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Military Logistics pp 43–71Cite as

The Proposal of Demand Estimation of Repairable Items for the Weapon Systems During the Initial Provisioning Period: F-16 Case Study

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Part of the book series: Operations Research/Computer Science Interfaces Series ((ORCS,volume 56))

Abstract

Every country that has military systems such as aircraft, radar, warship or tank has to meet the operational needs of those military systems in order to keep them ready for military operations . Logistics support needs are defined basically either before or after acquisition. If they are defined before acquisition, they are called “initial support requirement” , otherwise called “sustainment support requirement”. Our study is focused on the initial support requirement phase since the new weapon systems will be added into the Turkish military inventory . In addition to that, it is focused on repairable items since most of the material acquisition cost within the initial support budget is allocated to repairable items. The flight hour parameter is used for computing the initial support requirements of repairable items in the United States of Air Force (USAF) whereas the usage parameter is used in that of repairable items in Turkey. Based on these calculations, a new parameter called SORTIE, which is the one cycle of take-off and landing, is generated. Taking the consideration of flight hour, usage and SORTIE parameters, 24 scenarios (eight for each parameter) have been created by using real data set of F-16 with a quantity of 894 repairable items. Each scenario is named according to the usage of past data in years. The data set which covers the last 11 years (44 quarters) is divided into two parts: the first 8 years data is used for running the scenarios, and the last 3 years data is used for comparing the results of scenarios with the actual values. While evaluating the effectiveness of scenarios, parameters of mean absolute error and mean percentage error are used. In addition to the traditional approach that tries to find the best parameter common for all data, two new approaches are formed up. The first approach requires grouping the repairable items according to the supply group corresponding to the first two digits of NATO Stock Number (NSN). The other approach treats each NSN independent from each other. Each scenario is run under the three approaches including the traditional one and results are recorded. The Friedman and Wilcoxon Sign Test are applied for determining whether the results are significantly different from each other at the confidence level of 95 %. The approaches that decrease mean absolute error down to the level of 55 % can provide significant cost savings. On the other hand, repairable items whose mean absolute error and standard error values are higher than 3 and 5 respectively are recommended for future detailed studies.

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Notes

  1. 1.

    The term ‘DOTMPLF’, used in force planning procedures in NATO, stands for Doctrine, Organization, Training, Material, Personnel, Leadership and Facilities.

  2. 2.

    Failure rate is the frequency with which weapon system or components fail per unit time.

  3. 3.

    1 year = 4 quarters, 1 quarter = 3 months = 91 days.

  4. 4.

    TOIMDR algorithm, unlike the RDS does, takes the history date as back as possible. The maintenance factor data is calculated based on 8 year at most in this study.

  5. 5.

    OIM PROG at PFP: Abbreviation of “Organizational or Intermediate Maintenance Program at Program Forecast Period”. It shows the number of flying hours expected per month per A/C during the planning horizon. It is quarterly basis as in RDS.

  6. 6.

    OIM ANN DEM: Abbreviation of “Organizational or Intermediate Maintenance Annual Demand”.

  7. 7.

    APPL PCT: Abbreviation of “Application Percent”. It show the percentage of the particular item apply to the fleet of weapon systems.

  8. 8.

    QPEI: Acronym of “Quantity Per End Item”.

  9. 9.

    SORTIE is the one cycle of take-off and landing of an A/C. It can be short such as 10–30 min, or long such as 2 h or even much more. Sortie duration can changes according to the several constraints such as mission type, capacity of A/C etc.

  10. 10.

    FPS: Acronym of “Failures per sortie”.

  11. 11.

    The Friedman test is the nonparametric equivalent of a one-sample repeated measures design or a two-way analysis of variance with one observation per cell. Friedman tests the null hypothesis that k related variables come from the same population. For each case, the k variables are ranked from 1 to k. The test statistic is based on these ranks (IBM-SPSS Statistics Base 17.0 User Guide)

  12. 12.

