The (αX, βX)-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 ${\hat {e}} $eˆ, ( ${\widehat {TP}} $TPˆ), ( ${\widehat {LT}} $LTˆ) and ( ${\widehat {WIP}} $WIPˆ)? 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 $α,β)-precise estimates ( ${\widehat {MTBF}} $MTBFˆ) and ( ${\widehat {MTTR}} $MTTRˆ), where $\alpha $α represents estimate's accuracy and $\beta $β its probability. Specifically, the paper calculates ( $\alpha_X,\beta_X $αX,βX)-precise estimates of $X\in\{e,TP,LT,WIP\} $X∈{e,TP,LT,WIP} induced by ( ${\widehat {MTBF}} $MTBFˆ) and ( ${\widehat {MTTR}} $MTTRˆ), and evaluates the smallest number of machines' up- and downtime measurements, which ensure the desired precision of $\hat{X} \in \{\hat{e},\widehat{TP},\widehat{LT},\widehat{WIP}\} $Xˆ∈{eˆ,TPˆ,LTˆ,WIPˆ}. In addition, the paper develops a method for evaluating the smallest number of parts quality measurements to ensure ( $\alpha_q,\beta_q $αq,βq)-precise estimate of machines' quality parameter q and the desired ( $\alpha_{TP_q},\beta_{TP_q} $αTPq,βTPq)-precise estimate of good parts throughput, $\widehat{TP}_q $TPˆq. The results obtained are intended for production systems managerial/engineering/research personnel as a tool for designing continuous improvement projects with analytically predicted outcomes.