Question

1. A tool wears at the rate of .004 centimeters per piece, i.e., the metal shaft will increase by .004 centimeters per piece. The process sigma = .02 centimeters. Specifications are set at 15.0 to 15.2 centimeters. A three-sigma cushion is set. Determine the number of shafts that can be processed before tool replacement becomes necessary. Round all values to a maximum of three decimals.
   1. The process mean starts at three-sigma above the lower specification limit.

(Determine this)

2. The process mean ends when it is three-sigma below the upper specification limit: (Determine this)
3. Determine the number of shafts that can be processed before tool replacement becomes necessary

Answer 1

It has been given that

A tool wears at the rate of .004 centimeters per piece,

The process Sigma is .02 centimeters

Lower Specification limit (L.S.L)=15

Upper Specification Limit(U.S.L)=15.2

Also given that A three-sigma cushion is set

So three Sigma will be

a)

The process mean starts at three-sigma above the lower specification limit

So Initial(Start) process mean=

b)

The process mean ends when it is three-sigma below the upper specification limit:

So End Process Mean=

c)

We have to determine the  number of shafts that can be processed before tool replacement becomes necessary

Number of Shafts=(End Mean-Starting mean)/Wear rate=

20 shafts can be processed before tool replacement becomes necessary