X charts with supplementary samples to control the mean and variance

A standard X chart for controlling a process takes regular individual observations, for instance every half hour. This article proposes a modification of the X chart that allows one to take supplementary samples. The supplementary sample is taken (and the (X) over bar and R values computed) when the current value of X falls outside the control limits. With the supplementary sample, the signal of out-of-control is given by an (X) over bar value outside the (X) over bar chart's control limits or an R value outside the R chart's control limit. The proposed chart is designed to hold the supplementary sample frequency, during the in-control period, as low as 5% or less. In this context, the practitioner might prefer to verify an out-of-control condition by simply comparing the (X) over bar and R values with the control limits. In other words, without plotting the (X) over bar and R points. The X chart with supplementary samples has two major advantages when compared with the standard (X) over bar and A charts: (a) the user will be plotting X values instead of (X) over bar and R values; (b) the shifts in the process mean and/or changes in the process variance are detected faster.

Joint (X)over-bar and R charts with two-stage samplings

When joint (X) over bar and R charts are in use, samples of fixed size are regularly taken from the process, and their means and ranges are plotted on the (X) over bar and R charts, respectively. In this article, joint (X) over bar and R charts have been used for monitoring continuous production processes. The sampling is performed, in two stages. During the first stage, one item of the sample is inspected and, depending on the result, the sampling is interrupted if the process is found to be in control; otherwise, it goes on to the second stage, where the remaining sample items are inspected. The two-stage sampling procedure speeds up the detection of process disturbances. The proposed joint (X) over bar and R charts are easier to administer and are more efficient than the joint (X) over bar and R charts with variable sample size where the quality characteristic of interest can be evaluated either by attribute or variable. Copyright (C) 2004 John Wiley Sons, Ltd.

Economic design of two-stage (X)over-bar charts: the Markov chain approach

When the (X) over bar chart is in use, samples are regularly taken from the process, and their means are plotted on the chart. In some cases, it is too expensive to obtain the X values, but not the values of a correlated variable Y. This paper presents a model for the economic design of a two-stage control chart, that is. a control chart based on both performance (X) and surrogate (Y) variables. The process is monitored by the surrogate variable until it signals an out-of-control behavior, and then a switch is made to the (X) over bar chart. The (X) over bar chart is built with central, warning. and action regions. If an X sample mean falls in the central region, the process surveillance returns to the (Y) over bar chart. Otherwise. The process remains under the (X) over bar chart's surveillance until an (X) over bar sample mean falls outside the control limits. The search for an assignable cause is undertaken when the performance variable signals an out-of-control behavior. In this way, the two variables, are used in an alternating fashion. The assumption of an exponential distribution to describe the length of time the process remains in control allows the application of the Markov chain approach for developing the cost function. A study is performed to examine the economic advantages of using performance and surrogate variables. (C) 2003 Elsevier B.V. All rights reserved.

VSSI (X)over-bar charts with sampling at fixed times

A standard (X) over bar chart for controlling the process mean takes samples of size no at specified, equally-spaced, fixed-time points. This article proposes a modification of the standard (X) over bar chart that allows one to take additional samples, bigger than no, between these fixed times. The additional samples are taken from the process when there is evidence that the process mean moved from target. Following the notation proposed by Reynolds (1996a) and Costs (1997) we shortly call the proposed (X) over bar chart as VSSIFT (X) over bar chart: where VSSIFT means variable sample size and sampling intervals with fixed times. The (X) over bar chart with the VSSIFT feature is easier to be administered than a standard VSSI (X) over bar chart that is not constrained to sample at the specified fixed times. The performances of the charts in detecting process mean shifts are comparable.

Economic design of (X)over-bar charts with variable parameters: the Markov chain approach

This paper presents an economic design of (X) over bar control charts with variable sample sizes, variable sampling intervals, and variable control limits. The sample size n, the sampling interval h, and the control limit coefficient k vary between minimum and maximum values, tightening or relaxing the control. The control is relaxed when an (X) over bar value falls close to the target and is tightened when an (X) over bar value falls far from the target. A cost model is constructed that involves the cost of false alarms, the cost of finding and eliminating the assignable cause, the cost associated with production in an out-of-control state, and the cost of sampling and testing. The assumption of an exponential distribution to describe the length of time the process remains in control allows the application of the Markov chain approach for developing the cost function. A comprehensive study is performed to examine the economic advantages of varying the (X) over bar chart parameters.

Hereditary equine regional dermal asthenia in three related Quarter horses in Brazil

Hereditary equine regional dermal asthenia belongs to a group of inherited, congenital connective tissue dysplasias usually described as hyperelastosis cutis, cutaneous asthenia, dermatosparaxis, or Ehlers-Danlos-like syndrome. This report presents the clinical and histological features of three related Quarter horses affected with regional dermal asthenia. These horses had bilateral asymmetric lesions of the trunk and lumbar regions, where the skin was hyperextensible. Handling of the skin elicited a painful response and superficial trauma led to skin wounds. The skin was thinner than normal in the affected areas, with thickened borders and harder fibrotic masses (pseudotumours). The histopathological findings included thinner and smaller collagen fibrils, and a loose arrangement of collagen fibres in the middle, adventitial and deep dermis. Masson's trichrome and Calleja stains did not reveal any abnormality of collagen and elastic fibres. Electron microscopy showed no abnormalities. As in human patients, pseudotumour histopathological findings included fibroplasia and neovascularization. The pedigree chart of these animals supports an autosomal recessive type of inheritance, which has been suggested by other studies. This is the first report of this disease in Brazil. Its clinical and histological features resemble those described in horses affected with this condition in the United States.

