Case Study $1$: Roller bearing failure

The following set of eleven $(11)$ data represent the life span $($successive time to failure in hours,

and represented in the sequential order of the successive bearing replacement$)$ of a roller bearing

as used in an industrial lubricating oil pump.

$600012500120501315013400119001280013000116501325012300$

Whenever the bearing has failed, the average repair time is $8$ hours $(1$ day work$).$ Since the cost of a

bearing is Rs $25,000,$ the production manager of the company has to approve and sign the purchase

order form in order to buy a new bearing. It should also be noted that the bearing is available in only

one specialized shop in Port$-$Louis but the shop does not hold any stock for such a bearing. Thus,

upon receiving a purchase order, the shop will import the bearing, and the time interval between

placing the order at the shop, and subsequently receiving the bearing at the company is seven $(7)$

working days. Furthermore, the failure of the bearing does not lead to failure of any other component,

and does not lead to a hazardous condition. The current maintenance strategy for this roller bearing

is to run to failure.

Using appropriate calculations, perform relevant analysis, and advise the maintenance manager

about the appropriateness of the current maintenance strategy together with any recommendation$($s$).$