* "/> * " />
1967-02-01

On the Distribution and Prediction of Excess Time * 670630

This paper considers a system whose components, upon failure, are repaired or replaced. Only two system states, the “operating” state and the “failed” state are distinguished. The time to failure and the time to repair of the system are assumed to be random variables with general distribution functions. A criterion of system worth is the random variable “excess time,” denoted by B(t), and defined as the total time the system is down for t units of time spent in the operating state. The following questions are answered in this paper: (a) What is the distribution function of B(t)? (b) What are the moments of B(t)? (c) What is the asymptotic behavior of B(t) for large t? (d) How can one make approximate probability statements about B(t)? It is shown that the gamma distribution is a suitable approximation for the conditional distribution of B(t), given that at least one failure has occurred, and that for t greater than 20 mean failure times the distribution of B(t) is practically normal.

SAE MOBILUS

Subscribers can view annotate, and download all of SAE's content. Learn More »

Access SAE MOBILUS »

Members save up to 18% off list price.
Login to see discount.
Special Offer: Download multiple Technical Papers each year? TechSelect is a cost-effective subscription option to select and download 12-100 full-text Technical Papers per year. Find more information here.
X