The article "Stochastic Modeling for Pavement Warranty Cost Estimation" (J. of Constr. Engr. and Mgmnt., 2009: 352-359) proposes the following model for the distribution of Y = time to pavement failure. Let X, be the time to fail- ure due to rutting, and X, be the time to failure due to trans- verse cracking; these two rvs are assumed independent. Then Y = min(X, X). The probability of failure due to either one of these distress modes is assumed to be an increasing function of time t. After making certain distribu- tional assumptions, the following form of the cdf for each mode is obtained: (a + b)/(c + dt + eru where is the standard normal cdf. Values of the five parameters

a, b,

c, d, and e are -25.49, 1.15, 4.45, -1.78, and .171 for cracking and -21.27, .0325, .972, -.00028, and .00022 for rutting. Determine the probabil- ity of pavement failure within 5 years and also t = 10 years.