    The Wilcoxon signed-rank test is a nonparametric statistical hypothesis test used when comparing two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e. it is a paired difference test). It can be used as an alternative to the paired Student's t-test, t-test for matched pairs, or the t-test for dependent samples when the population cannot be assumed to be normally distributed. (http://en.wikipedia.org/wiki/ Wilcoxon_signed-rank_test)

Abbreviations

A/C:

Aircraft

APPL PCT:

Application Percentage

DDR:

Daily Demand Rate

DOTMPLF:

Doctrine, Organization, Training, Material, Personnel, Leadership and Facilities

EF:

Expected Failures

FPS:

Failures per sortie

IBA:

Item Based Approach

METRIC:

Multi-Echelon Technique for Recoverable Item Control

NRTS:

Not Repairable at This Station

NSG:

NATO Supply Group

NSN:

NATO Stock Number

OIM ANN DEM:

OIM Annual Demand

OIM:

Organizational or Intermediate Maintenance

PFP:

Program Forecast Period

QPEI:

Quantity Per End Item

RDS:

Requirement Distribution System

RTS:

Repairable at This Station

TOIMDR:

Total Organizational or Intermediate Maintenance Demand Rate

TURAF:

Turkish Air Force

USAF:

United States of Air Force

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Author information

Authors and Affiliations

  1. Hv.K.K.ligi Karargahi Harekat Baskanligi, 06100, Bakanliklar-Ankara, Turkey

    Bahtiyar Eren

  2. Gazi Universitesi Endustri Muhendisligi Bolumu, Ankara, Turkey

    Serpil Erol

Authors
  1. Bahtiyar Eren
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  2. Serpil Erol
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Corresponding author

Correspondence to Bahtiyar Eren .

Editor information

Editors and Affiliations

  1. Dept. of Financial & Mgmt Engineering, University of the Aegean, Chios, Greece

    Vasileios Zeimpekis

  2. Department of Military Science, Hellenic Army Academy, Vari, Attiki, Greece

    George Kaimakamis

  3. Department of Military Science, Hellenic Army Academy, Vari, Attiki, Greece

    Nicholas J. Daras

Appendix

Appendix

 

1-Year forecast perioda

2-Year forecast period

3-Year forecast period

Nu.

Scenario nameb

Mean

Std. dev.

Scenario name

Mean

Std. dev.

Scenario name

Mean

Std. dev.

1

TOIMDR (1)

3.90

6.40

RDS (1)

7.45

13.29

RDS (1)

11.61

20.09

2

SORTIE (1)

3.90

6.40

TIOIMDR (1)

7.51

13.32

SORTIE (1)

11.99

20.54

3

RDS (1)

3.90

6.41

SORTIE (1)

7.52

13.33

RDS (2)

11.12

20.56

4

RDS (2)

3.89

6.57

RDS (2)

7.33

13.76

TIOIMDR (1)

12.02

20.59

5

SORTIE (2)

3.92

6.82

SORTIE (2)

7.39

14.05

SORTIE (2)

11.16

20.60

6

TIOIMDR (2)

3.98

7.09

TIOIMDR (2)

7.55

14.62

TIOIMDR (2)

11.27

20.94

7

RDS (3)

4.21

7.14

RDS (3)

8.06

15.25

RDS (3)

12.05

22.49

8

SORTIE (3)

4.22

7.49

SORTIE (3)

8.10

15.77

SORTIE (3)

12.04

22.65

9

RDS (8)

4.33

7.59

TIOIMDR (3)

8.29

16.35

TIOIMDR (3)

12.23

23.08

10

RDS (4)

4.38

7.59

RDS (4)

8.27

16.45

RDS (4)

12.42

24.26

11

RDS (6)

4.38

7.69

RDS (8)

8.32

16.51

SORTIE (4)

12.52

24.33

12

RDS (7)

4.34

7.72

RDS (6)

8.29

16.65

RDS (8)

12.23

24.36

13

TIOIMDR (3)

4.29

7.79

RDS (7)

8.23

16.72

RDS (6)

12.22

24.68

14

RDS (5)

4.41

7.86

SORTI (4)

8.44

16.89

TIOIMDR (4)

12.76

24.71

15

SORTIE (4)

4.41

7.93

RDS (5)

8.35

17.03

SORTIE (8)

12.50

24.80

16

SORTIE (6)

4.49

8.10

SORTIE (8)

8.61

17.14

RDS (7)

12.13

24.81

17

SORTIE (8)

4.46

8.11

SORTIE (6)

8.55

17.21

SORTIE (6)

12.52

24.88

18

SORTIE (7)

4.45

8.13

SORTIE (7)

8.49

17.26

SORTIE (7)

12.41

25.04

19

SORTIE (5)

4.51

8.17

TIOIMDR (4)

