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Economic Control Chart Models with Cycle Duration Constraints

solution n = 45, L = 2.02, and h = 37.61 hours yields an hourly cost of $0.98, with T₀ut having 95th percentile equal to 60.03 hours and standard deviation a_out = 16.58 hours. When the 95th percentile is constrained to not

exceed 30 hours, the optimal solution becomes n* = 57, L* = 2.05, and h* = 26.9 hours with an hourly cost of $1.04 and standard deviation a₀ut ⁼ 9.77 hours. By accepting a 6% increase in the hourly cost, the 95th percentile is halved and ct_s reduced by 41%. We feel that this would be considered a desirable tradeoff in many applications. FigurÄ™ 1 illustrates, for this example, the relation between total cost and the 95th percentile of T₀ut- The FigurÄ™ is consistent with our numerical results, showing that p^ can be substantially

reduced with little impact on hourly cost.

Other examples illustrate situations where achieving a reduction in variability is relatively expensive. Consider the p-chart model of Case 5. To reduce the 95th percentile of T_0U( by 12%, from 6.28 to 5.51, requires a 50% increase in the hourly cost, from $5.52 to $8.27. We cannot generally conclude that variability can be reduced at Iow cost.

FigurÄ™ 1. Impact on Hourly Cost of Constraining the Distribution of T₀ut

in Case 6.