The (α _X, β _X)-precise estimates of production systems performance metrics

Estimates of production systems performance metrics, such as machine efficiency, e, system throughput, TP, lead time, LT, and work-in-process, WIP, are necessary for evaluating effectiveness of potential system modifications. Calculating these estimates requires machines MTBF and MTTR, which can be obtained by measuring up- and downtime realizations on the factory floor. A question arises: What is the smallest number of measurements required to ensure the desired accuracy of the induced estimates (Formula presented.), ((Formula presented.)), ((Formula presented.)) and ((Formula presented.))? This paper provides an answer to this question in terms of serial lines with exponential machines. The approach is based on the theory of ((Formula presented.))-precise estimates ((Formula presented.)) and ((Formula presented.)), where (Formula presented.) represents estimate's accuracy and (Formula presented.) its probability. Specifically, the paper calculates ((Formula presented.))-precise estimates of (Formula presented.) induced by ((Formula presented.)) and ((Formula presented.)), and evaluates the smallest number of machines' up- and downtime measurements, which ensure the desired precision of (Formula presented.). In addition, the paper develops a method for evaluating the smallest number of parts quality measurements to ensure ((Formula presented.))-precise estimate of machines' quality parameter q and the desired ((Formula presented.))-precise estimate of good parts throughput, (Formula presented.). The results obtained are intended for production systems managerial/engineering/research personnel as a tool for designing continuous improvement projects with analytically predicted outcomes.