EXAMINING MANNING RELATIONSHIPS BETWEEN US AIR FORCE ENTERPRISES AND CAREER FIELDS A US Air Force (USAF) dataset containing 6 attributes and over 400,000 funded authorizations (paid workforce positions) is analyzed for significant manning relationships among 12 Service Core Functions (SCFs) and 32 functional areas. The authorizations are collapsed into 375 groups of 32 functional equities ranging from Acquisitions to Weather career fields. The SCFs are managed by 7 Core Function Leads (CFLs) who are typically Major Command (MAJCOM) commanders. Logistic fit analyses via logistic odds ratio (OR) comparisons and contingency table analyses reveal significant manning shortfalls in all 12 CFLs. The results of the analysis hope to better inform the USAF Strategic, Planning & Programming Process (SP3). The SP3 is a Chief of Staff of the Air Force (CSAF)-approved framework that guides strategic decision making. Keywords: Logistic Regression, Personnel risk, Relative Risk, Strategic risk, Odds Ratio Introduction The primary objective of this cross-sectional observational study is to examine ways to assess manning data that may help senior Air Force leaders manage personnel capability and enhance maximization of readiness. The desired endstate is a more defensible, rigorous methodology to better inform SCF (Figure 1) strategic risk assessments. This would enable SCF personnel planners to assess manning shortages to more accurately inform the USAF budget, thereby, enabling the CSAF to better manage personnel combat capability. Manning is defined as the ratio of the number of personnel and the number of funded authorizations: Manning = Number of ( assigned ) personnel Number of funded authorizations' Each USAF unit has a unit manning document (UMD) which stipulates the number of personnel and funded authorizations. Each authorization represents a funded position. Ideally, funded authorizations should have assigned, trained personnel filling the positions, but this is usually not achieved across the USAF. Air Force Core Functions r Nuclear Deterrence Ops )( Global Precision Attack i Air Superiority II Special Operations L Space Superiority JL Rapid Global Mobility r Cyberspace Superiority T Personnel Recovery L Command and Control JL Agile Combat Support L Global Integrated ISR JL Personnel & Training Figure 1: USAF Service Core Functions (SP3 2011) Career fields are often undermanned, which results in a stressed, overworked workforce that equates to increased military risk. As of July 2016, there were over 400,000 active duty military and civil servants in the USAF. Of the 400,000+ personnel, 55% are enlisted, 13% are officer and the remaining 32% are civil servants (See Appendix II). The USAF has over 300 career field specialties or Air Force Specialties (AFS). AFSs are further compartmentalized into Air Force 1 Specialty Codes or AFSCs. The AFSCs are condensed into 32 functional equities (FEs) across the 12 SCFs. A mapping of the career fields to the functional equities is provided in Figure 2. Mapping from AFS to Functional area Acq 60C, 63A/F/G/S Distribution 25E. 2F0, 2P0, 2TX, 2XX Mx 21A, 2AX, 2M0, 2R0, 2R1 S&T 61X, 62X, 8E0 Airfld Ops 1AX, IPX, 1TX Fin 65X, 6F0, 6F5 Materiel 2S0 Safety ISO, 1S1 C2 Sys Ops 1CX Force Supt 30X, 34X, 36-38X, 3DX, 3M, 3R03SX Msn Assur 17X, 81-83, 85, 8X, 90G, 92X, 95-99, 9X 1B0,1B4,1F4, 39X, 3AX, 3F4, 3T0, 3V0, 69E, 6A3, 72, 75, 76, 7D Sec Forces 31F, 31P, 3 IS, 3P0 CE 32E/G/S, 3EX Health Srvs 40-48X, 4X, 9S1 Muns 21M, 2WX Space/Miss 13X Chaplain 52R, 5R0 Hist 3H0, 84H Ops Mgt 86M, 86P SpecInv 71, 71S, 750 Combat Sys 12X Inspection 87G/I/Q, 8IO/T Ops Plans 10C,16X Wx 151,15W, 1W0 Comm- 33S7 33V7-3€fr"3Cl Intelligence 14N, 1NX Pilot 11X CC 