3.9 The National Bread Company delivers multiple orders daily by truck from its

Question

3.9 The National Bread Company delivers multiple orders daily by truck from its regional distribution center to stores in the Wayman's Supermarket chain. One measure of its supply chain performance is the number of late deliveries. The company's goal is to make all deliveries within one day, so a delivery is late if it exceeds one day. The late deliveries for each of the past 20 days are as follows DAY LATE DELIVERIES DAY LATE DELIVERIES 16 12 12 3 10 4 19 15 16 12 10 12 8 18 9 20 20 10 Construct a c-chart for late deliveries with 3 control limits and indicate if the delivery process was out of control at any time

Explanation / Answer

Nmumber of days = 20

Sum of number of late deliveries = 7+16+14+8+19+12+10+14+8+7+6+12+15+10+17+16+14+12+18+20 = 255

C-bar = Sum of number of late deliveries/ Number of days = 255/20 = 12.75

Using a three sigma control limit,the value of Z = 3

UCL = C-bar + [Z(Sqrt of C-bar)]

= 12.75 + [3(Sqrt of 12.75)]

= 12.75 + (3X3.57)

= 12.75 + 10.71

= 23.46

LCL = C-bar - [Z(Sqrt of C-bar)]

= 12.75 - [3(Sqrt of 12.75)]

= 12.75 - (3X3.57)

= 12.75 - 10.71

= 2.04

The process is in control because the number of late deliveries lies between the upper control limit i.e 23.46 and the lower control limit i.e 2.04

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