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1. Brief Discussion The Weibull Distribution is used to assess product reliability and model failure times. We can determine if the number of failures is increasing with time, decreasing with time, or remaining constant. The following equations are used to compute for the Weibull Distribution of a product: Density Function xa-le Ba where x > 0, a > 0,3 > 0 f(x) = ga * P(X 0) = \f(x) dx = e-(0) Cumulative Distribution Function (CDF) 1- Mean 1 u = E(X) = B. (1 1+ = Variance o+=ven3 =$*{r(1+2) [r(1+2))} g? = V(X) = B2 Alpha (a) Properties Also known as Shape Parameter, Weibull Scope, or Threshold Parameter. Beta () Properties Also known as Scale Parameter or Characteristic Life Paramter. If a1, failure rate increases with time. If a=1, failure rate is constant. Here is an example of the Probability Density with respect to time (x): 0.025 0.020 08 0.015 38 Probability Density Figure 1: Taken from http://www.engineeredsoftware.comasa/weibull.htm 0.010 D1 0.005 0.000 0 200 100 Based on Figure 1, failure rates can increase or decrease with respect to time and depending on the alpha and beta properties of the product. 2. Task Write the C++ program that will replicate the Weibull Distribution below. Weibull Distribution = 10, p = 0.5