20C, 80C, 91C, 91W Legal 5LI, 5J0 PA 35X, 3NX Cons 64A, 64P, 6C0 Log Plans 21G/L/R/T, 221, 2G0 RPA 18X, 1V0 Figure 2: Functional Equity Mapping This results in a dataset of 375 observations 1 . Figure 3 is a bi-chart which shows the assigned USAF personnel by the 12 SCFs along with associated manning rates. Figure 4 shows manning rates by FE. The mean and median are the same for the FEs. The SCFs are unequally weighted (i.e. the amount of personnel differs by the SCF). Each of the twelve SCFs are supported by Core Function Support Plans (CFSPs) and developed and approved by one of the seven CFLs. CFSPs translate the vision for the specific CFs into risk-informed, resource-constrained, planning force proposals that guide follow-on Program Objective Memorandum (POM) and Science & Technology (S&T) decisions and activities (NAP, 2014). 1 The reader should be advised not all 32 functional equities are represented in every SCF, so although 32 x 12 is 384, there are actually only 375 observations. 2 Figure 3: USAF SCF Manning Summary Figure 4: USAF Functional Equity Manning Summary Data Overview This study consists of over 416,485 authorizations collapsed into 375 subsets as of July of 2016 from the Air Force Manpower, Personnel and Services database. Each subset represents a group of FE by SCF. Each observation contains 6 variables listed in Table 1. The variable type characteristics are categorical (to include nominal and ordinal) and numeric. 3 Table 1: Variables for categorical analysis Name Description and effect type Type Levels and notes SCF Service Core Function (Fixed) Nom. There are 12 USAF SCFs. Functional Equity (FE) Career Field Family (Fixed) Nom. There are 32 FEs. Manning category Binned manning categories between > 100% and < 80% (Fixed) Ord. 6 ordered categories Manning rate Assigned personnel vs Authorizations (Used to determine ‘Fully Manned’ & ‘Manning category’) Cont. This is a continuous value. Fully Manned (Y/N) Factor which consists of (Fixed) either fully manned or not Nom. Binomial variable (outcome) Overage/Shortage (-) Number of surplus/shortage of authorizations (Fixed) Disc. This is a discrete value. Research Question & Application of Techniques In the world of doing either the same amount of workload or less workload with fewer resources, how does one effectively manage resources with respect to assessing personnel capability? In the past, USAF has developed numerous MAJCOM manpower assessments using various techniques. However, since 2010, the USAF has adopted a broader enterprise-level approach via the SCF. A SCF may utilize several MAJCOMs in order to execute its mission. One enduring challenge is accurately assessing personnel deficiencies across the USAF by SCF. If planners could more accurately assess and identify the personnel SCF sight picture, this would help substantiate the risk associated with a lack of required manpower to deliver wartime and peacetime capability. A valid manning assessment can help identify capability gaps and serve as a good planning tool as a means of validating risk. This further enables senior leaders to qualify risk with analysis and increase the odds of filling or mitigating personnel capability gaps. The improved strategic manning assessment could then be used to improve the strategic planning & programming process and enable the CSAF to better advocate for personnel resources. The subsequent research questions and hypothesis (a = 0.05) are as follows: • Is there a meaningful manning relationship between USAF SCFs and full manning levels? Null Hypothesis (H 0 ): There is an association between SCF and Full manning levels. Alternate Hypothesis (H A ): There is no association between SCF and Full