8.63

17.43

RDS (5)

12.47

25.16

20

TIOIMDR (4)

4.48

8.21

SORTIE (5)

8.53

17.48

SORTIE (5)

12.67

25.19

21

TIOIMDR (6)

4.58

8.44

TIOIMDR (6)

8.83

17.85

TIOIMDR (6)

12.82

25.40

22

TIOIMDR (5)

4.58

8.46

TIOIMDR (7)

8.81

17.93

TIOIMDR (8)

12.95

25.54

23

TIOIMDR (7)

4.56

8.49

TIOIMDR (8)

8.98

17.94

TIOIMDR (7)

12.80

25.58

24

TIOIMDR (8)

4.60

8.52

TIOIMDR (5)

8.77

18.00

TIOIMDR (5)

12.80

25.59

  1. aFreidman Test results for 1-Year Forecast Period χ2 (23)=35,1, p=0.005, for 2-Year Forecast Period χ2 (23)=164.8, p=0.000 and 3-Year Forecast Period χ2 (23) = 266.9, p=0.000
  2. bThe number in parenthesis shows the number of years past data are included for computing scenario projections

Approach-I (Significantly different scenarios based on Wilcoxon Sign Test)

Pairwise comparison

z-valuea

p-value

Pairwise comparison

z-value

p-value

Pairwise comparison

z-value

p-value

SORTIE (7)—TOIMDR (7)

− 3.590 (Positive rank)

0.000

SORTIE (6)—SORTIE (2)

− 2.837 (Negative rank)

0.005

TOIMDR (8)—RDS (3)

− 2.336 (Negative rank)

0.019

SORTIE (3)—TOIMDR (8)

− 3.531 (Positive rank)

0.000

SORTIE (7)—TOIMDR (6)

− 2.818 (Positive rank)

0.005

TOIMDR (7)—TOIMDR (3)

− 2.301 (Negative rank)

0.021

SORTIE (7)—TOIMDR (8)

− 4.945 (Positive rank)

0.000

TOIMDR (7)—TOIMDR (2)

− 2.733 (Negative rank)

0.006

TOIMDR (2)—RDS (8)

− 2.300 (Positive rank)

0.021

SORTIE (8)—TOIMDR (8)

− 4.097 (Positive rank)

0.000

SORTIE (2)—TOIMDR (8)

− 2.756 (Positive rank)

0.006

SORTIE 8—SORTIE (7)

− 2.285 (Negative rank)

0.022

TOIMDR (8)—TOIMDR (3)

− 3.517 (Negative rank)

0.000

SORTIE (3)—TOIMDR (7)

− 2.772 (Positive rank)

0.006

TOIMDR (2)—RDS (4)

− 2.259 (Positive rank)

0.024

SORTIE (3)—TOIMDR (4)

− 3.529 (Positive rank)

0.000

SORTIE (6)—TOIMDR (5)

− 2.699 (Positive rank)

0.007

SORTIE (5)—RDS (2)

− 2.220 (Negative rank)

0.026

SORTIE (3)—TOIMDR (5)

− 3.932 (Positive rank)

0.000

SORTIE (6)—TOIMDR (6)

− 2.718 (Positive rank)

0.007

TOIMDR (5)—TOIMDR (4)

− 2.205 (Negative rank)

0.027

TOIMDR (4)—TOIMDR (2)

− 3.375 (Negative rank)

0.001

SORTIE (4)—SORTIE (2)

− 2.662 (Negative rank)

0.008

SORTIE (2)—RDS (6)

− 2.203 (Positive rank)

0.028

TOIMDR (5)—TOIMDR (2)

− 3.267 (Negative rank)

0.001

SORTIE (2)—TOIMDR (7)

− 2.596 (Positive rank)

0.009

TOIMDR (8)—TOIMDR (6)

− 2.200 (Negative rank)

0.028

TOIMDR (5)—TOIMDR (3)

− 3.335 (Negative rank)

0.001

SORTIE (4)—SORTIE (3)

− 2.570 (Negative rank)

0.010

SORTIE 8—TOIMDR (3)

− 2.156 (Negative rank)

0.031

SORTIE (2)—TOIMDR (5)

− 3.315 (Positive rank)

0.001

SORTIE 8—SORTIE (3)

− 2.562 (Negative rank)

0.010

TOIMDR (8)—RDS (8)

