An adaptive chart for monitoring the process mean and variance

Traditionally, an (X) over bar chart is used to control the process mean and an R chart is used to control the process variance. However, these charts are not sensitive to small changes in the process parameters. The adaptive ($) over bar and R charts might be considered if the aim is to detect small disturbances. Due to the statistical character of the joint (X) over bar and R charts with fixed or adaptive parameters, they are not reliable in identifing the nature of the disturbance, whether it is one that shifts the process mean, increases the process variance, or leads to a combination of both effects. In practice, the speed with which the control charts detect process changes may be more important than their ability in identifying the nature of the change. Under these circumstances, it seems to be advantageous to consider a single chart, based on only one statistic, to simultaneously monitor the process mean and variance. In this paper, we propose the adaptive non-central chi-square statistic chart. This new chart is more effective than the adaptive (X) over bar and R charts in detecting disturbances that shift the process mean, increase the process variance, or lead to a combination of both effects. Copyright (c) 2006 John Wiley & Sons, Ltd.

Synthetic control chart for monitoring the pprocess mean and variance

In this article, we consider the synthetic control chart with two-stage sampling (SyTS chart) to control the process mean and variance. During the first stage, one item of the sample is inspected; if its value X, is close to the target value of the process mean, then the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and the statistic T = Sigma [x(i) - mu(0) + xi sigma(0)](2) is computed taking into account all items of the sample. The design parameter is function of X-1. When the statistic T is larger than a specified value, the sample is classified as nonconforming. According to the synthetic procedure, the signal is based on Conforming Run Length (CRL). The CRL is the number of samples taken from the process since the previous nonconforming sample until the occurrence of the next nonconforming sample. If the CRL is sufficiently small, then a signal is generated. A comparative study shows that the SyTS chart and the joint X and S charts with double sampling are very similar in performance. However, from the practical viewpoint, the SyTS chart is more convenient to administer than the joint charts.

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.

Monitoring the process mean and variance using a synthetic control chart with two-stage testing

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A synthetic control chart for monitoring the process mean and variance

Purpose - The aim of this paper is to present a synthetic chart based on the non-central chi-square statistic that is operationally simpler and more effective than the joint X̄ and R chart in detecting assignable cause(s). This chart will assist in identifying which (mean or variance) changed due to the occurrence of the assignable causes. Design/methodology/approach - The approach used is based on the non-central chi-square statistic and the steady-state average run length (ARL) of the developed chart is evaluated using a Markov chain model. Findings - The proposed chart always detects process disturbances faster than the joint X̄ and R charts. The developed chart can monitor the process instead of looking at two charts separately. Originality/value - The most important advantage of using the proposed chart is that practitioners can monitor the process by looking at only one chart instead of looking at two charts separately. © Emerald Group Publishing Limted.

Monitoring process mean and variability with one non-central chi-square chart

Traditionally, an (X) over bar -chart is used to control the process mean and an R-chart to control the process variance. However, these charts are not sensitive to small changes in process parameters. A good alternative to these charts is the exponentially weighted moving average (EWMA) control chart for controlling the process mean and variability, which is very effective in detecting small process disturbances. In this paper, we propose a single chart that is based on the non-central chi-square statistic, which is more effective than the joint (X) over bar and R charts in detecting assignable cause(s) that change the process mean and/or increase variability. It is also shown that the EWMA control chart based on a non-central chi-square statistic is more effective in detecting both increases and decreases in mean and/or variability.

Describing fatigue crack growth and load ratio effects in Al 2524 T3 alloy with an enhanced exponential model

The fatigue crack behavior in metals and alloys under constant amplitude test conditions is usually described by relationships between the crack growth rate da/dN and the stress intensity factor range Delta K. In the present work, an enhanced two-parameter exponential equation of fatigue crack growth was introduced in order to describe sub-critical crack propagation behavior of Al 2524-T3 alloy, commonly used in aircraft engineering applications. It was demonstrated that besides adequately correlating the load ratio effects, the exponential model also accounts for the slight deviations from linearity shown by the experimental curves. A comparison with Elber, Kujawski and "Unified Approach" models allowed for verifying the better performance, when confronted to the other tested models, presented by the exponential model. (C) 2012 Elsevier Ltd. All rights reserved.

Thermal relationships and exercise physiology in anuran amphibians: Integration and evolutionary implications

Thermal and water balance are coupled in anurans, and species with particularly permeable skin avoid overheating more effectively than minimizing variance of body temperature. In turn, temperature affects muscle performance in several ways, so documenting the mean and variance of body temperature of active frogs can help explain variation in behavioral performance. The two types of activities studied in most detail, jumping and calling, differ markedly in duration and intensity, and there are distinct differences in the metabolic profile and fiber type of the supporting muscles. Characteristics of jumping and calling also vary significantly among species, and these differences have a number of implications that we discuss in some detail throughout this paper. One question that emerges from this topic is whether anuran species exhibit activity temperatures that match the temperature range over which they perform best. Although this seems the case, thermal preferences are variable and may not necessarily reflect typical activity temperatures. The performance versus temperature curves and the thermal limits for anuran activity reflect the thermal ecology of species more than their systematic position. Anuran thermal physiology, therefore, seems to be phenotypically plastic and susceptible to adaptive evolution. Although generalizations regarding the mechanistic basis of such adjustments are not yet possible, recent attempts have been made to reveal the mechanistic basis of acclimation and acclimatization. (C) 2007 Elsevier B.V. All rights reserved.

