Currently, a manufacturing company experiences an average of 0.75 equipment-related shutdowns per shift and the downtimes are exponentially distributed. In testing, a new maintenance program reduced the frequency of equipment-related shutdowns to an average of 0.20 per shift, exponentially distributed.

The new maintenance program is expensive, but the company will install it if it can help achieve the target of four consecutive shifts without an equipment-related shutdown.

a. Under the current system, what is the probability that the plant would run four or more consecutive shifts without an equipment-related shutdown?

b. Using the computer decision model, what is the probability that the plant could run four or more consecutive shifts without an equipment-related shutdown? Has the decision model helped the company achieve its goal?

c. What would be the maximum average number of shutdowns allowed per day such that the probability of experiencing four or more consecutive shifts without an equipment-related shutdown is greater than or equal to 0.70?