Question

Marlon Audio Company manufactures video tapes. The desired speed of its model SF2000 is 3 inches per second. Any deviation from this value distorts pitch and tempo, resulting in poor sound quality. The company sets the quality specification to 3 ± 0.26 inch per second because an average customer is likely to complain and return the tape if the speed is off by more than 0.26 inch per second. The cost per return is $37. The repair cost before the tape is shipped, however, is only $2 per tape.

Required:

1. Compute L(x) if x is 3.12 inches per second.

2. Estimate the tolerance for the firm to minimize its quality-related cost (loss).

(For all requirements, round your intermediate calculations to the nearest whole dollar amount. Round your answers to 4 decimal places.)

Answer 1

1.

Compute cost coefficient as follows:

k = Cost per return / (Tolerance allowed)^2

k = 37 / (0.26)^2

k = 37 / 0.0676

k = 547

Compute L(x) as follows:

where x = 3.12

L (x) = 547 * ( 3.12 - 3)^2

L (x) = 547 * 0.0144

L (x) = 7.8768

2.

Compute tolerance level as follows:

Total quality cost = tolerence^2 * k

2 = tolerence^2 * 547

tolerence^2 = 2 / 547

tolerence^2 = 0.00366

tolerence = 0.06046

Thus, tolerance range will be +/- 0.06046