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**Additional info for ASME B16 1.11-2005 Forged Fittings, Socket-Welding and Threaded**

**Example text**

1)lPn+1 nCk 0 = -(k ? kl)Pn ? kPn-1 ? 4 Reduced Equations 0 = - kPn-1 ? nlPn 0 = - kPn-1 ? 5 Probability on n Units in the System Using the reduced equations and the notation q = k/l, the probability of n units in the system are as below. P0 = = = = n = (0,k) When n is k ? 1 and larger, the reduced equations yield the relations listed below. kn-k]P0 Pn Pn n = (0,k) n[k At n = k, both of the above equations are the same; and because probabilities across all values of n sum to unity, the relation below applies.

LhP1(t) ? o(h) Pn(t ? h) = (1 - kh - lh)Pn(t) ? khPn-1(t) ? lhPn+1(t) ? 12 Differential Equations Differential equations are obtained from the difference equations when the time increment h approaches zero. They are needed in an interim manner to subsequently yield the equilibrium equations. To convert, the three identities listed below are applied. The first shows how the derivative is formed. The second expresses the probability without the increment of h, and the third concerns the function o(h).

They have one trailer for rent at $100 per day. 5 days. Customers will not wait for the trailer if it is out. Below are some of the statistics for the agency. 50 40 5 One Server, No Queue (M/M/1/1) Computations: q = ss/sa P0 = 1/(1 ? q) P1 = q/(1 ? 0 when one service facility, exponential arrival times, exponential service times and no queue capacity. The measures listed are:Ploss, qe and SL. Note, the higher the utilization ratio, q, the greater the portion of lost customers, Ploss. Also note how rho effective, qe, is always less than one.