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.
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.
To replace oil for a machine with 130-gallon oil sump (bigger machines can have oil sumps up to 500 gallons) costs 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:
The Weibull 2-Parameter distribution values are:
Brand A: Weibull (Beta 6.644, Eta 343.8)
Brand B: Weibull (Beta 7.943, Eta 392.2)
You can compare the Eta lifes using contour plots to check if they are significantly different.
Since the contours plots do not overlap along Eta axis, we can say that the 2 brands are significantly different with 75% confidence.
Let’s query the Mean Oil-Life-Before-Drain with the built-in calculator…
The Mean life (Mean Oil-Life-Before-Drain) with 90% confidence:
Brand A: between 299.7 to 343.1 hours.
Brand B: between 344 to 395.9 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 369.2 hours respectively. Hence, the oil running cost per hour for Brand A is $3.12 and Brand B is $2.71 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 – 2.71) = $ 1,230 per machine (per year).
Expected number of oil change per year are 3,000/320.7 (or 9.35 times) and 3,000/369.2 (8.12 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.
Comments and Conclusions
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 75% confidence.
Can we use t-test instead? Here are the issues with t-test:
- T-test assume the two groups have an approximately normal distribution. Most Life Data does not follow normal distribution, and I would just say that this requires engineering judgement to make such assumption.
- Homogeneity of variances (the 2 samples have the same variance). We are not sure in this case.
- Conventional t-test does not handle the censored data, as in this case.
Life Data Analysis approach provides an elegant solution for this type of problem. The results are very visual, intuitive and convincing.
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