Question

(Chapter 6) A team in an accounting group has been working on improving the processing of invoices. The team is trying to reduce the cost of processing invoices by decreasing the fraction of invoices with errors. The team developed the following operational definition for a defective invoice: an invoice is defective if it has incorrect price, incorrect quantity, incorrect coding, incorrect address, or incorrect name. The team decided to pull a random sample of 100 invoices per day. If the invoice had one or more errors it was defective. The data from the last 6 days are given in the table. Develop the control limits for the p-chart and draw the p-chart as well. 4. Number Fraction Defective Day Invoices Inspected (n) Defective (np) (p) 100 100 100 100 100 100 24 20 18 24 0.22 0.33 0.24 0.20 0.18 0.24 4 6

Answer 1

Sample	n.p	p = n.p / 100
1	22	0.2200
2	33	0.3300
3	24	0.2400
4	20	0.2000
5	18	0.1800
6	24	0.2400
Average		0.2350

The average proportion defective (p_bar) = 0.235

Std. Error (S_p) = (p_bar * (1 - p_bar) / n)^1/2 = sqrt(0.235*(1 - 0.235)/100) = 0.0424

UCL_p = p_bar + 3 * S_p = 0.235 + 3 * 0.0424 = 0.3622
LCL_p = Max(0, p_bar - 3 * S_p)= Max(0, 0.235 - 3 * 0.0424) = 0.1078

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