Effects of imprecise measurement on the two dependent processes control for the autocorrelated observations

The observations from the process output are always assumed to be independent when using a control chart to monitor a process. However, for many processes the observations are autocorrelated and including the measurement error due to the measurement instrument. This autocorrelation and measurement error can have a significant effect on the performance of the process control. This paper considers the problem of monitoring the mean of a quality characteristic X on the first process, and the mean of a quality characteristic Y on the second process, in which the observations X can be modeled as an ARMA model and observations Y can be modeled as an transfer function of X since the state of the second process is dependent on the state of the first process. To distinguish and maintain the state of the two dependent processes with measurement errors, the Shewhart control chart of residuals and the cause-selecting control chart, based on residuals, are proposed. The performance of the proposed control charts is evaluated by the rate of true or false alarms. By numerical analysis, it shows that the performance of the proposed control charts is significantly influenced by the variation of measurement errors. The application of the proposed control charts is illustrated by a numerical example .     

Optimal control policy for dependent process steps with over-adjusted means and variances

Over-adjustment to processes may result in shifts in process mean and variance, ultimately affecting the quality of products. An economic adjustment model is developed for the joint design of X̄-S² control charts and ē-S_e² cause-selecting control charts to control both means and variances of two dependent process steps using the Markov chain approach. The objective is to determine the optimal control policy of the proposed control charts, which effectively detect and distinguish the shifts of means and variances on the dependent process steps and minimize the total quality control cost. Application of the proposed control charts is illustrated through a numerical example.     

An approach to controlling two dependent process steps with autocorrelated observations

The observations from the process output are always assumed independent when using a control chart to monitor a process. However, for many processes the process observations are autocorrelated. This autocorrelation can have a significant effect on the performance of the control chart. This paper considers the problem of monitoring the mean of a quality characteristic X on the first process step and the mean of a quality characteristic Y on the second process step, in which the observations X can be modeled as an AR(1) model and observations Y can be modeled as a transfer function of X since the state of the second process step is dependent on the state of the first process step. To effectively distinguish and maintain the state of the two dependent process steps, the Shewhart control chart of residual and the cause-selecting control chart are proposed. The proposed control charts’ performance is measured by the rate of alarm on the proposed charts. From numerical analysis, it shows that the performance of the proposed control charts is much better than the misused Hotelling T² control chart and the individual Shewhart X and Y control charts.     

Nonparametric profile monitoring in multi-dimensional data spaces

Profile monitoring has received increasingly attention in a wide range of applications in statistical process control (SPC). In this work, we propose a framework for monitoring nonparametric profiles in multi-dimensional data spaces. The framework has the following important features: (i) a flexible and computationally efficient smoothing technique, called Support Vector Regression, is employed to describe the relationship between the response variable and the explanatory variables; (ii) the usual structural assumptions on the residuals are not required; and (iii) the dependence structure for the within-profile observations is appropriately accommodated. Finally, real AIDS data collected from hospitals in Taiwan are used to illustrate and evaluate our proposed framework.     

Assessing growing season beginning and end dates and their relation to climate in Taiwan using satellite data

Due to the close relationship between climate and plant phenology, changes in plant phenological patterns have been used as a surrogate of climate change. We analysed Moderate Resolution Imaging Spectroradiometer (MODIS) images to investigate the onset, offset and length of growing season, as well as spatial and inter-annual patterns of Normalized Difference Vegetation Index (NDVI) across six types of vegetation/land use in Taiwan. Regression models indicate that temperature was moderately to strongly related to NDVI for each of the six vegetation/land-use types (coefficients of determination (R ²) = 0.45–0.86). There was a 1–2 month lag time between changes in temperature and NDVI in the forests that are distributed in mid- to high-elevation areas, but not in low-elevation unirrigated fields, paddy fields and urban areas. The relationship between precipitation and changes in NDVI was only significant for unirrigated fields and urban areas (R ² = 0.37–0.43). Growing season ended considerably earlier at low elevations than at high elevations, possibly because of the earlier start and more severe dry period in low-elevation areas, such that the length of the growing season was longer in the forests than in the unirrigated fields, paddy fields and urban areas.     

Process control using VSI cause selecting control charts

The article considers the variable process control scheme for two dependent process steps with incorrect adjustment. Incorrect adjustment of a process may result in shifts in process mean, process variance, or both, ultimately affecting the quality of products. We construct the variable sampling interval (VSI) Z_{[`(X)]</sub>-Z<sub>SX<sup>2</sup></sub>{Z_{\overline{X}}-Z_{S_X^2}} and Z<sub>[`(e)]}-Z_Se²{Z_{\bar{{e}}}-Z_{S_e^2}} control charts to effectively monitor the quality variable produced by the first process step with incorrect adjustment and the quality variable produced by the second process step with incorrect adjustment, respectively. The performance of the proposed VSI control charts is measured by the adjusted average time to signal derived using a Markov chain approach. An example of the cotton yarn producing system shows the application and performance of the proposed joint VSI Z_{[`(X)]</sub> -Z<sub>SX<sup>2</sup></sub> {Z_{\overline{X}} -Z_{S_X^2 }} and Z<sub>[`(e)]} -Z_Se² {Z_{\bar{{e}}} -Z_{S_e^2 }} control charts in detecting shifts in mean and variance for the two dependent process steps with incorrect adjustment. Furthermore, the performance of the VSI Z_{[`(X)]</sub>-Z<sub>SX<sup>2</sup></sub> {Z_{\overline{X}}-Z_{S_X^2 }} and Z<sub>[`(e)]} -Z_Se² {Z_{\bar{{e}}} -Z_{S_e^2 }} control charts and the fixed sampling interval Z_{[`(X)]</sub> -Z<sub>SX<sup>2</sup></sub> {Z_{\overline{X}} -Z_{S_X^2 }} and Z<sub>[`(e)]} -Z_Se² {Z_{\bar{{e}}} -Z_{S_e^2 }} control charts are compared by numerical analysis results. These demonstrate that the former is much faster in detecting small and median shifts in mean and variance. When quality engineers cannot specify the values of variable sampling intervals, the optimum VSI Z_{[`(X)]</sub>-Z<sub>SX<sup>2</sup></sub> {Z_{\overline{X}}-Z_{S_X^2 }} and Z<sub>[`(e)]} -Z_Se² {Z_{\bar{{e}}} -Z_{S_e^2 }} control charts are also proposed by using the Quasi-Newton optimization technique.     

Improvement inconsistency of the metallic film thickness of computer connectors

The variation of the film thickness and associated increase in cost are vital problems to computer connector producers. However, no scientific adjustment method is currently available. Transfer function and engineering process control are proposed to adjust the production processes for improving the quality of the metallic film of the connectors and reducing the cost of production. The analyses of the confirmatory experiments from using the two proposed approaches show significant gains in quality improvement and cost reduction. Furthermore, the engineering process control approach reveals a better improvement over the transfer function approach. Thus this approach is recommended to improve the quality of the film thickness and reduce the production cost in the computer connector industry