Natural history of Peucetia flava (Araneae, Oxyopidae): seasonal density fluctuation, phenology and sex ratio on the glandular plant Rhyncanthera dichotoma (Melastomataceae)

The seasonal density fluctuation, phenology and sex ratio of Peucetia flava (Oxyopidae) on Rhyncanthera dichotoma (Melastomataceae) were investigated during a year in a swamp in southeastern Brazil. Peucetia flava displayed an unusual non-seasonal life cycle and the population size varied little over the year. The density of Peucetia spiders increased with the increase in abundance of leaves and number of arthropods adhered to glandular trichomes on R. dichotoma leaves. Our findings suggest that seasonal density fluctuation of Peucetia may be influenced by foraging site availability (i.e. leaves) and prey supply (i.e. arthropods adhering to glandular trichomes). The unusual seasonal stability of P. flava may be related to the type of habitat in which this spider occurs (swamp), because of the constant input of allochthonous resources from the water source, i.e. aquatic insects that migrate to the terrestrial environment.

Second-order statistics for equal gain and maximal ratio diversity-combining reception

Exact and closed-form expressions for the level crossing rate and average fade duration are presented for equal gain combining and maximal ratio combining schemes, assuming an arbitrary number of independent branches in a Rayleigh environment. The analytical results are thoroughly validated by simulation.

Economic design of (X)over-bar and R charts under Weibull shock models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Size distribution and sex ratio in the spider crab Epialtus brasiliensis (Dana 1852) associated with seaweed on a rocky shore in southeastern Brazil (Crustacea, Decapoda, Brachyura, Majoidea, Epialtidae).

This study analyzed a population of the spider crab Epialtus brasiliensis, in regard to its size distribution, sex ratio and Sexual maturity. The study was conducted on a rocky shore in the Ubatuba region, state of Silo Paulo, Brazil, where a wide strip of algae covers the intertidal zone. A total of 378 specimens were obtained: 200 males (128 juvenile and 72 adult crabs) and 178 females (46 juveniles and 132 adults). Their Sizes ranged from 3.4 to 16.7 mm carapace length (CL). Taking into account that the pubertal and terminal molts are coincident in majid crabs, the maximum sizes attained by males and females are especially dependent on the factors that influence sexual maturity, mainly food resources, temperature and intraspecific competition. Males of E. brasiliensis occurred in all size classes, whereas females occurred only as far the 10th size class (12-13 min CL). file total sex ratio did not differ statistically from 1 : 1, but when the juvenile and adult specimens were analyzed separately the differences between sexes were significantly different, with higher proportions of immature males and mature females. The CL50 calculated for males and females was 10.4, and 6.9 min CL, respectively. Thus, males reach their sexual maturity at a larger size than females. This feature may be important for the reproductive strategy of this species, because larger males probably have greater reproductive Success.

Relationship between the dielectric and mechanical properties and the ratio of epoxy resin to hardener of the hybrid thermosetting polymers

The relationship between the dielectric properties (dielectric constant, ε′, and loss factor, ε; activation energy, E a) and the ratio of epoxy resin (OG) to hardener of the epoxy resin thermosetting polymers was investigated. The amplitude of the ε″ peak decreases with increasing OG content until about 73 wt.% and slightly increases at higher OG content. The temperature of the position of the ε″ peak increases with the increasing of OG content, reaching maximum values for compositions in the range of 67 and 73 wt.%, and then it decreases sharply at higher OG content. The activation energy obtained from dielectric relaxation increased with increasing wt.% OG up to around 70 wt.%. Further increase in concentration of OG up to 83 wt.% reduced E a. The curves of tensile modulus and fracture toughness mechanical properties as a function of OG content presented a similar behavior. ©2006 Sociedade Brasileira de Química.

A simple and portable instrument for determination of captopril in pharmaceutical formulations

Objective: This article describes the application and the performance of a cheap, simple and portable device that can be used for colorimetric quantitative determination of captopril (CPT) in pharmaceutical preparations. Methods: The sensor is a light detector resistor (LDR) placed into a black PTFE cell and coupled to a low cost multimeter (Ohmmeter). The instrument has been tested and is easy and fast to use. The quantitative study is based mainly on reduction of ammonium molybdate by captopril, in the presence of sulphuric acid, producing a green-yellow compound (max 407 nm). The calibration curves were obtained by plotting the electric resistance of the LDR against the CPT concentration on the range of 4.60 x 10-4 to 1.84 x 10-3 mol l-1 with a good coefficient of determination (R2 = 0.9962). Results: Statistical analysis of the obtained results showed no significant difference between the proposed methodology and the official reported method as evident from the t-test and variance ratio at 95% confidence level. Conclusion: The results of this study demonstrate that the instrument can be used for simple, accurate, precise, fast, in situ and low-cost colorimetric analysis of captopril in pharmaceuticals products.

Utility of inline milk fat and protein ratio to diagnose subclinical ketosis and to assign propylene glycol treatment in lactating dairy cows

The objective was to identify a fat-to-protein ratio (FPR) cut-off to diagnose subclinical ketosis (SCK) and to evaluate the effect of propylene glycol (PPG) treatment of cows with high FPR. The optimized cut-off was > 1.42; sensitivity (Se) = 92%; specificity (Sp) = 65%. A cut-off > 1.5 was selected for the PPG trial for balanced Se-Sp. Fat-to-protein ratio cut-offs > 1.25, 1.35, 1.50, 1.60, and 1.70 resulted in Se-Sp of 100% to 49%, 96% to 59%, 75% to 78%, 33% to 90%, and 8% to 96%, respectively. The proportions of cows with FPR > 1.25, 1.35, 1.42, 1.50, 1.60, and 1.70 were 60%, 50%, 44%, 30%, 14%, and 6%, respectively. Incidences of clinical ketosis and milk yield were similar between cows that received 400 mL of PPG (n = 34) and control cows (n = 38). Prevalence of SCK at enrollment was 29.2%; therefore, FPR > 1.5 is not indicated for treatment. Lower cut-offs should be used for screening.