A stochastic shift model for economically designed charts constrained by the process stage configuration

An economic model including the labor resource and the process stage configuration is proposed to design g charts allowing for all the design parameters to be varied in an adaptive way. A random shift size is considered during the economic design selection. The results obtained for a benchmark of 64 process stage scenarios show that the activities configuration and some process operating parameters influence the selection of the best control chart strategy: to model the random shift size, its exact distribution can be approximately fitted by a discrete distribution obtained from a relatively small sample of historical data. However, an accurate estimation of the inspection costs associated to the SPC activities is far from being achieved. An illustrative example shows the implementation of the proposed economic model in a real industrial case. (C) 2011 Elsevier B.V. All rights reserved.

Joint control charts for monitoring location and dispersion

The T-2 and the generalized variance vertical bar S vertical bar charts are used for monitoring the mean vector and the covariance matrix of multivariate processes. In this article, we propose for bivariate processes the use of the T-2 and the VMAX charts. The points plotted on the VMAX chart correspond to the maximum of the sample variances of the two quality characteristics. The reason to consider the VMAX statistic instead of the generalized variance vertical bar S vertical bar is the user's familiarity with the computation of simple sample variances; we can't say the same with regard to the computation of the generalized variance vertical bar S vertical bar.

A hierarchy of adaptive (X)over-bar control charts

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A single statistic for monitoring the covariance matrix of bivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

X̄ charts with variable sample size

The usual practice in using a control chart to monitor a process is to take samples of size n from the process every h hours. This article considers the properties of the X̄ chart when the size of each sample depends on what is observed in the preceding sample. The idea is that the sample should be large if the sample point of the preceding sample is close to but not actually outside the control limits and small if the sample point is close to the target. The properties of the variable sample size (VSS) X̄ chart are obtained using Markov chains. The VSS X̄ chart is substantially quicker than the traditional X̄ chart in detecting moderate shifts in the process.

Effects of stocking density on growth of channel catfish, Ictalurus punctatus, fingerlings in Southern Brazil

Channel catfish, Ictalurus punctatus, fingerlings (mean length: 4.0±0.5 cm) were stocked into sixteen 16-m2 tanks with cement walls and earth bottoms. Four stocking densities were used: 10, 15, 20, and 25 fish/m2. Fish were fed a prepared diet containing 36% protein according to a fish size/water temperature-dependant chart for 120 days. Fish were stocked on January 20, 1992. Average water temperature varied from 19.7°C to 28.5°C. Final mean values of individual fish length and weight were significantly higher (P < 0.05) for the density of 10 fish/m2 and averaged 19.4±2.6 cm and 70.0±16.9 g, respectively. Food conversion ratio was significantly higher (P < 0.05) for fish stocked at rate of 25 fish/m2. Survival rates averaged 91.4%, with no significant differences (P > 0.05) found among treatments. These results demonstrate the viability of channel catfish fingerling growth in southern Brazil.

Growth of Channel Catfish, Ictalurus punctatus, in Southern Brazil

Despite successful introduction of channel catfish into Brazil in 1980, no studies have been conducted to assess the performance of channel catfish, Ictalurus punctatus, farming in southern Brazil. Fingerlings (27.0 ± 2.2 g) were stocked in sixteen 16-m2 tanks with cement walls and earthen bottoms. Four stocking densities were used: 0.5, 0.75, 1.0, and 1.25 fish/m2. Fish were fed a diet containing 32% protein according to a feeding chart for 257 days (from April to December). Water temperature ranged from 16.4°C to 30°C during the study. Final average weight (727.1 ± 70.6 g) was significantly higher (P < 0.05) for fish raised at 0.5 fish/m2. Food conversion ratio (FCR) was significantly higher (P < 0.05) for fish stocked at 1.25 fish/ m2. Survival averaged 95.4%, and no significant differences (P > 0.05) were found among treatments. There was no significant difference (P > 0.05) in tank production among the densities of 0.75, 1.0, and 1.25 fish/m2, but they were higher (P < 0.05) than the density of 0.5 fish/ m2. These results demonstrate the viability of channel catfish growth in southern Brazil.

VSSI X̄ charts with sampling at fixed times

A standard X̄ chart for controlling the process mean takes samples of size n0 at specified, equally-spaced, fixed-time points. This article proposes a modification of the standard X chart that allows one to take additional samples, bigger than n0, between these fixed times. The additional samples are taken from the process when there is evidence that the process mean moved from target. Following the notation proposed by Reynolds (1996a) and Costa (1997) we shortly call the proposed X chart as VSSIFT X chart where VSSIFT means variable sample size and sampling intervals with fixed times. The X chart with the VSSIFT feature is easier to be administered than a standard VSSI X chart that is not constrained to sample at the specified fixed times. The performances of the charts in detecting process mean shifts are comparable. Copyright © 1998 by Marcel Dekker, Inc.

Joint X̄ and R Charts with Variable Sample Sizes and Sampling Intervals

Recent studies have shown that the X̄ chart with variable sampling intervals (VSI) and/or with variable sample sizes (VSS) detects process shifts faster than the traditional X̄ chart. This article extends these studies for processes that are monitored by both the X̄ and R charts. A Markov chain model is used to determine the properties of the joint X and R charts with variable sample sizes and sampling intervals (VSSI). The VSSI scheme improves the joint X̄ and R control chart performance in terms of the speed with which shifts in the process mean and/or variance are detected.