Comparing reliability performance of lubricating oil from different manufacturers

A mining company has a policy to replace the lubricating oil of its fleet of machines when the oil TAN (Total Acid Number) value reaches a critical level. Recently, the engineer tested 2 brands on their machines.


Followings are the Oil-Life-Before-Drain, in hours (Time-To-Failure) collected by the engineer.

Figure 1, Time-to-Failure (TTF) datasets for Brand A and B

The TTF is obtained through monitor the degradation of TAN content at a regular operating time interval, and the oil level is topped-up (with new oil) after the measurement if necessary.

When there is an engine failure, or the lubricating oil is found to have high water content, the oil will be completely drained. These data points are treated as suspension.

The company is currently using Brand A, and brand B is the oil supplied by the competitor.

A machine with 130-gallon oil sump (bigger machines can have oil sumps up to 500 gallons) cost more than US$ 1,000. The Brand B manufacturer provided enough lubricating oil for 13 machines.

The engineer wished to know if there is any statistical justification to switch to Brand B.

The dataset is fitted to a 2-Parameter Weibull distribution with MLE setting:

Figure 2, Probability Weibull plots

The Weibull 2-Parameter distribution values are:

Brand A: Weibull (Beta 6.644, Eta 343.8)

Brand B: Weibull (Beta 5.249, Eta 396.7)

You can compare the Eta lifes using contour plots to check if they are significantly different.

Figure 3, Contour plots at 90% confidence level

Since the contours plots do not overlap along Eta axis, we can say that the 2 brands are significantly different with 90% confidence.

Let’s query the Mean Oil-Life-Before-Drain with the built-in calculator…

Figure 4, The Mean life (Mean Oil-Life-Before-Drain) with 90% confidence, 2-sided bound

The Mean life (Mean Oil-Life-Before-Drain) with 90% confidence:

Brand A: between 299.7 to 343.1 hours.

Brand B: between 329 to 405.4 hours.

Assume the cost of both brands is the same - $1,000 for each oil change.

The Mean Oil-Life-Before-Drain of Brand A and Brand B are 320.7 and 365.2 hours respectively. Hence, the oil running cost per hour for Brand A is $3.12 and Brand B is $2.74 per machine.

Further, assume that each machine accumulates 3,000 operating hours a year, the cost saving would have been 3,000 x (3.12 – 2.74) = $ 1,140 per machine (per year).

Expected number of oil change per year are 3,000/320.7 (or 9.35 times) and 3,000/365.2 (8.22 times) for Brand A and Brand B respectively. Potentially, a 12% reduction in labor cost associated with oil changing.

In the case of 24/7 operations, the saving is even more significant. There will also be a saving due to lower downtimes i.e., an increase in availability.

Form the above Life Data Analysis, Brand B has a significant cost benefit over Brand A, in terms of oil, labor and downtime costs.

Other comments

Note that the confidence bound calculated above is not a property of Brand A or B. It is a measurement of the uncertainty due to sampling size. The larger the dataset, the smaller the bound.

In this example, we have enough samples to demonstrate that the 2 populations are different with 90% confidence.