BooksCDs.com sells books, videos, DVDs, and CDs through its Internet Website. Th

Question

BooksCDs.com sells books, videos, DVDs, and CDs through its Internet Website. The company ships thousands of orders each day from seven national distribution centers. BooksCDs.com wants to establish a p-chart to monitor the quality of its distribution process, specifically the number of "problem" orders. A problem order is one that is delivered to a customer late (i.e., after five days), incorrect or incomplete. The company sampled 500 orders every other day for 20 samples and tracked them to final customer delivery, the results of which are as follows:

Sample (First Number 1-20) Number of Problem Orders (Second Number 14,22,36,17, etc.)

1, 14 11, 38

2, 22 12, 24

3, 36 13, 15

4 ,17 14, 12

5, 25 15, 10

6, 41 16, 16

7, 18 17, 9

8, 19 18, 21

9, 26 19, 18

10, 28 20, 12

Construct a p-chart with 3 limits for invoice errors and indicate if the process was out of control at any time. Round your answer to 3 decimal places.

1. What is the average percent of problem orders?

2. What is the 3 upper control limit?

Explanation / Answer

Total number of problem orders = Sum of problem orders of 20 samples = 421

Sample size = n = 500

Number of samples = 20

Therefore, proportion problem orders = pbar = 421 / ( 20 x 500 ) = 0.0421

Average percent of problem orders = 0.0421 x 100 =4.21 %

AVERAGE PERCENT OF PROBLEM ORDERS = 4.21%

Therefore,

Control limits of a 3sigma p chart :

Upper Control Limit = UCL = Pbar + 3x Square root ( pbar x ( 1- pbar) / n)

                                                 = 0.0421 + 3 x Square root ( 0.0421 x 0.9579/500)

                                                  = 0.0421 + 3 x 0.00898

                                                   = 0.0421 + 0.0269

                                                    = 0.069

Center line = Pbar =     0.0421

Lower Control Limit = LCL

= Pbar – 3 x Square root ( pbar x ( 1 – pbar/n)

= 0.0421 – 3 x Square root ( 0.0421 x 0.9579/500)

= 0.0421 – 3 x 0.00898

= 0.0421 – 0.0269

= 0.0152

3 SIGMA UPPER CONTROL LIMIT = 0.0152

AVERAGE PERCENT OF PROBLEM ORDERS = 4.21%

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.