The no-central chi-square chart with two-stage samplings

Throughout this article, it is assumed that the no-central chi-square chart with two stage samplings (TSS Chisquare chart) is employed to monitor a process where the observations from the quality characteristic of interest X are independent and identically normally distributed with mean μ and variance σ2. The process is considered to start with the mean and the variance on target (μ = μ0; σ2 = σ0 2), but at some random time in the future an assignable cause shifts the mean from μ0 to μ1 = μ0 ± δσ0, δ >0 and/or increases the variance from σ0 2 to σ1 2 = γ2σ0 2, γ > 1. Before the assignable cause occurrence, the process is considered to be in a state of statistical control (defined by the in-control state). Similar to the Shewhart charts, samples of size n 0+ 1 are taken from the process at regular time intervals. The samplings are performed in two stages. At the first stage, the first item of the i-th sample is inspected. If its X value, say Xil, is close to the target value (|Xil-μ0|< w0σ 0, w0>0), then the sampling is interrupted. Otherwise, at the second stage, the remaining n0 items are inspected and the following statistic is computed. Wt = Σj=2n 0+1(Xij - μ0 + ξiσ 0)2 i = 1,2 Let d be a positive constant then ξ, =d if Xil > 0 ; otherwise ξi =-d. A signal is given at sample i if |Xil-μ0| > w0σ 0 and W1 > knia:tl, where kChi is the factor used in determining the upper control limit for the non-central chi-square chart. If devices such as go and no-go gauges can be considered, then measurements are not required except when the sampling goes to the second stage. Let P be the probability of deciding that the process is in control and P 1, i=1,2, be the probability of deciding that the process is in control at stage / of the sampling procedure. Thus P = P1 + P 2 - P1P2, P1 = Pr[μ0 - w0σ0 ≤ X ≤ μ0+ w 0σ0] P2=Pr[W ≤ kChi σ0 2], (3) During the in-control period, W / σ0 2 is distributed as a non-central chi-square distribution with n0 degrees of freedom and a non-centrality parameter λ0 = n0d2, i.e. W / σ0 2 - xn0 22 (λ0) During the out-of-control period, W / σ1 2 is distributed as a non-central chi-square distribution with n0 degrees of freedom and a non-centrality parameter λ1 = n0(δ + ξ)2 / γ2 The effectiveness of a control chart in detecting a process change can be measured by the average run length (ARL), which is the speed with which a control chart detects process shifts. The ARL for the proposed chart is easily determined because in this case, the number of samples before a signal is a geometrically distributed random variable with parameter 1-P, that is, ARL = I /(1-P). It is shown that the performance of the proposed chart is better than the joint X̄ and R charts, Furthermore, if the TSS Chi-square chart is used for monitoring diameters, volumes, weights, etc., then appropriate devices, such as go-no-go gauges can be used to decide if the sampling should go to the second stage or not. When the process is stable, and the joint X̄ and R charts are in use, the monitoring becomes monotonous because rarely an X̄ or R value fall outside the control limits. The natural consequence is the user to pay less and less attention to the steps required to obtain the X̄ and R value. In some cases, this lack of attention can result in serious mistakes. The TSS Chi-square chart has the advantage that most of the samplings are interrupted, consequently, most of the time the user will be working with attributes. Our experience shows that the inspection of one item by attribute is much less monotonous than measuring four or five items at each sampling.

Planning accelerated life tests under Exponentiated-Weibull-Arrhenius model

Purpose - The purpose of this paper is to present designs for an accelerated life test (ALT). Design/methodology/approach - Bayesian methods and simulation Monte Carlo Markov Chain (MCMC) methods were used. Findings - In the paper a Bayesian method based on MCMC for ALT under EW distribution (for life time) and Arrhenius models (relating the stress variable and parameters) was proposed. The paper can conclude that it is a reasonable alternative to the classical statistical methods since the implementation of the proposed method is simple, not requiring advanced computational understanding and inferences on the parameters can be made easily. By the predictive density of a future observation, a procedure was developed to plan ALT and also to verify if the conformance fraction of the manufactured process reaches some desired level of quality. This procedure is useful for statistical process control in many industrial applications. Research limitations/implications - The results may be applied in a semiconductor manufacturer. Originality/value - The Exponentiated-Weibull-Arrhenius model has never before been used to plan an ALT. © Emerald Group Publishing Limited.

