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The aim of this paper is to present an online economical quality-control procedure for attributes in a process subject to quality deterioration after random shift and misclassification errors during inspections. The process starts in control (State I) and, in a random time, it shifts to out of control (State II). Once at State II, the non-conforming fraction increases according to a non-decreasing function (z), where z is the number of items produced after a shift. The monitoring procedure consists of inspecting a single item at every m produced items, which is examined r times independently to decide its condition. Once an inspected item is declared non-conforming, the process is stopped and adjusted. A direct search technique is used to find the optimum parameters which minimize the expected cost function. The proposed model is illustrated by a numerical example.conforming items) to the out-of-control state (the percentage of non-conforming items greater than 0%). Using mathematical symbols, the probability of non-conforming items shifts from p 1 = 0 (State I) to p 2 >0 (State II). The monitoring procedure consists of inspecting a single item at every m produced items. If the inspected item is judged conforming, the production process goes on; otherwise, the process is stopped for adjustment.This type of procedure to monitor process was studied by many authors as Adams and Woodall [2], Srivastava and Wu [3][4][5][6][7][8], Box and Kramer [9], Box and Luceno [10], Chou and Wang [11], Nandi and Sreehari [12,13], and Wang and Yue [14]. Examples that put into practice this kind of procedure may include the automatic process of soldering, production of semiconductors, production of diode, production of printed circuit boards and chemical processes [15][16][17]. Generally, production systems that employ some type of automatic control by collecting individual observations may be improved by the procedure here discussed.In Taguchi et al.[1], the authors assumed implicitly a uniform distribution to describe the shift from State I to State II. Such a condition provided a simpler cost function; however, it does not cover most practical situations. Nayebpour and Woodall [18] developed an alternative procedure assuming a geometric distribution to model the random shifts. They concluded that their approach was more appropriate than Taguchi's proposal mainly for p 2 >0. Nandi and Sreehari [12] developed a model under the assumption that the production process is subject to two assignable causes (in their paper, they are named minor and major).Borges et al. [19] noted that the procedures discussed in Taguchi et al.[1] and further papers may present inspection errors, compromising the determination of the optimum sampling interval. To this effect, they not only developed an approach that incorporates inspection errors but also evaluated the impact when those errors are not taken into account. About the effects of inspection errors on quality control, see Johnson et al. [20], Ranjan et al. [21], and Wang [22].Previous studies as...

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-As reflected in the literature, solid-fluid flow characteristics in spouted beds can vary widely when particles are coated by a suspension. This work is aimed at describing the effect of interparticle forces on airflow distribution in conical spouted beds of inert particles coated by Eucalyptus black liquor. The simulator developed earlier is modified to incorporate this effect. Two corrective functions with adjustable parameters are introduced into the simulator gas-flow model to generate the minimum spouting conditions in beds wetted by this liquor. These functions are assumed to be dependent on characteristic suspension groups and bed height. Using the particle swarm optimization (PSO) technique, expressions for these functions are obtained. Simulated results are presented and discussed to validate this technique. Implications of these results on drying Eucalyptus black liquor in conical spouted beds are analyzed.

This paper proposes a new control chart, denoted by X rec ; to evaluate the stability of a process mean when a small sample is available. This chart is based on attribute inspection rather than the physical measurements (taken with an instrument, such as a caliper or precision balance) of the quality characteristics of interest of the sampled items. The main goal is to recover measurements on a continuous scale by generating random measurements using the frequencies observed for the sample as inputs. The average sample obtained using these recovery measures (X rec ) is calculated and used to draw the standard X chart. The average sample X rec can be shown to be a mixture of normal distributions. The values of the lower control limit (LCL) and the upper control limit (UCL) are chosen to minimize the average run length (ARL).