− 2.137 (Negative rank)

0.033

TOIMDR (8)—TOIMDR (7)

− 3.200 (Negative rank)

0.001

SORTIE (6)—TOIMDR (2)

− 2.530 (Negative rank)

0.011

TOIMDR (2)—RDS (5)

− 2.105 (Positive Rank)

0.035

SORTIE (6)—TOIMDR (8)

− 3.032 (Positive Rank)

0.002

SORTIE 8—SORTIE (2)

− 2.550 (Negative rank)

0.011

SORTIE (4)—TOIMDR (8)

− 2.093 (Positive rank)

0.036

SORTIE (5)—SORTIE (2)

− 3.077 (Negative rank)

0.002

TOIMDR (6)—TOIMDR (3)

− 2.523 (Negative rank)

0.012

RDS (4)—RDS (2)

− 2.085 (Negative rank)

0.037

SORTIE (5)—SORTIE (3)

− 3.080 (Negative Rank)

0.002

SORTIE (2)—RDS (4)

− 2.476 (Positive rank)

0.013

SORTIE (2)—RDS (5)

− 2.080 (Positive rank)

0.037

TOIMDR (4)—TOIMDR (3)

− 3.163 (Negative rank)

0.002

SORTIE (7)—SORTIE (2)

− 2.469 (Negative rank)

0.014

SORTIE (7)—TOIMDR (2)

− 2.079 (Negative rank)

0.038

SORTIE (2)—TOIMDR (6)

− 3.041 (Positive Rank)

0.002

SORTIE (6)—SORTIE (3)

− 2.465 (Negative rank)

0.014

SORTI3—RDS (4)

− 2.063 (Positive rank)

0.039

TOIMDR (6)—TOIMDR (2)

− 2.990 (Negative rank)

0.003

SORTIE (4)—TOIMDR (5)

− 2.454 (Positive rank)

0.014

SORTIE (5)—TOIMDR (8)

− 2.066 (Positive rank)

0.039

TOIMDR (8)—TOIMDR (2)

− 2.997 (Negative rank)

0.003

SORTIE (5)—TOIMDR (3)

− 2.422 (Negative Rank)

0.015

SORTIE (6)—TOIMDR (7)

− 2.061 (Positive Rank)

0.039

SORTIE (4)—TOIMDR (2)

− 2.922 (Negative Rank)

0.003

TOIMDR (5)—RDS (2)

− 2.406 (Negative rank)

0.016

SORTIE 8—RDS(7)

− 2.054(Negative rank)

0.040

SORTIE (5)—TOIMDR (2)

− 2.984 (Negative rank)

0.003

SORTIE (2)—RDS (8)

− 2.420 (Positive Rank)

0.016

SORTIE (4)—TOIMDR (4)

− 2.031 (Positive rank)

0.042

SORTIE (2)—TOIMDR (4)

− 2.915 (Positive rank)

0.004

SORTIE 8—TOIMDR (2)

− 2.388 (Negative rank)

0.017

TOIMDR (8)—RDS (2)

− 2.002 (Negative rank)

0.045

SORTIE (3)—TOIMDR (6)

− 2.908 (Positive rank)

0.004

TOIMDR (8)—RDS (7)

− 2.374 (Negative Rank)

0.018

SORTIE (2)—RDS(7)

− 1.957 (Positive rank)

0.050

TOIMDR (8)—RDS (7)

− 2.374 (Negative rank)

0.018

TOIMDR (5)—SORTIE (5)

− 2.478 (Negative rank)

0.013

   
  1. a“Positive Rank” means the significant difference is based on the first scenario. “Negative Rank” means the significant difference is based on the second scenario

The Friedman Test Results based on NSG for 1-Year Forecast Period

NSG No.

NSG name

n

Mean

Std. dev.