Quality of performance of the operation of sugarcane mechanized planting in day and night shifts

The sugarcane mechanized planting is becoming increasingly widespread in Brazil due to a higher operability and better working conditions offered to workers compared to other types of planting. Studies related to this topic are insufficient or scarce in Brazil. In this context, the aim of this study was to evaluate the operation quality of sugarcane mechanized planting in two operation shifts, by means of statistical process control. The mechanized planting was held on March 2012 and statistical design was completely randomized with two treatments, totaling 40 replications for the day shift and 40 replications for the night shift. The variables evaluated were: speed, engine rotation, engine oil pressure, water temperature of the engine, effective field capacity and the time consumption hourly and effective fuel. The use of statistical control charts showed that random intrinsic do not cause this process. The tractor alignment error showed outliers in the day and night shifts operations, indicating a possible delay in receiving the signal. The water temperature of the engine and the effective fuel consumption showed lower variability in nighttime operation with average values of 81°C and 22.66 L ha-1, respectively. The hourly fuel consumption had greater variability and consequently lower quality during the night of the operation, with an average consumption of 25.46 L h-1 while the day shift showed 26.86 L h-1.

Desempenho de trator agrícola em duas profundidades de escarificação e dois teores de água no solo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Variabilidade espacial e diagnóstico da qualidade do processo em semeadura de amendoim

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Utilização do controle estatístico de processo na unidade de produção e desenvolvimento de derivados de soja - UNISOJA - F.C.F. - UNESP

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Análise da variabilidade do processo de filtração em filtros de tambor rotativo contínuo a vácuo para lodo de caldo de cana de açúcar

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo do desempenho dos gráficos de controle quando a média do processo oscila de acordo com o modelo AR(1)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Qualidade da operação de plantio mecanizado de cana-de-açúcar nos turnos diurno e noturno

Pós-graduação em Agronomia (Produção Vegetal) - FCAV

Qualidade da operação de plantio mecanizado de cana-de-açúcar em sistema meiosi

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Perdas na colheita mecanizada de cana-de-açúcar crua em função do desgaste das facas do corte de base

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A evasão escolar na educação tecnológica: estudo de uma Unidade do Centro Estadual de Educação Tecnológica Paula Souza

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Gráficos de controle de X para monitoramento de processos autocorrelacionados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influence of the sample area in the variability of losses in the mechanical harvesting of soybeans

The mechanical harvesting is an important stage in the production process of soybeans and, in this process; the loss of a significant number of grains is common. Despite the existence of mechanisms to monitor these losses, it is still essential to use sampling methods to quantify them. Assuming that the size of the sample area affects the reliability and variability between samples in quantifying losses, this paper aimed to analyze the variability and feasibility of using different sizes of sample area (1, 2 and 3 m²) in quantifying losses in the mechanical harvesting of soybeans. Were sampled 36 sites and the cutting losses, losses by other mechanisms of the combine and total losses were evaluated, as well as the water content in seeds, straw distribution and crop productivity. Data were subjected to statistical analysis (descriptive statistics and analysis of variance) and Statistical Control Process (SCP). The coefficients of variation were similar for the three frames available. Combine losses showed stable behavior, whereas cutting losses and total losses showed unstable behavior. The frame size did not affect the quantification and variability of losses in the mechanical harvesting of soybeans, thus a frame of 1 m² can be used for determining losses.

Quality of cut and basecutter blade configuration for the mechanized harvest of green sugarcane

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)