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It s reasonable to ask, Can we categorize all sequences as either arithmetic or geometric The answer is no! Consider U = 10, 13, 17, 22, 28, 35, 43, This sequence shows a pattern, but it s neither arithmetic nor geometric The difference between the first and second terms is 3, the difference between the second and third terms is 4, the difference

between the third and fourth terms is 5, and so on The difference keeps increasing by 1 for each succeeding pair of terms This is a fairly simple example of a nonarithmetic, nongeometric sequence with an identifiable pattern

Here s a challenge!

We face a basic problem when we try to incorporate the risk plan into the project plan. We are planning for what might not happen. Any given risk event might not happen. But, life being what it is, some of the risk events are almost certain to occur. We just do not know which ones. The solution is a contingency. A contingency is an amount of time or money set aside to be used if and when risk events occur. For example, we might say to the customer: If our project goes exactly as planned, it will cost $100,000 and take ten weeks. But we ve made a list of what might cause trouble, and we d like to ask for an additional $20,000 and one extra week to use if we need them. We will only spend the extra money and take the extra time if something goes wrong, if one of the risk events occurs. In this

Suppose a particular species of cell undergoes mitosis (splits in two) every half hour, precisely on the half hour We take our first look at a cell culture at 12:59 pm, and find three cells At 1:00 pm, mitosis occurs for all the cells at the same time, and then there are six cells in the culture At 1:30 pm, mitosis occurs again, and we have 12 cells How many cells are there in the culture at 4:01 pm

There are 3 hours and 2 minutes between 12:59 pm and 4:01 pm This means that mitosis takes place 7 times: at 1:00, 1:30, 2:00, 2:30, 3:00, 3:30, and 4:00 Table 19-1 illustrates the scenario We look at the culture repeatedly at 1 minute past each half hour There are 384 cells at 4:01 pm, just after the mitosis event that occurs at 4:00 pm

his chapter deals with situations where a single variable is manipulated to satisfy the specification of a certain combination of controlled variables. In any system with a single manipulated variable, only one controlled variable is capable of independent specification. To put it in other words, there can be only one independent set point at any given time. This, however, does not exclude the incorporation of several controlled variables, as long as their combination contains but one degree of freedom. Thus we encounter the cascade control system, where the final element is manipulated through an intermediate or secondary controlled variable whose value is dependent on the primary. In ratio control systems, a specification is set on a designated mathematical combination of two or more measured variables. Selective control embodies the logical assignment of the final element to whichever controlled variable (of several) is in danger of violating its specified limits. Finally, adaption is the act of automatically modifying a controller to satisfy a combination of func153

example, we have asked for a 20% contingency fund for money, but only a 10% contingency for our time schedule Some companies track two separate contingency funds for each project One is for risk and the other is for change requests that come from the customer If a risk event occurs, and it will increase cost or delay our schedule as we work to deliver on the original plan, we draw from the contingency for risk On the other hand, if the customer makes change requests, not to x errors, but to add new features, we draw from the contingency for change requests Basically, we are saying, If you want this, we ll do it But you ll have to pay for it, and you ll have to give us time to do it right Scope creep is a big risk for a project.