# We know that 68 of the area under a normal curve is

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We know that 68% of the area under a normal curve is within one s of the average of the distribution. Since, the area under a probability curve corresponds with probability measures, we can state the following conclusion: A random variable drawn from a normal distribution has a 0.68probability of being within one s of the distribution average. In terms of project duration, the interpretation is similar: There is a 68 % chance that the actual project duration will be within one o of the estimated average length of the project, T e . There is more than 95 % chance that the project duration will be within 2o of the estimated average, and It is almost certain (99.7 %) that the project duration will not be more than 3o away. [Source: Introduction to Management Science, 5th edition, by Bernard W. Taylor III, Prentice Hall, Englewood, New Jersey] 22.3.5 Project Crashing and Time-Cost Trade-Off Project duration can be reduced by assigning more labor to project activities, often in the form of overtime, and by assigning more resources (material, equipment, etc). However, additional labor and resources cost money and hence increase the overall project cost. Thus, the decision to reduce the project duration must be based on an analysis of the trade-off between time and cost. Project crashin g is a method for shortening the project duration by reducing the time of one or more of the critical project activities to a time that is less than the normal activity time. This reduction in the normal activities times is called 'crashing'. Crashing is achieved by devoting more resources (in terms of money) to the activities to be crashed. Many times it is felt that the project duration as estimated from arrow diagram is long and it is desired by management to accomplish the project in a shorter duration of time in order to secure progress payments or to avoid lateness penalties, etc. To do so various possibilities are explored. Work study techniques of systematic questioning (as in critical examination under method study) are employed to every (critical) activity to seek the possibilities of reducing their duration. The critical path activities as classified as Do and Ancillary activities. Ancillary activities are those which support Do activities. For example, cutting of threads on a bar is Do activity whereas making the set up for cutting threads is an Ancillary activity. After identification, Do activities are subjected to systematic questioning technique embodying series of questions as regards purpose, place, sequence, person and means. The second method is to trade off or transfer some resources from the activities having float to the critical activities, in order to reduce their duration. Trading-off redistributes the resources and accompanies changes in duration. The

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266 resources maybe workforce, amount of equipment and machinery, money, (better and more suitable) materials, etc.
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