Question 1. A company buys springs to use in an assembly. The specification requires the "rate", i.e. the force required to compress the spring by one centimetre, to be 44 Newtons ± 2.5 Newtons. A sample of one hundred springs was selected and the rate was measured using a standard testrig, with the results shown in the table below. 

(a) Does it seem that the "rates" are Normally distributed?

(b) If the distribution were Normal, what proportion of all springs would be expected to lie outside the specification?

(c) From the sample, does it seem that the population mean is on target?

(d) A pharmaceuticals company has an automatic line to fill phials with a drug preparation. They believe the accuracy of the filling process is affected by the speed of the production line. The table below shows the deviations from the target quantity of the preparation in each phial (in arbitrary units).  Does the data suggest that the accuracy is affected by the line speed?

Examine the residual values for the cells.  What useful information do they show?

Question 2:

A logistics company in Hong Kong has monitored the performance of their parcel-sorting machinery. The planned Availability (A_i) requires a maximum allowable Time to Repair (TTR) of one and a half hours. They have recorded the TTR when the machinery breaks down, and the results are summarised below:

(a) What distribution would seem most appropriate to model the TTR data?

(b) If your suggested model were valid what proportion of TTR values is likely to exceed the maximum allowable?

(c) Their calculation of A_i requires the Mean Time to Repair (MTTR).  Within what limits can the MTTR be quoted with 95% confidence?

The Singapore branch of the same firm uses a different version of the parcel-sorting machinery. A pilot study on the TTR for this machine gave the following results:

(d) Is the TTR in Singapore significantly better than in Hong Kong?