This paper can be considered as an extension of the work of Tran et al (for monitoring compositional data using a multivariate exponentially weighted moving average MEWMA-compositional data [CoDa] chart) by taking into account potential measurement errors that are known to highly affect production processes. A linearly covariate error model with a constant error variance is used to study the impact of measurement errors on the MEWMA-CoDa control chart. In particular, the influence of the device parameters (σ M ,b), the number of independent observations m, and the the number of variables p are investigated in terms of the MEWMA optimal couples (r,H) as well as in terms of their corresponding ARLs. A comparison between the Hotelling-CoDa T 2 and the proposed chart is made in order to show that the MEWMA-CoDa chart is more efficient in detecting shifts in the presence of measurement errors. A real-life example of muesli production, using multiple measurements for each composition, is used to estimate the parameters and also to demonstrate how the MEWMA-CoDa can handle measurement errors to detect shifts in the process.
Genetically modified, insect-resistant Bacillus thuringiensis (Bt) cotton is cultivated extensively in Pakistan. Past studies, however, have raised concerns about the prevalence of Bt cotton varieties possessing weak or nonperforming insect-resistance traits conferred by the cry gene. We examine this issue using data drawn from a representative sample of cotton-growing households that were surveyed in six agroclimatic zones spanning 28 districts in Pakistan in 2013, as well as measurements of Cry protein levels in cotton tissue samples collected from the sampled households’ main fields. The resultant dataset combines information from 593 sampled households with corresponding plant tissue diagnostics from 70 days after sowing, as well as information from 589 sampled households with corresponding diagnostics from 120 days after sowing. Our analysis indicates that 11 percent of farmers believed they were cultivating Bt cotton when, in fact, the Cry toxin was not present in the tested tissue at 70 days after sowing (i.e., a Type I error). The analysis further indicates that 5 percent of farmers believed they were cultivating non-Bt cotton when, in fact, the Cry toxin was present in the tested tissue (i.e., a Type II error). In addition, 17 percent of all sampled farmers were uncertain whether or not they were cultivating Bt cotton. Overall, 33 percent of farmers either did not know or were mistaken in their beliefs about the presence of the cry gene in the cotton they cultivated. Results also indicate that toxic protein levels in the plant tissue samples occurred below threshold levels for lethality in a significant percentage of cases, although these measurements may also be affected by factors related to tissue sample collection, handling, storage, and testing procedures. Nonetheless, results strongly suggest wide variability both in farmers’ beliefs and in gene expression. Such variability has implications for policy and regulation in Pakistan’s transgenic cotton seed market.
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