A certain manufacturing process requires a continuous supply of water. The water comes from a tank and is maintained at a constant level with a pump. Should the pump stop, an alarm sounds, and the tank has enough water to last 2.5 hours. If the tank runs dry the process must be stopped, and the cost is $8,000 per hour. Suppose the most common failure mode of the pump is a seized bearing. A bearing has a MTBF of 3 years and requires 4 hours to replace. It is possible to anticipate when a bearing is about to fail by checking the sound of the pump once a week. Such a bearing can be replaced during a shift when the process is not running. It takes 20 minutes for a $30-an-hour inspector to perform the sound check. The process runs 50 weeks a year. a. Is it cost effective to perform the weekly sound check? b. A common way to avoid system failure is with standby equipment. Suppose a standby pump is to be installed for use when the first pump fails. Is the standby pump a good idea if the annual capital and operating cost of the pump is $800?

Nicholas, John. Lean Production for Competitive Advantage: A Comprehensive Guide to Lean Methodologies and Management Practices (p. 199). CRC Press. Kindle Edition.