Fifty automobiles using a new type of motor oil were monitored over a period of several months to determine when the oil needed replacing due to the level of contaminants. These times were recorded in...

Fifty automobiles using a new type of motor oil were monitored over a period of several months to determine when the oil needed replacing due to the level of contaminants. These times were recorded in tens of miles. Several units were censored from the study as a result of vehicle losses. Motor-oil failures are believed to follow a gamma distribution. Derive the maximum likelihood estimates and determine a replacement interval in miles based upon a 95-percent design life. Compare this to the mean time to failure.