Degrees of freedom

χ2

p-value

Recommended scenarios for decision makers (the first 5)a

10

Weapon

14

2.03

2.71

23

49.80

0.001

RDS (8), RDS (7), SORTIE (8), RDS (5), RDS (6)

12

Fire control equipment

46

5.83

8.66

23

36.25

0.04

RDS (1), SORTIE (1), RDS (2), SORTIE (2), TOIMDR (1)

15

A/C structural components

44

2.83

4.21

23

70.54

0.000

SORTIE (1), TOIMDR1, TOIMDR (2), SORTIE (2)

16

A/C comp.& accessories

124

5.11

8.38

23

31.40

0.113

RDS (1)

28

Engines, turbines, and components

58

9.23

9.25

23

57.61

0.000

SORTIE (3), RDS (3), TOIMDR (3), SORTIE (2), RDS (1)

29

Engines accessories

38

4.69

6.17

23

45.39

0.004

SORTIE (1), RDS (1), TOIMDR1, SORTIE (5), TOIMDR (5)

43

Pumps and compressors

5

2.80

4.21

23

9.44

0.994

RDS (1)

48

Valves

28

2.22

3.13

23

31.29

0.116

RDS (1)

49

Maintenance shop equip.

11

0.80

0.85

23

33.08

0.080

RDS (5), RDS (6), SORTI5, RDS (4)

58

Communication equipment

45

3.19

4.02

23

32.64

0.088

TOIMDR1, SORTIE (2), RDS (2), TOIMDR (2), RDS (1)

59

Electrical, electronic equipment

286

2.18

3.91

23

17.36

0.791

RDS (1)

61

Electric wire, and power a equipment

71

3.30

5.17

23

73.40

0.000

RDS (2), RDS (3), SORTIE (2), RDS (4), SORTIE (3), RDS (1)

62

Lighting fixtures, lamps

16

2.74

1.94

23

7.65

0.999

RDS (1)

63

Alarm, signal and security systems

5

1.37

0.30

23

15.99

0.856

RDS (1)

66

Instruments and lab. equipment

87

3.55

5.23

23

28.34

0.203

RDS (1)

70

Automatic data processing

8

3.00

1.96

23

13.37

0.944

RDS (1)

 

Total

886b

      
  1. aThe scenarios written in bold are primarily recommended for use. The scenario RDS (1) is recommended for the NSGs that are not resulted in significantly different at the α = 5 % in the end of Friedman and Wilcoxon Sign Test
  2. b8 repairable items that belong to the five different NSGs are not included in this table due to the insufficient number of observations

The Friedman Test results based on NSG for 2-Year Forecast Period

NSG No.

NSG name

n

Mean

Std. dev.

Degrees of freedom

χ2

p-value

Recommended scenarios for decision makers (the first 5)

10

Weapon

14

3.28

3.24

23

33.7

0.070

SORTIE (8), TOIMDR (8), SORTIE (7), RDS (8), TOIMDR (7)

12

Fire control equipment

46

11.98

16.9

23

73.5

0.000

RDS (1), SORTIE (1), RDS (2), SORTIE (2), RDS (3)

15

A/C structural components

44

3.59

3.62

23

36.2

0.040

RDS (1), SORTIE (1), RDS (2), TOIMDR (2), SORTIE (2)

16

A/C comp.& accessories

124

8.43

10.1

23

28.3

0.206

RDS (1)

28

Engines, turbines, and components

58

17.74

22.7

23

56

0.000

RDS (2), SORTIE (2), TOIMDR (2), RDS (1), RDS (3)

29

Engines accessories

38

9.24

11.5

23

48.1

0.002

SORTIE (1), RDS (1), TOIMDR (2), SORTIE (2), TOIMDR (3)

43

Pumps and compressors

5

3.00

2.55

23

8.19

0.998

RDS (1)

48

Valves

28

4.43

4.74

23

36.2

0.039

TOIMDR (2), TOIMDR (3), SORTIE (3), SORTIE (2), RDS (3), RDS (1)

49

Maintenance shop equip.

11

1.77

1.57

23

34.4

0.059

RDS (4), RDS (3), RDS (5), SORTIE (4), RDS (6), RDS (1)

58

Communication equipment

45

7.58

9.44

23

104

0.000

RDS (1), SORTIE (1), SORTIE (2), TOIMDR (2)

59

Electrical, electronic equipment

286

3.67

6.50

23

155

0.000

RDS (1), SORTIE (1), RDS (2), SORTIE (2), TOIMDR (2)

61

Electric wire, and power a equipment

71

7.17

10.4

23

121

0.000

RDS (2), SORTIE (2), TOIMDR (2), RDS (3), RDS (1)

62

Lighting fixtures, lamps

16

4.89

3.84

23

33.8

0.068

SORTIE (1), RDS (2), RDS (1), SORTIE (2), RDS (4)

63

Alarm, signal and security systems

5

2.55

1.30

23

18.7

0.719

RDS (1)

66

Instruments and lab. equipment

87

9.70

20.7

23

74.2

0.000

RDS (2), RDS (8), SORTIE (1), RDS (6), RDS(7), RDS (1)

70

Automatic data processing

8

3.91

1.39

23

23.4

0.439

RDS (1)

 

Total

886

      

The Friedman Test Results based on NSG for 3-Year Forecast Period

NSG No.

