Statistics for Maintenance Modelling: Continuous Lifetime Distributions 2

# The Normal Distribution¤

The normal distribution plays a central role in statistics partly because of the central limit theorem which says that the distribution of any reasonably well behaved function of a sample mean tends to the normal distribution as the sample size increases to infinity. So it is perhaps not surprising that one of the most common distributions used for lifetime modelling is the normal distribution (sometimes referred to as the Gaussian distribution, particularly in engineering settings).

The probability density function of the normal distribution is
f(t) = . The mean is and the standard deviation is . Hence just alters the position and not the shape of the curve. The effects of changing can be seen in these graphs of f(t), but you can click on them for an interactive version in Excel where you can experiment with different values of and yourself.