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Over the years, acceptance sampling plans have been crucial to quality assurance in manufacturing. Sample plans are designed using operating characteristic curve conditions to safeguard producers and customers. We propose a conditional probability-based Bayesian generalized multiple-dependent state sampling technique in this paper. The technique relies on Gamma-Poisson distribution. Other performance indicators and acceptance probability are calculated. Also, the new plan's operational method is discussed. The proposed technique is also compared to current attribute sampling schemes for efficacy. Optimal plan parameters for the plan's economic structure are also generated, adding managerial insights to the suggested plan. The entire cost study showed that the suggested plan is cheaper than existing sample plans under identical conditions. To account for inspection flaws, the plan is adjusted. We examine how Type I and Type II errors affect sampling plan outcomes. The plan is demonstrated with numerical examples and a data-driven application. [ABSTRACT FROM AUTHOR]

Detrital zircon (DZ) geochronology is based on a multistage, hierarchical sampling process in which sampling errors (statistical variance) and non-sampling errors (sampling bias) are endemic. Most of these errors are related to 1) initial collection of a non-random grab sample (typically from outcrop); 2) processing the grab sample to obtain a non-random grain-size sample of restricted grain size(s) (effectively a processed population); 3) randomly and/or non-randomly selecting DZs (often based on their size, shape, and colour) from the grain-size sample to obtain a hand-picked sample (effectively an analysed population); and 4) randomly and/or non-randomly radiometrically dating only certain DZs (due to limitations of instrument spot size and grain imperfections) from the hand-picked sample to obtain an analysed sample. Claims that hand-picked samples and analysed samples are randomly chosen are questionable, since these samples likely represent haphazard sampling attempting to emulate randomness. Non-randomness has major implications for calculations that determine sample size and inter-sample 'sameness' comparison, as both techniques generally depend on randomly chosen samples. The use of inter-sample comparison is particularly troublesome in that sameness is determined for the analysed sample, which is not representative of the initial grab sample. Yet more bias occurs with a 'leap of inference', the generalization of DZ ages from the analysed sample to the target population (the strata of interest) or to a general population (DZs derived from ultimate and proximate sources). Sampling bias can be reduced by unambiguously defining the sampled population (the population that inferential statistics apply), selecting representative samples (if possible, randomization should be used at every stage in the sampling process), and preserving the representativeness of subsamples by using correct sampling devices such as a microsplitter. It may be timely for standardized sampling, interpreting, and reporting guidelines so that detrital geochronology data are scientifically meaningful and replicable. [ABSTRACT FROM AUTHOR]