NSG Name

n

Mean

Std. Dev.

Degrees of freedom

χ2

p-value

Recommended scenarios for decision makers (the first 5)

10

Weapon

14

3.70

3.51

23

20.61

0.605

RDS (1)

12

Fire control equipment

46

17.65

23.22

23

30.19

0.144

RDS (1)

15

A/C structural components

44

5.98

5.02

23

46.60

0.003

TOIMDR (2), SORTIE (2), RDS (2), RDS (1)

16

A/C comp.& accessories

124

13.38

16.56

23

24.32

0.386

RDS (1)

28

Engines, turbines, and components

58

27.59

35.85

23

18.29

0.742

RDS (1)

29

Engines accessories

38

15.74

18.63

23

24.98

0.352

RDS (1)

43

Pumps and compressors

5

0.998

18.80

23

8.020

0.998

RDS (1)

48

Valves

28

5.87

5.71

23

36.15

0.040

TOIMDR (3), SORTIE (3), SORTIE (4), TOIMDR (4), RDS (5), RDS (1)

49

Maintenance shop equip.

11

1.98

1.29

23

37.64

0.028

RDS (4), SORTIE (4), RDS (1), TOIMDR (4), RDS (6)

58

Communication equipment

45

10.69

14.66

23

40.55

0.013

RDS (1), TOIMDR1, SORTIE (1), RDS (2), SORTIE (2)

59

Electrical, electronic equipment

286

5.30

10.09

23

220.7

0.000

TOIMDR1, SORTIE (3), RDS (1), TOIMDR (3), TOIMDR (2)

61

Electric wire, and power a equipment

71

12.13

18.51

23

64.94

0.000

RDS (2), SORTIE (2), TOIMDR (2), RDS (3), SORTIE (3), RDS (1)

62

Lighting fixtures, lamps

16

8.53

6.50

23

15.90

0.860

RDS (1)

63

Alarm, signal and security systems

5

5.46

2.70

23

29.03

0.179

RDS (1)

66

Instruments and lab. equipment

87

12.53

24.90

23

73.40

0.000

RDS (2), SORTIE (1), SORTIE (2), RDS (1), RDS (8)

70

Automatic data processing

8

8.73

6.39

23

24.67

0.367

RDS (1)

 

Total

886

      

The Results of Wilcoxon Sign Test for the Recommended Scenarios in Appendix-III for 1-Year Forecast Period

NSG

N

Pairwise comparison

z-value

p-value

10

14

RDS (1)-RDS (8)**a

− 2.386 (Positive rank)

0.017

RDS (1)-RDS (6)**

− 2.232 (Negative rank)

0.026

RDS(7)-RDS (8)

− 1.476 (Negative rank)

0.140

SORTIE (8)-RDS (8)

− 2.220 (Positive rank)

0.826

RDS (5)-RDS (8)

− 1.538 (Negative rank)

0.124

RDS (6)-RDS (8)**

− 2.043 (Negative rank)

0.041

12

46

SORTIE (1)-RDS(1)

− 0.405 (Negative rank)

0.685

RDS (2)—RDS (1)

− 0.635 (Negative rank)

0.525

SORTIE (2)— RDS (1)

− 0.688 (Negative rank)

0.491

TOIMDR1—RDS (1)

− 0.894 (Negative rank)

0.371

15

44

SORTIE (1)-RDS (1)**

− 2.048 (Negative rank)

0.041

TOIMDR1-RDS (1)

− 0.060 (Negative rank)

0.952

TOIMDR (2)-SORTIE (1)

− 1.655 (Negative rank)

0.098

SORTIE (2)-SORTIE (1)

− 1.674 (Negative rank)

0.094

28

58

RDS (3)-SORTI3

− 0.230 (Negative rank)

0.818

TOIMDR (3)-SORTI3

− 0.350 (Negative rank)

0.727

SORTIE (2)-SORTI3

− 0.354 (Positive rank)

