A Model to Determine the Optimal Sampling Schedule of Diet Components¹

Graphical representation of a quality cycle: 1/λ = mean time process is in-control, τ = expected time of occurrence of abrupt change after last sampling while in control, T_c = expected time between the occurrence of abrupt change and the next sampling time, h = sampling interval, T_e = expected time until an out-of-control signal occurs, T₁ = expected time to investigate the cause of the change, T₂ = expected time to reformulate and implement new diets, and T_f = expected time to investigate the cause of the change, reformulate, and implement new diets.

Effect of number of cows in the herd (N_c) on optimal sampling design and total quality cost per day; —— = the sampling interval (h); —Δ— = number of standard deviations used as control limits of the X-bar chart (L); —♢— = number of samples taken (n); —■— = the total daily quality cost (C); and —○— = the total daily quality cost from current sampling design in the dairy industry (h = 30 d, n = 1, L = 2 SD).