manning levels. • Given, SCFs are unique: is there a rigorous way to compare manning levels among SCFs and FEs? USAF manning levels typically do not vary much during non-presidential election years and historically, attempts at trying to predict manning beyond a given Fiscal Year Defense Plan (FYDP) have been mostly fruitless. The goal of this study is not to develop a model to predict future manning levels. The goal of this study is to build a SCF and FE comparative manning assessment that strategic leaders can utilize for personnel capability advocacy. Techniques explored will focus on logistic analysis in the form of contingency tables, logistic odd ratios and other methods to compare the SCFs and FEs against the manning levels. 4 Exploratory Analyses The next portion uses descriptive statistics to examine if the 12 SCF populations that consist of primarily 32 functional equities are statistically similar. The analysis is performed using JMP 11 Pro. The study uses a significance level (also known as a) of 0.05 or simply there is a 5% likelihood of committing a Type I error (rejecting the null hypothesis, when it is true). Figure 5 provides standard box and whisker plots by SCF population size intersected by a grand mean; lists the respective SCF standard deviations; and shows a Tukey test pairwise comparison among the SCF means. The plots show evidence of SCF dissimilarity. The standard deviation range among the SCFs is relatively large. The majority of the Tukey test results reveal the SCFs are statistically dissimilar. 130% • 120 %- 110 %- 100% 90%“ S0% ? 70%“ c c ^ 60%“ 50% 40%- 30%~ 20 % io%- 0 % P [1 ACS - AS - C2 - cs - GISR - GM - GPA NDO P &T PR SO ■ ss ■ ■Agile Combat Support Air Superiority ■ Command & Control Cyberspace Superiority - Global ISR - Global Mobility - Global Precision Attack - Nuclear Deterrence Ops - Personnel & Training - Personnel Recovery -Special Ops - Space Superiority CJ 0 : g 13 SCF 0.14 0.12 0.10 0.08 * • * * * 0.06 0.04 0.02 0.00 • • • « • * ACS AS C2 CS GISR GM GPA NDO P&T PR SO SS SCF Std dev manning range: 4% -12.5% (i.e. large) < Cl. O Q TL (— Cl. Connecting Letters Report Level Mean GM A 10309713 PR B 10051307 ACS c 0399745! C2 D 0.9665473 SS E 09365637 GISR F 09331010 SO G 03235S5O P&T G 09232152 NDO H 031*1729 GPA | 0-90SS132 CS 1 0-9071673 AS J 03971833 Levels net connected by seme letter ere siflnif ieently different, O ' $ Figure 5: Descriptive Statistics of SCF Manning Levels Contingency Analyses The main outcome variable or response is a binary categorical variable (i.e. > 100% manned or not) and the other factors are fixed nominal and ordinal variables. We use contingency analysis to examine if there are meaningful associations between SCFs and manning levels as well as studying associations between SCFs and FEs (Figure 6). 5 T Contingency Analysis ol Fully Manned(Y/N) By SCF 4 Mosaic Plot SCF Tests u DF -LogLtke RSquare(U) 375 11 13.907225 0.0613 Test ChiSquare Frob>Chi5q Likelihood Ratio 27.314 0.0035* ^ * Contingency Analysis of Fully Manned[Y/N> By Functional Equity J Mosaic Plot FuriftiOnal Equity Tests N DF -LogUke R Square 0U3 375 31 25,203551 01120 Test CbiSquare Prob>ChiSq Likelihood Ratio 50.407 0.0153* Figure 6: SCF and FE manning Contingency Analysis Figure 6 via the Likelihood Ratio test statistic shows the chi-square values from the SCF and FE observations, which are 27.814 and 50.507 respectively. Since, the p-value is less than a (0.05) this demonstrates there is a significant association between manning levels and SCF. The manning categorical variable (‘Mann_Cat’) is an ordinal response with six levels. We test this response for homogeneity among the SCF and FE variables. Since, the Likelihood ratio p-values are smaller than a, the results of tests suggests the difference in manning levels across SCF and FE are statistically significant (Figure 7). 