Negative Binomial charts for monitoring high-quality processes

Good control charts for high quality processes are often based on the number of successes between failures. Geometric charts are simplest in this respect, but slow in recognizing moderately increased failure rates p. Improvement can be achieved by waiting until r > 1 failures have occurred, i.e. by using negative binomial charts.In this paper we analyze such charts in some detail. On the basis of a fair comparison, we demonstrate how the optimal r is related to the degree of increase of p. As in practice p will usually be unknown, we also analyze the estimated version of the charts. In particular, simple corrections are derived to control the non-negligible effects of this estimation step

Application of Bernoulli Process-based Charts to Electronic Assembly

The application of protective gel, which is a subprocess of the electronic assembly of the exhaust gas recirculation sensor, is a highly capable process with the fraction of nonconforming units as low as 200 ppm. Every unit is inspected immediately after gel application. The conventional Shewhart chart is of no use here, and the approach based on the Bernoulli process is therefore considered. The number of conforming items in a row until the occurrence of first or the r-th nonconforming is determined and CCC-r, CCC-r EWMA, and CCC CUSUM charts are applied. The aim of the control is to detect the process deterioration, and so the one-sided charts are used. So that the charts based on the geometric or negative binomial distribution can be compared, their performance is assessed through the average number of inspected units until a signal (ANOS). Our study confirmed that CCC-r EWMA and CCC CUSUM are able to detect the process shift more quickly than the CCC-r chart. Of the two charts, the first is easier to construct

New attributes and variables control charts under repetitive sampling

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On the constrained economic design of control charts: a literature review

The economic design is an appealing approach to settle the design parameters of a control chart. Unfortunately, the economic models to design control charts have been scarcely implemented by quality practitioners due to the simplifying assumptions when representing the multifaceted complexity and constraints present within manufacturing and transactional environments. Although there has been an increasing scepticism about the economic models usefulness in practice, some recent studies proposed in literature face the problem of the control charts economic design from a new point of view: the objective is to achieve a well balanced trade-off between the operational and the statistical aspects. Under this perspective, the economic design problem can be intended in a broader sense as the constrained design of a SPC inspection procedure. This paper presents a discussion of some recent trends in the economic design stream of research and outlines the importance of considering the constraints related to SPC resources availability and modelling the occurrence of random shifts

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)

Economic design of X-bar control chart using simulated annealing

Control charts are widely used in industry for monitoring and controlling manufacturing processes. They should be designed economically in order to achieve minimum quality control costs. The major function of control chart is to detect the occurrence of assignable causes so that the necessary corrective action can be taken before a large quantity of nonconforming product is manufactured. The X-bar control chart dominates the use of any other control chart technique if quality is measured on a continuous scale. In the present project, the economic design of the X-bar control chart using Simulated Annealing has been developed to determine the values of the sample size, sampling interval, width of control limits such that the expected total cost per hour is minimized. Simulated annealing is a solution method in the field of combinatorial optimization based on an analogy with the physical process of annealing. Solving a combinatorial optimization problem amounts to finding the best or optimal solution among a finite or countable infinite number of alternative solutions. A program has been developed using Matlab software to optimize the cost. The result was compared with the literature and found to be superior to the initial cost obtained