A maintenance engineer recorded the cavitation damage index, DDD, for 8 industrial water pumps. To simplify calculations, he used the coding v=D−kmv = \frac{D - k}{m}v=mD−k, where kkk and mmm are positive constants. His results are summarized in the table below.
| DDD | 105 | 125 | 95 | 115 | 90 | 130 | 100 | 120 |
|---|---|---|---|---|---|---|---|---|
| vvv | 5.0 | 9.0 | 3.0 | 7.0 | 2.0 | 10.0 | 4.0 | 8.0 |
Find the value of kkk and the value of mmm.
The engineer also recorded the total operating time, hhh thousand hours, for each of these 8 pumps. The data is summarised as follows:
Shh=6.40Svv=60.00Shv=17.50 S_{hh} = 6.40 \quad S_{vv} = 60.00 \quad S_{hv} = 17.50 Shh=6.40Svv=60.00Shv=17.50Calculate the product moment correlation coefficient (PMCC) between hhh and vvv.
State, with a reason, the value of the PMCC between hhh and DDD.
The engineer identifies the total accumulated damage and total load cycles for two further pumps, XXX and YYY.
| Pump | Total Accumulated Damage | Total Load Cycles |
|---|---|---|
| XXX | 63000 | 500 |
| YYY | 40000 | 400 |
Assuming the damage index DDD represents damage per load cycle, suggest which pump is most likely to have the higher operating time. Justify your answer.