6 A Test Response H om ogeneity Test ChISquare Prob>ChiSq Likelihood Ratio 75.1017 0.0371* M.ann Cat 100% or more 95-99% 90-94% 85-89% 80-84% <80% 117 41 74 54 35 54 375 31.20 10.93 19.73 14.40 9.33 14.40 32 32 32 28 32 32 32 32 32 21 32 3 2 375 Share Chart Acquisition A«rficld Operations C2 Systems Ops CE_ Chaplaincy Combat Systems (12XJ Commarader/Sr Leader [Contracting Distribution Fi nal nee Force Su pport Health Services Historian Inspections _ ]ntelli pence Legal _ Logistics Plans . Main tenance Materiel Mission Assurance Munitions Ops Mqt ■Ops Planning JPA Pilot RPA SfltT Safety SF_ Spacc/N uke/Mbsi le Ops Sotrial Invest. _ Wither Test Response Homogeneity Test ChtSquare Prab>Chi5q Likelihood Ratio 247.623 <.0001* Figure 7: Ordinal Categorical Analysis Modeling Approach Although, the focus of this study is to explore not to necessarily predict manning levels among SCFs and FEs, the data are investigated to see if a nominal logistic regression model can provide more meaningful insight among the SCFs and FEs as it relates to being fully manned or not. Logistic regression analysis describes how a binary (0 or 1) response variable is associated with a set of explanatory variables (categorical or continuous). The general logistic function is n(x ) = e (oc+/?x) 1 + e (0C+/?x) odds 1+odds where x is the independent variable or factor and e is the exponential function, and 7r(x) is the probability of being at least 100% manned. For this nominal outcome variable, each factor is examined individually and associated model statistics are compared to a joint (combined) model. The manning categorical (ordinal) factor is not a statistically significant effect in any of the models as the p-values for the parameter estimates were greater than a. Figure 8 provides a summary of the results. 7 Whole Model Test Model Difference Full Reduced -Log Likelihood 41.69940 183.43230 225.13170 DF Ch[Square 42 83.39879 Combined Prob>ChiSq 0 . 0001 * RSquare(U) AICc BIC Observations (or Sum Wgts) Measure Entropy RSquare Generalized RSquare Mean -Log p RMSE Mean Abs Dev Miselassification Rate 0,1852 464.297 621,722 375 Goodness Of Fit Statistic Chi Square DF Prob>ChiSq Pearson 362.3808 332 0,1209 Deviance 366.3646 332 0,09] LI N Training Definition 0.1852 1-Logllke[model)/Loglike(0) 0.2853 (1 -(L(0)/L(model)) A (2/n))/a - L£0) A (2/n)) 0,4892 X-Log(p(j])/n 0.4026 VX(y[j]-ptj])Vn 0.3253 X|y|J]-plj]|M AUC 0.2400 X(p(j]*pMax)/n 0.78223 375 n Figure 8: SCF & FE manning Model Comparison Results from the joint model from the ‘Whole Model Test’ shows significance. The accuracy rates (1- misclassification rate) regarding predictability classifies success 76% of the time. The Goodness of Fit (GoF) statistic suggest the model is adequate as the Deviance values are above a. The joint model has an Area under the Curve (AUC) of 0.782. This suggests the modeling predictions have more than a ‘chance’ of being accurate. In fact, a strict interpretation of this model is that when presented randomly with a given number of SCF and FE manning observations that are > 100% and < 100%, there is a 78.2% chance of correct classification. Figure 9 depicts the model probability estimates of being 100% or more manned by SCF and FE. 8 ACS | AS | C2 | es | GISR 1 GM | GPA | MDO | F&T | PR | SO I SS Acquisition 04193 0234 02514 0.4613 02036 0.6146 0234 02514 0.4606 . 