A two-pronged truncated deferred sampling plan (TTDSP) for log-logistic distribution

This paper is aimed at developing a new truncated sampling plan that uses information from precedent and successive lots for lot disposition with a pretention that the life-time of a particular product assumes a Log-logistic distribution. A new Two-pronged Truncated Deferred Sampling Plan (TTDSP) for Log-logistic distribution is proposed when the testing is truncated at a precise time. The best possible sample sizes are obtained under a given Maximum Allowable Percent Defective (MAPD), Test Suspension Ratios (TSR) and acceptance numbers (c). A formula for calculating the operating characteristics of the proposed plan is also developed. The operating characteristics and mean-ratio values were used to measure the performance of the plan. The findings of the study show that: Log-logistic distribution has a decreasing failure rate; furthermore, as mean-life ratio increase, the failure rate reduces; the sample size increase as the acceptance number, test suspension ratios and maximum allowable percent defective increases. The study concludes that the new minimum sample sizes were smaller which makes the plan a more economical plan to adopt when cost and time of production is costly and the experiment being destructive.

Using confidence intervals to determine adequate item sample sizes for vocabulary tests: An essential but overlooked practice

The last three decades have seen an increase of tests aimed at measuring an individual’s vocabulary level or size. The target words used in these tests are typically sampled from word frequency lists, which are in turn based on language corpora. Conventionally, test developers sample items from frequency bands of 1000 words; different tests employ different sampling ratios. Some have as few as 5 or 10 items representing the underlying population of words, whereas other tests feature a larger number of items, such as 24, 30, or 40. However, very rarely are the sampling size choices supported by clear empirical evidence. Here, using a bootstrapping approach, we illustrate the effect that a sample-size increase has on confidence intervals of individual learner vocabulary knowledge estimates, and on the inferences that can safely be made from test scores. We draw on a unique dataset consisting of adult L1 Japanese test takers’ performance on two English vocabulary test formats, each featuring 1000 words. Our analysis shows that there are few purposes and settings where as few as 5 to 10 sampled items from a 1000-word frequency band (1K) are sufficient. The use of 30 or more items per 1000-word frequency band and tests consisting of fewer bands is recommended.