0.723

RDS (2)-SORTI3

− 0.496 (Positive rank)

0.620

RDS (1)-SORTI3

− 0.416 (Positive rank)

0.677

29

38

RDS (1)-SORTIE (1)

− 1.539 (Positive rank)

0.124

TOIMDR1-SORTIE (1)

− 0.604 (Negative rank)

0.546

SORTI5- SORTIE (1)

− 1.499 (Negative rank)

0.134

TOIMDR (5)-SORTIE (1)

− 1.155 (Negative rank)

0.248

49

11

RDS (6)-RDS (5)

− 1.531 (Negative rank)

0.126

SORTI5-RDS (5)

− 0.540 (Negative rank)

0.589

RDS (3)-RDS (5)**

− 2.070 (Negative rank)

0.038

RDS (4)-RDS (5)

− 0.806 (Negative rank)

0.420

RDS (1)-RDS (5)

− 1.836 (Negative rank)

0.066

58

45

SORTIE (2)-TOIMDR1

− 0.780 (Positive rank)

0.436

RDS (2)-TOIMDR1

− 0.020 (Positive rank)

0.984

TOIMDR (2)-TOIMDR1

− 0.255 (Positive rank)

0.798

RDS (1)-TOIMDR1

− 1.091 (Negative rank)

0.275

61

71

RDS (3)-RDS (2)

− 0.358 (Negative rank)

0.720

SORTIE (2)-RDS (2)

− 1.108 (Negative rank)

0.268

RDS (4)-RDS (2)

− 0.707 (Negative rank)

0.480

SORTI3-RDS (2)

− 0.805 (Negative rank)

0.421

RDS (1)-RDS (2)

− 1.547 (Negative rank)

0.122

  1. aBased on Wilcoxon Test results, the one that is significantly different from the other one in pairwise comparison is marked with “**” in Appendix-IV

The Results of Wilcoxon Sign Test for the Recommended Scenarios in Appendix-III for 2-Year Forecast Period

NSG

n

Pairwise comparison

z-value

p-value

10

14

TOIMDR (8)-SORTIE (8)

− 0.220 (Negative rank)

0.826

SORTIE (7)-SORTIE (8)

− 1.412 (Negative rank)

0.158

TOIMDR (7)-SORTIE (8)

− 1.664 (Negative rank)

0.096

RDS (1)-SORTIE (8)**

− 2.480(Negative rank)

0.013

12

46

SORTIE (1)-RDS (1)

− 1.082 (Negative rank)

0.279

RDS (2)-RDS (1)

− 0.428 (Positive rank)

0.668

RDS (3)-RDS (1)

− 0.019 (Negative rank)

0.985

15

44

SORTIE (1)-RDS (1)

− 1.929 (Negative rank)

0.054

TOIMDR (2)-RDS (1)

− 0.607 (Negative rank)

0.544

RDS (2)-RDS (1)

− 0.617 (Negative rank)

0.537

28

58

SORTIE (2)-RDS (2)

− 0.235 (Negative rank)

0.814

TOIMDR (2)-RDS (2)

− 0.410 (Negative rank)

0.682

RDS (1)-RDS (2)

− 0.667 (Negative rank)

0.505

29

38

RDS (1)-SORTIE (1)

− 0.182 (Negative rank)

0.855

TOIMDR (2)-SORTIE (1)

− 0.116 (Negative rank)

0.908

SORTIE (2)-SORTIE (1)

− 0.849 (Negative rank)

0.396

48

28

TOIMDR (3)-TOIMDR (2)

− 0.586 (Positive rank)

0.558

SORTI3-TOIMDR (2)

− 0.214 (Positive rank)

0.830

RDS (1)-TOIMDR (2)

− 0.942 (Negative rank)

0.346

49

11

RDS (3)-RDS (4)

− 0.206(Negative rank)

0.837

RDS (5)-RDS (4)

− 1.523 (Positive rank)

0.128

RDS (1)-RDS (4)

− 1.131 (Negative rank)

0.258

58

45

SORTIE (1)-RDS (1)

− 1.108 (Negative rank)

0.268

RDS (2)-RDS (1)**

− 2.000 (Positive rank)

0.046

SORTIE (2)-RDS (1)

− 1.902 (Positive rank)

0.057

TOIMDR (2)-RDS (1)

− 1.929 (Positive rank)