0.1658 0.5777 Airfield Operations 0.2576 0.1665 0.1387 0.2816 01122 0.4334 0.1665 0.1387 0.2305 0.5211 0,0371 9,3961 C2 Systems Ops 0.3523 0.2383 0.202 0.3923 0,1658 0.5458 0,2389 0.202 0.3816 0.S31 0,1304 0,5078 CE 0.3523 0.2383 0202 0 3923 0.1658 0.5459 0.2389 0202 03816 0.631 0.1304 0.507G Chaplaincy 0.2064 0.1302 01077 0.2358 00865 0.3644 0.1302 0.1077 02348 0 0667 03296 Combat Systems f!2X 0.1656 0.1026 0.0844 0.1906 0.0674 0.3Q44 0.1026 0.0844 0.1898 0.3837 0,0518 0.2723 CC/SL 0.7222 05394 0,5468 0,7551 0.4864 0.8514 0,5334 0,5468 0.7541 0.8307 0,4168 0.3308 Contracting 0.4433 03135 02746 0.4318 0.2231 0.6426 0.3135 0.2746 0.4304 0.7133 0.1832 0.6066 Distribution 0.4433 03195 02746 0.4918 0.2291 0.6426 03195 0.2746 0.4904 0,7139 0,1832 0.6066 Finance 0.0732 0.0472 0.0384 0.0926 0,0304 0.1594 0.0472 0.0384 0.0821 0.2124 0.0231 0.1338 Force Support 0,165$ 0.1026 0.0844 01906 0.0674 0,3044 0,1026 0.0344 01898 0.3837 00518 0.2728 Health Services 0.165S 01026 00844 0.1306 0 0674 0.3044 0.1026 0.0844 0.1898 0.3837 0.0518 02729 Historian 0.4196 0.294 0,2514 0.4619 0.2086 0.6146 0294 0.2514 0.4606 v| 0.1659 0,5777 Inspections 0.0732 Oj0472 0.0384 0.0326 0.0304| 0.1584 O.0472 O.0384 0.0821 0,2124 0.0231 0.1338 Intelligence 0.4433 0.3135 02746 0,4318 0.2231 0,6426 0,3195 0.2746 0.4904 0.7139 0.1832 08066 Legal 0.16S6 01026 00844 0.1306 0 0674 0.3044 OJ026 0.0844 01898 0.3837 0.0518 02729 Logistics Plans 0.0732 0.0472 0.0384 0.0926 0.0304 0.1534 0.0472 0.0384 0.0821 0.2124 0,0231 n 1333 Maintenance 0.3523 0.2389 0.202 0.3923 0.1658 0,5459 0,2383 0.202 0.3816 0.631 0.1304 0.5078 Materiel 01656 01026 0.0844 0.1306 0 0674 0.3044 0.1026 0.0844 01899 03837 0.0518 0.2729 Mission Assurance 0.3529 0.2389 0.202 0.3329 0.1858 0.5453 0.2389 0.202 03916 0.631 0.13O4 05076 Munitions 0.3523 0.2389 0.202 0.3929 0.1658 0.5453 0.2383 0.202 0.3816 0.631 G.1304 0.5078 Ops Mgt 0.2576 0.1685 0.1337 0,2316 0.1122 0.4334 0,1665 0.1387 0.2905 0.5211 0,0871 0,3381 Ops Planning 0.4433 03195 02746 0.4318 0.2231 0.6426 0.3135 0.2746 O.4304 0.7139 0.1832 06066 Pilot 0.335 0.2731 0.2325 0.1921 0.59 0.2731 0.2325 0.4352 0.6718 0,1522 0.5524 PA 0.5442 0.4073 0.3565 0.5862 0.3031 0.7247 0.4073 0.3565 0.5843 0.7832 0.2471 0.893 FSPA 0.6036 0.4871 0.4141 . 0,3568 0.7705 04671 0,4141 0,6425 0.8269 0.2351 07422 S&T 3E-08 2E-08 2E-08 4E-08 IE-08 7E-06 21-08 2E-03 4E-08| IE-07 3E-03 GE-OB Safely 0.41SS 0294 02514 0.4813 0.2086 0.6146 0,294 02514 O.4606 | 0.1659 05777 SF 3E03 2E-0S 2E-08 4E 08 IE 08 7E08 2E08 2EC3 4E 08l IE-07 9E-09 8E-0S Space/Muke/Missile C 0.2576 0.1665 01337 0.2916 0,1*22 0,4334 01665 0.1387 02905 0.5211 0.0871 0.3381 Special Invest/ 0335 02731 0.2325 ■ 0.1921 0.53 0.2731 0.2325 0.4352 0.6718 0.1522 05524 leather 0.4737 0.3412 0,2946 . 0.2469 0.6648 0.3412 0.2946 0.515 0,1833 0,6298 Likelihood oft 100% manning x < 0.15 Low | 0.15 < x > 0.25 Mod. 0.25 0.4 Sig 1.0 < x > 0.4 High Figure 9: SCF and FE Likelihood being fully manned 2 The results suggest none of the FEs by SCF are likely to be 100% manned or more. Notably, the Science & Technology (S&T) and Security Forces (SFs) FEs are highly likely to not be fully manned in any SCF or FE. Conversely, the commander or senior leader FEs has the potential in the Global Mobility (GM) and Personnel Recovery (PR) SCFs to have 100% or more manning. This is illustrated via the likelihood color palette scale in Figure 9. Arguably, rows (FEs) in red are highly less likely to be 100% or more manned. Model Results Figure 10 is a matrix of the modeling interpretations of the success/failure probabilities of the 375 observations. Probability of Success (( 1+e i 0 g it[n ( X ) ] )) is considered 100% or more manned or a green ‘Y\ otherwise a red ‘N’ in the matrix of cells. 