What are the characteristics of the exponential distribution?
In reliability engineering the exponential distribution has been found to adequately model the failure rate of electronics during their useful life [1]. The probability density function (PDF) for the exponential distribution is shown in Figure 1 and is given below by Equation 1. For any time period of interest, t, the area under the PDF curve from t to infinity is equal to the reliability, R(t). The area under the PDF curve to the left of t is equal to the probability of failure (1-R(t)). f(t)=le-lt [ 1 ] The cumulative distribution function (area under PDF curve) is obtained by integrating the PDF as shown in Figure 2 and given by Equation 2. [ 2 ] Figure 1 – Probability Density Function (Exponential Distribution) Figure 2 – Cumulative Distribution Function The reliability function (probability that a device will not fail), is given by Equation 3. R(t)=1-F(t)== e-lt [ 3 ] Figure 3 – Reliability Function (Exponential Distribution) The hazard function is given by Equation 4. For the exp
