The reliability of a piece of equipment is frequently defined to be the probability,p, that the equipment performs its intended function successfully for a given period of time under specific conditions (Render and Heizer, Principles of Operations Management, 1995).

Because p varies from one point in time to another.

some reliability analysts treat p as if it were a random variable. Suppose an analyst characterizes the uncertainty about the reliability of a particular robotic device used in an automobile assembly line using the following distribution:

1 05P'l f(p) = { 0 otherwise

a. Graph the analyst's probability distribution forp.

b. Find the mean and variance of p.

c. According to the analyst's probability distribution for p, what is the probability that p is greater than

.95? Less than .95?

d. Suppose the analyst receives the additional information that p is definitely between .90 and .95, but that there is complete uncertainty about where it lies bctween these values. Describe the probability distnbution the analyst should now use to describep.