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Project Activity Time Analysis: Expected Time, Variance, and Completion Probabilities

This document presents a detailed analysis of project activities, estimating their expected times and variances, including calculations for critical paths AC and BD. The expected completion times and their variances are computed, revealing significant differences in variability which affect project completion risks. By examining the normally distributed time to complete each path, we calculate the probabilities of finishing within a specified timeframe. Notably, we emphasize the implications of variability on project completion and why the critical path's probability does not equate to overall project completion likelihood.

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Project Activity Time Analysis: Expected Time, Variance, and Completion Probabilities

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  1. Problem 13-28 The estimated times (in weeks) and immediate predecessors for the activities in a project are given in the following table. Assume that the activity times are independent. Kelly Devilbiss - Problem 13-28

  2. (a) Calculate the expected time and variance for each activity. Kelly Devilbiss - Problem 13-28

  3. (b) What is the expected completion time of the critical path? What is the expected completion time of the other patient in the network? Critical Path AC takes 20 weeks Critical Path BD takes 18 weeks Kelly Devilbiss - Problem 13-28

  4. What is the variance of the critical path? What is the variance of the other path in the network? Critical Path AC: σ2CP = σ2A + σ2C = 4/36 + 4/36 = 8/36 = 0.222 Critical Path BD: σ2CP = σ2B + σ2D = 144/36 + 36/36 = 180/36 = 5 Kelly Devilbiss - Problem 13-28

  5. (d) If the time to complete path A-C is normally distributed, what is the probability that this path will be finished in 22 weeks or less? t = 20 variance (σ2)= 0.222 standard deviation (√0.222) = 0.47 P(x ≤ 22) = P[(22 – 20)/0.47] = 4.26 Using Appendix A: 4.26 = 1.00 Kelly Devilbiss - Problem 13-28

  6. (e) If the time to complete path B-D is normally distributed, what is the probability that this path will be finished in 22 weeks or less? t = 18 variance (σ2)= 5 standard deviation (√5) = 2.24 P(x ≤ 22) = P[(22 – 18)/2.24] = 1.79 Using Appendix A: 1.79 = 0.96327 Kelly Devilbiss - Problem 13-28

  7. (f) Explain why the probability that the critical path will be finished in 22 weeks or less is not necessarily the probability that the project will be finished in 22 weeks or less. Path B-D has more variability and has a higher probability of exceeding 22 weeks. Kelly Devilbiss - Problem 13-28

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