Question

Problem 2 (50 points) (Quality-Yield-Costs) Consider a printer circuit board manufacturing process. After processing and electrical testing/inspection, good PCB's are sent to packaging and shipping, and defective parts are sent to a Rework station. After rework, good parts are sent back to Testing and packaging/shipping, while bad parts are sent to a Scrap station for disposal. Only 20% of the PCB's reworked can be recovered as good parts. (Assume no failures at this stage). The processing and Rework stations have a yield of 70% and 30%, respectively. The table below shows the stages and costs incurred at each stage. Stage Processing Testing/Inspection Packing/shipping Rework Scrap Costs per PCB unit $30 $15 $10 $20 $5 a) Draw the material flow process and assume total units =x. Also, list out the yield equations and material flows at every stage of the process including costs of the stage. (10 points) [Please label all parts of the process and add the equations on the arrows corresponding to the relevant stages). Make the diagram big so it is clear to grade. b) Assume x= 2500 PCB's what is the total yield or number of good PCB's? (10 points) c) What is the scrapped amount? Check material balance flows: Are inputs equal to outputs? (10 points) d) What is the cost per PCB yield. Provide response upto 2 decimals using a table (10 points). (Do note that reworked portions go back to testing first.) e) If a process improvement addressing internal failure improves the recovery rate of reworked parts from 20% to 30% i) what happens to yield? (10 points).

Answer 1

a) Material Flow Process

Yield is the number of acceptable units at the end of the process divided by the number of starting pieces excluding scrap and rework.

Here we use the Material Flow Process to evaluate each individual process.

As per the given question the total unit is considered as X

Let us assume X as 100

It was provided in the question that the yield of processing station = 70%

Whereas the yield of Rework station = 30%

However, good parts from rework station is only 20%

Moreover,the cost of various process are given

such as processing = $30, Testing =15, Shipping =10, Rework = 20 ,Scrap =5 are also provided

We can draw process map using this information

Process 1 process Processing ($30) process 2 Inspection/T esting ($15) process 3 Packing/Ship ping ($10) process 4 Rework ($20) Scrap ($5) Here we get 70 units out of 100 Predicted as 30 unit 10 units out of 30 in process 4 i.e.,20% in reworked as good)

Cost of each process is given in brackets

Yield equation

Yield = Process 1 +Process 4 - 10% or e-DPU       Here DPU Means defective Product Units

b) If X = 2500

In Process 1 good yield = 70%

i.e., 2500* 70/100 = 1750 units

Then in process 4, 30% yield 2500 * 30/100= 750

out of 750 , 20% are good units hence 750*20/100 = 150 good units

So total Good PCB Units = 1750+150= 1900 units

c) Scrapped amount = Rework - Good units

Rework yield = 350

Out of that good units 150

Scrap = 350- 150 =200

Scrap value = 200 * 5 = 100       

d) cost per PCB = Total unit/ Cost per unit

Cost per unit = $30+$15+$10+$20+$5 = $80

I.e., 2500/ 80 = 31.25

e) If recovery rate increased from 20 to 30 then yield will improve

from 1900 to 1975

i.e in process 4 30% yield of 2500 = 750 units

out of that 30% as good unit means 750*30/100 = 225

then total unit = 1750 + 225

= 1975