Problem # 1 During one month, an accounting firm processed 51,000 invoices for A

Question

Problem # 1

During one month, an accounting firm processed 51,000 invoices for Alpha Corp, 49,000 for Beta Corp, and 25,000 for Gamma Corp. Of these, 510 of the Alpha, 525 of the Beta, and 480 of the Gamma invoices had to be reprocessed for errors.

a. What is the overall defect rate and the sigma level for each individual batch?

b. For all the batches combined?

Problem # 2

Alpha  Microprocessor Corporation sells 2,000 specialized microprocessor chips each month at a price of $1,500 each. Variable costs amount to $1,500,000, and fixed costs are $500,000. Currently the company has a defect rate of 8 percent (which are chips returned by customers, scrapped by VMC, and replaced). Note that the variable costs include the cost of producing the defective chips.

a. What is the hidden cost to the company of making this rate of defectives instead of 2,000 good chips each month?

b. Suppose a Six Sigma effort can reduce the defects to a six-sigma level (assume for simplicity that the defective rate is essentially zero). What is the impact on profitability?

Explanation / Answer

1. a ) Alpha corps defect rate = 510/51000 = 0.01; NORM.S.INV (0.99) + 1.5 = 3.826 sigma

   Beta corps defect rate = 525/49000 = 0.011;NORM.S.INV (0.989) + 1.5 = 3.79 sigma

Gamma corps defect rate = 480/25000= 0.019; NORM.S.INV (0.981) + 1.5 = 3.574 sigma

b) Combined defect rate = (510+525+480)/(51000+49000+25000) = 0.012; NORM.S.INV (0.988) + 1.5 = 3.757 sigma

2. a. No. of defective pieces = 160

Cost of making these defective pieces = (total costs x 160) /2000 = ((1500000+500000)x 160) /2000 = 160000$.

b. Profit = $160000+ Earlier proft

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