What is the nature of the effects of the factors studied in this experiment?

MAT 510 – Homework Assignment

 

 

 

The experiment data in below table was to evaluate the effects of three variables on invoice errors for a company. Invoice errors had been a major contributor to lengthening the time that customers took to pay their invoices and increasing the accounts receivables for a major chemical company. It was conjectured that the errors might be due to the size of the customer (larger customers have more complex orders), the customer location (foreign orders are more complicated), and the type of product. A subset of the data is summarized in the following Table.

 

Table: Invoice Experiment Error

Customer Size	Customer Location	Product Type	Number of Errors
–	–	–	15
+	–	–	18
–	+	–	6
+	+	–	2
–	–	+	19
+	–	+	23
–	+	+	16
+	+	+	21

Customer Size: Small (-), Large (+)

Customer Location: Foreign (-), Domestic (+)

Product Type: Commodity (-), Specialty (=)

 

Reference: Moen, Nolan, and Provost (R. D. Moen, T. W. Nolan and L. P. Provost. Improving Quality through Planned Experimentation. New York: McGraw-Hill, 1991)

 

Use the date in table above and answer the following questions in the space provided below:

1. What is the nature of the effects of the factors studied in this experiment?

 

 

 

 

Regression Model

Y=30 + 1×1 – 3.75×2 +4.75 x3 – 0.75x1x2 + 1.25 x1x3 + 2.5x2x3 + 1x1x2x3

 

Customer size has small effect on invoice errors. Product types has the biggest effect on invoice errors. Large, specialty invoices creates the largest invoice errors.

 

2. What strategy would you use to reduce invoice errors, given the results of this experiment?

To reduce invoice errors, orders will be divided into different batches based on the level of product type specialty and size of customer. Invoices based on specialty and then by location followed by location should help reduce invoices errors. This may increase paper work but it will help reduce the error by itemizing based on product type instead of customers alone.

 

 

b0 =30

b1=1

b2=-3.75

b3=4.75

b4=-0.75

b5 =1.25

b6=2.5

b7=1

Regression Coefficients

RunCustomer Size (x1)Customer Location (x2)Product Type (x3)x1 x2x1x3x2x3x1x2x3No. of ErrorsAverage RR

1Small (-)Foreign (-)Commodity (-)+++-1515

2Large (+)Foreign (-)Commodity (-)–++1818

3Small (-)Domestic (+)Commodity (-)-+-+66

4Large (+)Domestic (+)Commodity (-)+—22

5Small (-)Foreign (-) Specialty (+)+–+1919

6Large (+)Foreign (-)Specialty (+)-+–2323

7Small (-)Domestic (+)Specialty (+)–+-1616

8Large (+)Domestic (+)Specialty (+)++++2121

Customer Size (x1)

Customer Location (x2)

Product Type (x3)

x1 x2

x1x3

x2x3

x1x2x3

sum+

64

45

79

57

65

70

64

sum-

56

75

41

63

55

50

56

ave +

16

11.25

19.75

14.25

16.25

17.5

16

ave-

14

18.75

10.25

15.75

13.75

12.5

14

effect

2

-7.5

9.5

-1.5

2.5

5

2

Foreign (-)Domestic (+)Foreign (-)Domestic (+)

Small (-)156Small (-)1916

Large (+)182Large (+)2321

Mild InteractionNo interaction

Antagonistic interaction

Smaller effect

SPECIALTY (+)COMMODITY (-)

02468101214161820Small (-)Large (+)response rate

DomesticForeign

0510152025Small (-)Large (+)response rate

DomesticForeign

Commodity (-)Specialty (+)Commodity (-)Specialty (+)

Small (-)1519Small (-)616

Large (+)1823Large (+)221

No interactionMild interaction

Antagonistic interaction

Smaller effect

FOREIGN (-)DOMESTIC (+)

0510152025Small (-)Large (+)response rate

SpecialtyCommodity

0510152025Small (-)Large (+)response rate

CommoditySpecialty

Commodity (-)Specialty (+)Commodity (-)Specialty (+)

Foreign (-)1519Foreign (-)1823

Domestic (+)616Domestic (+)221

Mild interactionMild Interaction

Antagonisic interactionAnatagonistic interaction

Smaller effectSmaller effect

LARGE (+)SMALL (-)

02468101214161820Foreign (-)Domestic (+)response rate

CommoditySpecialty

0510152025Foreign (-)Domestic (+)response rate

CommditySpecialty