Defective Rate For Process Essay Discussion Paper

Consider a simple three-step manufacturing process as illustrated in the given figure. Assuming that demand is 1,000 units, what is the required input to meet demand? You’ll note that the required input is the same if the scrap rates are reversed for processes 1 and 3 . Assume that the scrap cost is $$5$ at process $1,$10$ at process 2 , and $$15$ at process 3 . The defective rates are $3%,5%$, and $7%$, respectively. Compute the total scrap cost for the given system and the system where the scrap rates are reversed. Which system would be preferred? Defective Rate For Process Essay Discussion Paper

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**Answer :**

As defective rate is given, the output from each process is given as the product of input units and (1-Defective Rate). In other words output from a process = Input*(1-Defective Rate)

Let Input to Process 1 be I1 and output from Process 1 be O1 As defective rate of process 1 is 3%. O1 = I1*(1-3%)=97%*I1

Now input of process 2 is the output of process 1 or O1. As defective rate for Process 2 is 5%, using similar notation as above

O2 = 97%I1(1-5%) = 95%*97%*I1

Input of process 3 is the output of process 2 or O2. As defective rate for Process 2 is 7%, using similar notation as above

O3 = 95%97%*I1(1-7%) = 93%*95%*97%*I1

Now it is given that the demand is 1000 so O3 should be equal to 1000. Using the above equation we get

1000 = 93%*95%*97%*I1 =0.857*I1

Hence, I1 = 1000/0.857 = 1166.86 \\small \\approx 1167 units

Hence the required inputs should be 1167 units to meet a demand of 1000 units

To compute the scrap rate, we will take an input of 1167 units and compute the scrap units and scrap cost at each process. In the first case where defective rates are 3%, 5% and 7% respectively. (Note that output units and defective units are rounded below)Defective Rate For Process Essay Discussion Paper

Output of process 1 = 1167*(1-3%) = 1132 and defective units = 1167*3% = 35. Hence scrap cost = 35*5 = 175

Output of process 1 = 1132*(1-5%) = 1076 and defective units = 1132*5% = 56. Hence scrap cost = 56*10 = 560

Output of process 1 = 1076*(1-7%) = 1000 and defective units = 1076*7% = 76. Hence scrap cost = 76*15 = 1140

Hence total scrap cost = 175+560+1140 = $1875

In case scrap rates are reversed, we have the below

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Output of process 1 = 1167*(1-7%) = 1085 and defective units = 1167*7% = 82. Hence scrap cost = 82*5 = 410

Output of process 1 = 1085*(1-5%) = 1030 and defective units = 1085*5% = 55. Hence scrap cost = 55*10 = 550

Output of process 1 = 1030*(1-3%) = 1000 and defective units = 1030*3% = 30. Hence scrap cost = 30*15 = 300

Hence total scrap cost = 410+550+300= $1410

I would prefer the second system where the scrap rates are reversed as we can see that the scrap cost in this system is less than the scrap cost in first system. Defective Rate For Process Essay Discussion Paper