Omar Ruiz

Organic banana production in Ecuador: Its implications on black Sigatoka development and plant–soil nutritional status

Black Sigatoka, caused by the leaf fungus Mycosphaerella fijiensis Morelet, is a major constraint to banana production around the world. In Ecuador, the biggest banana-exporting country in the world, this disease has become increasingly aggressive. This has resulted in more fungicide applications, which have significantly increased costs in production and for the environment. Consequently, many banana growers have shifted to organic production, which produces greater economic returns as a result of higher sale prices. In addition, production costs are lower as no fungicides are applied. These organic bananas receive substantial amounts of organic products. This study describes the black Sigatoka disease and nutrient status in an organic banana plantation and compares it with a conventionally fertilized and fungicide-treated plantation. Black Sigatoka symptoms were evaluated in the vegetative and flowering stages under both production conditions and in vitro conditions. Univariate and multivariate descriptive statistics were used to analyze the parameters. Disease symptoms were more severe in leaves from the organic field than in leaves from the inorganic field, but the nutrient status (soil and foliar) did not differ between the two farms. Banana plants from the organic farm had 12 functional leaves at flowering and eight functional leaves at harvest. Average banana yields were over 40% lower for organic versus inorganic management; however, the average price received for organic bananas was over two times higher. Profit–cost analysis has shown that the organic banana farm was substantially more profitable than the inorganic one during the time period analyzed. These results indicated that bananas can be grown commercially without fungicides, and the lower productivity levels are compensated by higher prices of organic fruits in international markets. In addition, organic production has beneficial impacts on social and environmental issues.

T2 Control Charts With Variable Dimension

This paper proposes a new multivariate T2 control chart, termed the variable dimension T2 (VDT2) chart, in which the number of monitored quality characteristics is variable. When there are p related variables to be monitored, the approach is useful if there is a subset of p1 variables that are easy and/or inexpensive to measure, while the remaining variables are difficult and/or expensive to measure but provide additional useful information on whether the process mean has shifted. The VDT2 chart adaptively determines the number of variables to be monitored (either p1 or p) depending on the last value of the charted statistic. We provide Windows®-based software to optimize the parameters of the control chart using a Markov chain model to compute the performance measures and a genetic algorithm to conduct the optimization. The optimized VDT2 chart is quite powerful, and we demonstrate the somewhat surprising result that it detects mean shifts faster than a standard T2 chart for which all p variables are always measured, while also reducing sampling costs.

The variable sample size variable dimension T2 control chart

In this paper, we describe the development of the variable dimension and variable sample size T2 control chart (VSSVDT2), which is an enhancement of the variable dimension T2 chart (VDT2). In the VDT2 control chart, the number of variables that are measured to compute the T2 statistic is made variable. Some of the variables are easy or inexpensive to measure and are always monitored. The variables that are more difficult or expensive to measure are measured only when the T2 value from the previous sample exceeds a specified threshold. The VDT2 control chart performs well for moderate and large shifts in the mean vector. However, its performance for small shifts is poor. To improve the chart’s performance in detecting such shifts, we propose the application of the variable sample size technique to the VDT2 control chart, resulting in the VSSVDT2 control chart. To promote the use of the VSSVDT2 chart, a user-friendly software has been developed, which the final user can use to find the best parameters of the VSSVDT2 chart for a particular process.

Optimum variable-dimension EWMA chart for multivariate statistical process control

ABSTRACT The variable-dimension T2 control chart (VDT2 chart) was recently proposed for monitoring the mean of multivariate processes in which some of the quality variables are easy and inexpensive to measure while other variables require substantially more effort or expense. The chart requires most of the times that only the inexpensive variables be sampled, switching to sampling all the variables only when a warning is triggered. It has good ARL performance compared with the standard T2 chart, while significantly reducing the sampling cost. However, like the T2 chart, it has limited sensitivity to small and moderate mean shifts. To detect such shifts faster, we developed an exponentially weighted moving average (EWMA) version of the VDT2 chart, along with Markov chain models for ARL calculation, and software (made available) for optimizing the chart design. The optimization software, which is based on genetic algorithms, runs in Windows© and has a friendly user interface. The performance analysis shows the great gain in performance achieved by the incorporation of the EWMA procedure.

The Variable-Dimension Approach in Multivariate SPC

With multivariate processes, it may happen that some quality variables are more expensive and/or difficult to measure than the other ones, or they may demand much more time to measure. Their measurement may even be destructive. For monitoring such processes, the variable dimension approach was recently proposed. The idea is to measure always (at each sampling time) the “non-expensive” variables and to measure the expensive ones only when the values of the non-expensive variables give some level of evidence that the process may be out of control. The procedure bears much similarity with the one of variable parameters (or adaptive) control charts, but differs in that it is not the sample size or sampling interval or control limits that are made dynamically variable, but rather the very variables being measured (thus the name “variable dimension”). We review and compare the several variants of the approach, the last one being an EWMA version. The approach may lead to significant savings in sampling costs (the savings depending, of course, on the ratio between the costs of measuring the “expensive” and the “inexpensive” variables). Also, in many cases, contradicting the intuition, the variable dimension control charts may detect special causes even faster than their fixed (full) dimension counterparts.