A production process consists of five sequential operations with defect rates of 2% ,4%, 3%, 2%, and 1%, respectively.A) How many units does the operations manager need to schedule for production,...

A production process consists of five sequential operations with defect rates of 2% ,4%, 3%, 2%, and 1%, respectively.

A) How many units does the operations manager need to schedule for production, if 500 units of defect free output is required to be delivered to the customer?

B) Find the yield loss for each operation.

C) Find the process yield.

Asked on by ctr175

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The production process has 5 sequential operations with defect rates of 2%, 4%, 3%, 2% and 1% respectively.

If we start with trying to produce x units, after the first process the number of defect free units are x*0.98. After the second process it reduces to x*0.98*0.96. This goes on and at the end of the production process we are left with x*0.98*0.96*0.97*0.98*0.99 = x*0.8854 defect free units. (0.8854 is obtained after rounding off till four decimal places)

To produce 500 defect free units, let the number of units that we have to start with be X

X*0.8854 = 500

=> X = 500/0.8854 = 564.7

The manager should schedule the production of 565 units to be able to achieve the required number of defect free units.

The yield loss at each step is equal to the corresponding defect rate.

The process yield as illustrated above is 88.54%.

ctr175's profile pic

ctr175 | Student, Undergraduate | (Level 1) Honors

Posted on

Just so I understand on the yield loss, I would do:

x(1-.02)=500

.98x=500

x=511

500/511=.98

Is that right?

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