Bearing Lot Acceptance with a Small Sample and an Outlier
A conveyor line uses 6205-2RS bearings. The supplier's catalog states an L10 life of 1,250 h under the line's radial load. Maintenance records from 16 randomly selected bearings from one production lot gave a sample mean of 1,180 h and a sample standard deviation of 90 h. The line loses $2,400 per hour when down, and replacement takes 4 h. Purchasing wants to reject the lot if the mean is below the catalog claim at α=0.05; the supplier argues the sample is small and 'the difference is only 70 hours.' Assume lives are approximately normal. Before the meeting, the reliability engineer must decide whether to recommend rejecting the lot, whether the result proves the supplier's claim is false, and what additional evidence would be needed before switching suppliers. A single bearing in the sample failed at 940 h, but no cause was recorded.
1. State H0 and H1, compute the one-sided t statistic and critical value at α=0.05, and decide whether to reject the lot.
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H0: μ≥1250 h; H1: μ<1250 h. Standard error =90/√16=22.5 h. t=(1180−1250)/22.5=−3.11 with df=15. The one-sided critical value at α=0.05 is −1.753. Since −3.11<−1.753, reject H0. The 95% two-sided confidence interval is 1180±2.131(22.5)=[1132, 1228] h; the entire interval is below 1250 h, consistent with the test. Report the p-value (~0.0036) and the assumptions: random sample, approximately normal lives, and no measurement bias.
2. The supplier says the 70 h difference is small. Explain how you would separate statistical significance from practical/engineering significance, including the downtime cost information.
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Statistical significance means the observed shortfall is unlikely under H0; engineering significance means the shortfall is large enough to justify action. A 70 h shortfall is about 5.6% of 1250 h. Translate that into downtime: one failure costs about $2,400/h × 4 h = $9,600 plus lost production. Over a fleet, even a modest mean shift changes expected failures and spare-parts demand. However, the sample is one lot, and the catalog value may assume different load, alignment, or lubrication. The decision should combine the confidence interval, cost of failures, and lot-to-lot variability, not rely on the t-test alone.
3. What should you do about the 940 h bearing and what sample-size or sampling concerns would you raise before switching suppliers?
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Treat the 940 h bearing as a low outlier, not an automatic deletion. Check its load zone, alignment, lubrication, mounting, and failure mode. If an assignable cause is found, analyze with and without it and report both results. Before switching suppliers, sample multiple lots, randomize bearing positions on the line, and perform a power/sample-size calculation. With n=16 the test has limited power for small differences. A larger sample, or a tolerance-interval approach for the fraction failing, would give stronger evidence than a single-lot hypothesis test.