Reliability of a robotic device. 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 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 by means of the following distribution:

a. Graph the analyst’s probability distribution for p.

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 between these values. Describe the probability distribution the analyst should now use to describe p.

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f(p) (1 0 p 1 otherwise