Question

Three independent operations (1, 2, and 3) are performed sequentially in the manufacture of a product. The first-pass yields (proportion conforming) for each operation are given by p₁ = 0.90, p₂ = 0.95, and p₃ = 0.80, respectively, for operations 1, 2, and 3. The unit production costs for each operation are u₁ = $5, u₂ = $10, and u₃ = $15, respectively.

1. What is the unit cost per conforming (or good) product?
2. Suppose, through quality improvement effort, the first-pass yield for each operation is improved to the following levels: p₁ = 0.94, p₂ = 0.96, and p₃ = 0.88. Relative to part (a), determine how much improvement in percentage terms in (production) capacity has taken place.
3. Management is completing a 100% inspection process after either operation 1 or 2. Assume that the inspection process is completely reliable (i.e., all units are identified correctly – conforming or not). Unit inspection costs after operations 1 and 2 are $0.10 and $0.20, respectively. Nonconforming parts are not forwarded to subsequent operations. Find the unit cost per conforming product for each plan for the improved process.

The wording in part c is weird so I'm wondering what others' interpretation of it would be.

Answer 1

Solution

Part (a)

‘The first-pass yields (proportion conforming) for each operation are given by

p₁ = 0.90, p₂ = 0.95, and p₃ = 0.80, respectively, for operations 1, 2, and 3.’ =>

If we start with 100 units at operation 1, only 90 units are fit to move to operation 2

where (90 x 0.95) = 85.5 units only are fit to move to operation 3 where again

(85.5 x 0.80) = 68.4 units only are conforming ……………………………....................……………….(1)

The above interpretation along with the given data that, ‘unit production costs for each operation are u₁ = $5, u₂ = $10, and u₃ = $15, respectively.’ =>

Total cost of production = (100 x 5) + (90 x 10) + (85.5 x 15) = 2682.5

And the final yield is only 68.4 conforming units. Thus, the the unit cost per conforming

(or good) product = 2682.5/68.4 = $39.22 Answer 1

Part (b)

Vide (1), final output under the present values of p1, p2 and p3 is 68.4 .......................................... (2)

By following the same principles, final output under the improved values of

p1, p2 and p3 is: [{(100 x 0.94) x 0.96} x 0.88] = 79.4 .......................................................................(3)

(2) and (3) => under the improved values of p1, p2 and p3, final yield has increased by

11 units over 68.4. Hence, improvement in percentage terms in (production) capacity

= 100 x (11/68.4)

= 16.09% Answer 2

Part (c)

Plan 1: 100% inspection process after operation 1

Again starting with 100 units at operation 1, total cost of production and 100% inspection process = 100 x (5 + 0.10) = 510.

Cost of production of 94 units at operation 2 = 94 x 10 = 940

Cost of production of 90.24 units at operation 3 = 90.24 x 15 = 1353.6

So, total cost = 2803.60

Hence, the unit cost per conforming product for Plan 1 = 2803.6/79

= $35.49 Answer 3

Plan 2: 100% inspection process after operation 2

Again starting with 100 units at operation 1, cost of production = 100 x 5 = 500.

Total cost of production and 100% inspection process Cost of production of 94 units at operation 2 = 94 x (10 + 0.20) = 958.8

Cost of production of 90.24 units at operation 3 = 90.24 x 15 = 1353.6

So, total cost = 2812.40

Hence, the unit cost per conforming product for Plan 2 = 2812.4/79

= $35.60 Answer 4

DONE