An analysis of the lubricant in a pump is done once per
month. The presence of ferrous particles indicates a failure, and the damage done to the
machine increases with time as this condition exists. It is estimated that when ferrous
particles are present the damage being inflicted on the machinery is $1.29 per run hour.
If an oil analysis costs $40, given the failure data in the file "OIL.DAT", how
often should an oil analysis be done?
The software will display the results in a frame at the bottom of the screen. For this example, if the pump has run for 244.3 hours without failure, an oil analysis should be done. If the pump is still running without failure after 425.1 hours another oil analysis should be done. If the pump is still running after 583.4 hours without failure, a third oil analysis should be taken.
Note that the time between each successive inspection is decreasing. This is because the failure rate is increasing. A shape parameter greater than 1.0 (the shape parameter was 1.904 for this example) indicates "wear-out", which is characterized by an increasing failure rate. The longer this pump runs, the more likely it is to fail. If the shape parameter is equal to 1.0, the time between successive inspections will be equal. If the shape parameter is less than 1.0, the time between each successive inspection will increase; the longer the item runs the less likely it is to fail.
This methodology can also be used to determine the frequency for quality inspections. For example, in paper mills, steel mills, and aluminum mills, the product is wound into coils. The only way to inspect for a defect in the process is to unwrap a coil, which has an associated cost. The cost of a defect in the process is a linear function of time. For example, the cost of producing defective steel may be $8,000 per hour.