0.054

59

286

SORTIE (1)-RDS (1)**

− 3.713 (Negative rank)

0.000

TOIMDR (2)-RDS (1)**

− 2.060 (Positive rank)

0.039

SORTIE (2)-RDS (1)**

− 2.045 (Positive rank)

0.041

RDS (3)-RDS (1)**

− 2.281 (Positive rank)

0.023

SORTIE (1)-RDS (1)**

− 3.713 (Negative rank)

0.000

61

71

SORTIE (2)-RDS (2)

− 1.284 (Negative rank)

0.199

TOIMDR (2)-RDS (2)

− 1.382 (Negative rank)

0.167

RDS (1)-RDS (2)

− 1.522 (Negative rank)

0.128

62

16

RDS (2)-SORTIE (1)

− 0.336 (Negative rank)

0.737

RDS (1)-SORTIE (1)

− 1.200 (Negative rank)

0.230

RDS (4)-SORTIE (1)

− 0.440 (Negative rank)

0.660

66

87

RDS (8)-RDS (2)

− 0.258 (Positive rank)

0.796

SORTIE (1)-RDS (2)

− 1.007 (Negative rank)

0.314

RDS (1)-RDS (2)

− 1.017 (Positive rank)

0.309

The Results of Wilcoxon Sign Test for the Recommended Scenarios in Appendix-III for 3-Year Forecast Period

NSG

n

Pairwise comparison

z-value

p-value

15

44

SORTIE (2)-TOIMDR (2)

− 0.134 (Positive rank)

0.894

RDS (2)-TOIMDR (2)

− 0.051 (Negative rank)

0.959

TOIMDR (3)-TOIMDR (2)**

− 2.195 (Negative rank)

0.028

RDS (1)-TOIMDR (2)

− 1.256 (Negative rank)

0.206

48

28

SORTI3-TOIMDR (3)

− 0.816 (Negative rank)

0.415

SORTI4-TOIMDR (3)

− 0.843 (Negative rank)

0.399

TOIMDR (4)-TOIMDR (3)

− 0.415 (Negative rank)

0.678

RDS (1)-TOIMDR (3)

− 1.172 (Negative rank)

0.241

49

11

SORTI4-RDS (4)

− 1.179 (Positive rank)

0.238

TOIMDR (4)-RDS (4)

− 1.179 (Positive rank)

0.238

RDS (5)-RDS (4)**

− 2.060 (Positive rank)

0.039

RDS (1)-RDS (4)

− 0.868 (Negative rank)

0.385

58

45

TOIMDR1-RDS (1)

− 1.427 (Negative rank)

0.154

SORTIE (1)-RDS (1)

− 1.329 (Negative rank)

0.184

RDS (2)-RDS (1)

− 1.393 (Positive rank)

0.164

SORTIE (2)-RDS (1)

− 1.230 (Positive rank)

0.219

59

286

SORTI3-TOIMDR1**

− 2.891 (Positive rank)

0.004

RDS (1)-TOIMDR1**

− 2.393 (Negative rank)

0.017

TOIMDR (3)-TOIMDR1**

− 3.393 (Positive rank)

0.001

TOIMDR (2)-TOIMDR1**

− 2.771 (Positive rank)

0.006

61

71

SORTIE (2)-RDS (2)

− 1.729 (Negative rank)

0.084

TOIMDR (2)-RDS (2)

− 1.779 (Negative rank)

0.075

RDS (3)-RDS (2)

− 1.333 (Positive rank)

0.895

SORTI3-RDS (2)

− 0.794 (Negative rank)

0.427

RDS (1)-RDS (2)

− 1.898 (Negative rank)

0.058

66

87

SORTIE (1)-RDS (2)

− 1.630 (Negative rank)

0.103

SORTIE (2)-RDS (2)

− 1.513 (Negative rank)

0.130

RDS (1)-RDS (2)

− 1.947 (Negative rank)

0.051

RDS (8)-RDS (2)

− 1.236 (Positive rank)

0.216

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Eren, B., Erol, S. (2015). The Proposal of Demand Estimation of Repairable Items for the Weapon Systems During the Initial Provisioning Period: F-16 Case Study. In: Zeimpekis, V., Kaimakamis, G., Daras, N. (eds) Military Logistics. Operations Research/Computer Science Interfaces Series, vol 56. Springer, Cham. https://doi.org/10.1007/978-3-319-12075-1_3

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