TOLERANCE INTERVAL K VALUE TABLE SOFTWARE

TOLERANCE INTERVAL K VALUE TABLE SOFTWARE

Suppose the lower tolerance bound based on a normal distribution is 1085.947, so the engineer can claim that at least 99% of all the light bulbs exceed approximately 1086 hours of burn time with 95% confidence ( Minitab 18 Statistical Software 2017). The engineer wants to calculate a 95%/99% lower tolerance bound, which is the burn time that at least 99% of all light bulbs exceed with 95% confidence. The engineer randomly collects a sample of 100 light bulbs and reports the times to failure. For example, a quality engineer in a light bulb manufacturer needs to evaluate light bulbsвЂ™ life spans. This tolerance interval can be denoted as a / tolerance interval. It can be interpreted as we are 100(1в€’ О±) % confidence that at least 100 ПЃ % of the population will be within the interval. A tolerance interval covers at least a specified proportion, ПЃ (0в‰¤ ПЃв‰¤1), of the population with a specified degree of confidence, 100(1в€’ О±) % with 0в‰¤ О±в‰¤1 ( Hahn and Meeker 1991). A prediction interval is an interval, with a specified degree of confidence, 100(1в€’ О±) %, that the single future observation or multiple future observations from a population will fall between. Confidence intervals provide a range of values that are likely to include the unknown parameter with a specified degree of confidence, 100(1в€’ О±) %, based upon a random sample. There are three types of statistical intervals commonly used in practice: confidence interval, prediction interval, and tolerance interval. We show that the proposed robust model selection approach performs well when the underlying distribution is unknown but candidate distributions are available. We also propose a robust model selection approach to obtain tolerance intervals that are relatively insensitive to the model misspecification. We study the performance of tolerance intervals when the assumed distribution is the same as the true underlying distribution and when the assumed distribution is different from the true distribution via a Monte Carlo simulation study. On the other hand, we also investigate the effect of misspecifying the underlying probability model on the performance of tolerance intervals. This paper aims to provide a comparative study of the computational procedures for tolerance intervals in some commonly used statistical software packages including JMP, Minitab, NCSS, Python, R, and SAS. Despite the usefulness of tolerance intervals, the procedures to compute tolerance intervals are not commonly implemented in statistical software packages. In many scientific fields, such as pharmaceutical sciences, manufacturing processes, clinical sciences, and environmental sciences, tolerance intervals are used for statistical inference and quality control. A tolerance interval is a statistical interval that covers at least 100 ПЃ % of the population of interest with a 100(1в€’ О±) % confidence, where ПЃ and О± are pre-specified values in (0, 1).

Tolerance interval k value table