Question

each day, a fedex competitor processes approximately 65,000 shipments. suppose that they use the same service quality index as fedex and identified the following number of errors during a 5-day week (see the \fedex: measuring service performance\ box). these values are hypothetical and do not reflect any real company’s actual performance.

description | weight | number of errors
--- | --- | ---
complaints reopened | 3 | 145
damaged packages | 10 | 20
international | 1 | 103
invoice adjustments | 1 | 286
late pickup stops | 3 | 204
lost packages | 10 | 1
missed proof of delivery | 1 | 26
right date late | 1 | 747
traces | 3 | 110
wrong day late | 5 | 20

compute the service quality indicator by finding the weighted sum of errors as a percentage of total shipments. do not round intermediate calculations. round your answer to three decimal places.

service quality indicator (sqi): %

hint check my work

Explanation:

Step1: Calculate weighted errors for each item

• Complaints reopened: \( 3 \times 145 = 435 \)
• Damaged packages: \( 10 \times 20 = 200 \)
• International: \( 1 \times 103 = 103 \)
• Invoice adjustments: \( 1 \times 286 = 286 \)
• Late pickup stops: \( 3 \times 204 = 612 \)
• Lost packages: \( 10 \times 1 = 10 \)
• Missed proof of delivery: \( 1 \times 26 = 26 \)
• Right date late: \( 1 \times 747 = 747 \)
• Traces: \( 3 \times 110 = 330 \)
• Wrong day late: \( 5 \times 20 = 100 \)

Step2: Sum all weighted errors

Total weighted errors \( = 435 + 200 + 103 + 286 + 612 + 10 + 26 + 747 + 330 + 100 \)
\( = 435+200=635; 635+103=738; 738+286=1024; 1024+612=1636; 1636+10=1646; 1646+26=1672; 1672+747=2419; 2419+330=2749; 2749+100=2849 \)

Step3: Calculate total shipments in 5 days

Daily shipments: \( 65,000 \), so 5 - day total: \( 65000 \times 5 = 325000 \)

Step4: Compute SQI (weighted sum / total shipments * 100)

\( SQI = \frac{2849}{325000} \times 100 \)
\( = \frac{284900}{325000} \approx 0.876615 \)
Rounded to three decimal places: \( 0.877 \)

Answer:

\( 0.877 \)