The (alpha(X), beta(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 (e) over cap, ((TP) over cap), ((LT) over cap) and ((WIP) over cap)? This paper provides an answer to this question in terms of serial lines with exponential machines. The approach is based on the theory of (alpha,beta)-precise estimates ((MTBF) over cap) and ((MTTR) over cap), where alpha represents estimate's accuracy and beta its probability. Specifically, the paper calculates (alpha x, beta x)-precise estimates of X is an element of {e, TP, LT, WIP} induced by ((MTBF) over cap) and ((MTTR) over cap), and evaluates the smallest number of machines' up- and downtime measurements, which ensure the desired precision of (X) over cap is an element of {(e) over cap, (TP) over cap, (LT) over cap, (WIP) over cap}. In addition, the paper develops a method for evaluating the smallest number of parts quality measurements to ensure (alpha(q), beta(q))-precise estimate of machines' quality parameter q and the desired (alpha(TPq), beta(TPq))-precise estimate of good parts throughput, (TP) over cap (q). The results obtained are intended for production systems managerial/engineering/research personnel as a tool for designing continuous improvement projects with analytically predicted outcomes.