2 [w Li ; w Ui ]; otherwise, it is disapproved in the characteristic i, where w Li and w Ui (obtained by an optimization) are respectively the lower and upper discriminating limits of the quality dimension X i . If the number of disapproved items in any quality characteristic is higher than a control limit, then the measurement of the q quality characteristics is taken on each unit of the second sub-sample and the statistic T 2 is calculated. If T 2 < L (L, the control limit) the process is judged as in control. The process will suffer intervention if both charts signal. The procedure has an advantage to not inspect the units of the second sub-sample if the first sub-sample indicates that the process is in control. This proposal shows a better performance than T 2 control chart for a large number of scenarios. The two control limits and discriminant limits are optimized to reach a desired value of ARL 0 and to minimize ARL 1 .
Generally, production systems as automatic welding process, production of ceramic products, making clothes use automatic control and to evaluate the quality of their production processes, they employ on-line process control. The control system consists of a periodic inspection of one item after every m produced items. The number of non-conformities is monitored in the inspected item and if it exceeds the control limit, then it is decided that the process is out-of-control and the process is stopped for adjustment, otherwise the production continues. The process starts in-control with a fixed non-conformities rate and, after an assignable cause, this rate increases leading the system to operate out of control. The process remains in these conditions until the change is detected and the process adjusted. After adjustment, the process returns to operate in-control. The aim of this paper is to present an economic approach to monitor the rate of non-conformities in a production by on-line process control. To design such type of process, an average cost per item produced is achieved through the properties of an ergodic Markov chain and the two required parameters: the inspection interval and the upper control limit are obtained by minimizing the average cost per produced item. A numerical example illustrates the proposal. It was identified the most important factors which result a considerable impact on the average cost per item: the probability of a shift in the parameter of Poisson distribution; cost to send non-conforming items to the customers; the in-control non-conformity rate; the specification limit and the cost of adjustment.
Este trabalho apresenta um estudo de confiabilidade em dados relativos ao tempo de vida de poços petrolíferos terrestres da Petrobras, produtores de óleo na Bacia Potiguar (RN/CE). O objetivo do estudo foi, com base em um conjunto de dados sobre ocorrências de falhas, verificar a existência do relacionamento entre o tempo de vida dos poços e algumas de suas características, como método de elevação, nível de produção, BSW (Basic Sediments and Water), razão gás óleo (RGO), unidade operacional de origem, entre outras. Os dados foram obtidos de um estudo retrospectivo de uma amostra com 450 poços-colunas que se encontravam em funcionamento no período de 2000 a 2006, escolhida de forma a representar todos os poços da bacia RN/CE. Foi realizada uma modelagem probabilística dos dados relativos à primeira falha através do ajuste do modelo de regressão Weibull. O modelo se mostrou apropriado para ajustar os dados e foi possível identificar, através do teste da razão de verossimilhança, quais e de que forma algumas características influenciam o tempo até a falha dos poços.
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