$...$ i$$in bir $$rnek g$$sManagers are also concerned with the availability of their products. Some products such as expensive medical equipment, telecommunications equipment, internet sales channels are typically used continuously and need to be operational all the time. The users of such products lose significant revenues or suffer from loss of customer satisfaction if their equipment is not available for service. Thus, managers try to ensure high availability in such products$$ designs.

A commonly used definition of availability is the percentage or fraction of time that a device is usable over an operational cycle.

The example below illustrates the uses of the concept of availability.

A part of a machine that is used in production has an expected usable lifetime of six months, after which it needs to be replaced. The replacements are obtained from a warehouse located away from the factory. If the part fails and needs to be replaced, it takes on average two days for this spare part to arrive and another day for the machine to be repaired. $($Assume for computational convenience that a month is $30$ days and a year is $360$ days.$)$

$1.$ Suppose that the management desires to use the machine $24/7$ during the year. What is the availability of the machine?

$2.$ What happens to the availability if spare parts are kept at the factory for such repairs?

$3.$ If the management estimates that not being able to use the machine for production costs $$10,000$ per day, how much would the firm benefit per year from keeping spare parts on site?

$4.$ What may be a reason for not keeping such spare parts at the factory?