Waiting average

TWA - time-waited average (acceptable for 8 hour per day, 40 hour per week)... 

The coimection between the Porter-Thomas P(lc) distribution and RRKM theory is made tln-ough the parameters j -and v. Waite and Miller [99] have studied the relationship between the average of the statistical... 

It is essential, however, to follow a r rous experimental protocol for such applications. To maintain the quantitadve character of NMR spectroscopy, the reped-tion rate of signal averaging experiments has to be at least five times the longest spin-latdce relaxadon dme present in the sample. This waiting period is necessary to ensure that the magnetizadon is probed in a reproducible state, corresponding to thermodynamic equilibrium. 

These improvements are more likely to occur at the program and element level. For example, at one chemical company a group of senior operators took an initiative to redesign the work permit process that reduced the number of forms required, reduced the time required to issue a permit from an average of two hours to 30 minutes and improved the workplace monitoring needed to ensure a safe work environment. The reduction in the time to issue permits increased maintenance productivity by at least 10 percent, by reducing maintenance worker time spent waiting for permits. This more responsive system also reduced the number of instances where work went ahead without the appropriate permit. 

As we have previously seen the theoretical expression for the average waiting time is given by... 

Waiting time, average, 318 Walter, J., 768 War gaming problems, 252 Wave equation, Schrodinger (See entries under Schrodinger)... 

In reality, the queue size n and waiting time (w) do not behave as a zero-infinity step function at p = 1. Also at lower utilization factors (p < 1) queues are formed. This queuing is caused by the fact that when analysis times and arrival times are distributed around a mean value, incidently a new sample may arrive before the previous analysis is finished. Moreover, the queue length behaves as a time series which fluctuates about a mean value with a certain standard deviation. For instance, the average lengths of the queues formed in a particular laboratory for spectroscopic analysis by IR, H NMR, MS and C NMR are respectively 12, 39, 14 and 17 samples and the sample queues are Gaussian distributed (see Fig. 42.3). This is caused by the fluctuations in both the arrivals of the samples and the analysis times. 

Fig. 42.4. The ratio between the average waiting time (iv) and the average analysis time (AT) as a function of the utilization factor (p) for a system with exponentially distributed interarrival times and analysis times (M/M/1 system).

Fig. 42.6. Probability that the waiting time is smaller than < (t given in units relative to the average analysis time).

Figure 24 Probability distributions for the waiting time for 10 dihedral transitions. Time is given in units of the average waiting time 10x. The distributions are peaked around 10 = 1 and are much broader than the Poisson distribution but approach it for high T. For low T, a high probability for short waiting times exists and a long time tail of the distribution develops.

A fictitious example illustrates the large potential value of even small improvements in the control of a manufacturing process. Suppose one has a continuous process in which the final product (a polymer) is sampled and analyzed to be sure the copolymer composition is within specifications. A sample is taken from the process once every 2 hours, and it takes about 2 hours for the lab to dissolve the polymer and measure its composition. This process produces a number of different copolymer compositions, and it transitions from one product to another about twice a month on average. The 2-hour wait for lab results means that during a transition the new product has been within specification limits for 2 hours before the operators receive lab confirmation and are able to send the product to the in-spec silo. Consequently, on every transition, 2-hours worth of in-spec polymers are sent to the off-spec silo. 

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