00180 ae1610738fe2b0daed20d48e9bab9f

181

Economic Contro! Chart Models with Cycle Duration Constraints

Figurę 2. Comparison of the Exact Density of S, + S₂ with Gibra’s Approximation. Numerica! Yalues Are from Case 9.

Summary and Conclusions

In this paper we have proposed the addition of a "cycle duration" constraint to the Lorenzen-Vance unified economic control chart model. The constraint consists of a specified bound on the 95th percentile of the distribution of out of control times. With the constraint added, the model minimizes long-run average ąuality related costs while allowing for control over unacceptable process behavior in individual ąuality cycles.

We develop distributional results necessary to implement the constrained approach, and apply it to a wide variety of examples taken from the economic control chart literaturę. These examples show that situations exist where the 95th percentile and, subseąuently, the variability in out of control times can be substantially reduced at relatively Iow cost. Since this tradeoff may be desirable in practice, we recommend that the constrained model be