2 Cells without values indicate the FE was not represented in the SCF. 9 Acquisition [ Airfield Operations [ C2 Systems Ops CIE Chapin nog Combat Systems (12X) | CCfSL Contracting Distribution Finance Force Support Health Services Historian Inspections j Intelligence Legal j Logistics Plans Maintenance Materiel Mission Assurance Munitions Ops Mqt Ops Planning Pilot ( p A FIP A S&T Safety | SF Sp a ce/Nuk e/Mis si] e Ops 1 Special Invest/ | Weather | Figure 10: Likelihood of 100% manning in binary form The full joint model equation is listed in Appendix I. Odds Ratio Analyses The outcome variable is a success/fail response variable so Odds Ratios (ORs) via logistic transformations (logits) are computed and compared among SCFs and FEs. The logistic odds is represented as Logit[n(x)] = log(odds) = log = Po + + ••• P p X p where /? 0 is the intercept, /? p (the parameter) is the log OR of one unit increase in x whereas e (P) is the OR of one unit increase in x (Agresti, 2013). The ORs are computed from the joint model previously P P discussed. A total of 1,034 (12 2 + 32 2) ORs are computed and compared of which 45 (34%) and 160 (16%) are considered ‘statistically significantly different than one,’ respectively. These overview statistics suggest there are significant differences in full manning levels among SCFs and FEs. Figure 11 is a matrix of the SCF ORs accompanied with a scale to aid in interpretation. 10 ACS - Agile Combat Support AS -AirSuperiority C2 - Command & Control CS - Cyberspace Superiority GISR - Global ISR GM -Global Mobility GPA -Global Precision Attack NDO - Nuclear Deterrence Ops P &T-Personnel & Training PR - Personnel Recovery SO -Special Ops SS - Space Superiority SO SS ACS AS C2 CS GISR GM GPA NDO P&T PR SO SS Relative Comparative Difference Scale x>6 High - 6 > x > 3 Sig ■ 3 > x > 1 Mod ■ 1 1 > x > 0 Low ^ 1.737 0.576 ^ 0.464 1.186 0.364 2.204 0.576 0.464 1.18 3.135 0.275 1.89 - 0.806 2.061 0.633 3.83 1 0.806 2.05 5.448 0.478 3.284 2.155 1.24 - 2.557 0.785 4.75 1.24 1 2.543 6.757 0.592 4.074 0.843 0.485 0.391 - 0.307 1.858 0.485 0.391 0.995 2.643 0.232 1.593 2.745 1.58 1.274 3.257 - 6.051 1.58 1.274 3.239 8.607 0.755 5.189 0.454 0.261 0.211 0.538 0.165 - 0.261 0.211 0.535 1.423 0.125 0.858 1.737 1 0.806 2.061 0.633 3.83 - 0.806 2.05 5.448 0.478 3.284 2.155 1.24 1 2.557 0.785 4.75 1.24 - 2.543 6.757 0.592 4.074 0.847 0.488 0.393 1.005 0.309 1.868 0.488 0.393 - 2.657 0.233 1.602 0.319 0.184 0.148 0.378 0.116 0.703 0.184 0.148 0.376 - 0.088 0.603 3.638 2.094 1.688 4.316 1.325 8.018 2.094 1.688 4.292 11.406 - 6.876 0.529 0.304 0.245 0.628 0.193 1.166 0.304 0.245 0.624 1.659 0.145 Interpretation of OR ACS AS CS GISR GM GPA NDO P&T PR Figure 11: SCF OR Comparison The matrix should be examined from left to right by row. For example, the Air Superiority (AS) SCF compared to the Agile Combat Support (ACS) SCF has 0.576, or low odds, of being fully manned. Conversely, ACS has 1.737 odds, or moderate odds, of being fully manned when compared to AS. The top 3 SCFs with better odds of full manning levels are Personnel Recovery, Global Mobility and Space Superiority. This is fairly intuitive as these rows are more green. The bottom 4 SCFs with lesser odds of full manning levels are Command & Control, Nuclear Deterrence Options, Global ISR and Special Operations. Further, the same matrix from Figure 11 overlaid with turquoise outlines is used in Figure 12 to illustrate which SCF ORs are considered significantly different. Similar analysis is performed by FE. The FE results are listed in Appendices III and IV. ACS AS C2 CS GISR GM GPA NDO P &T PR SO SS Comparisons Total OR ACS - 0.576 0.464 1.186 0.364 2.204 0.576 0.464 1.18 3.135 0.275 1.89 61 12.314 AS 1.737 - 0.806 2.061 0.633 3.83 1 0.806 2.05 5.448 0.478 3.284 60 22.133 C2 2.155 1.24 - 2.557 0.785 4.75 1.24 1 2.543 6.757 0.592 4.074 80 27.693 CS 0.843 0.485 0.391 - 0.307 1.858 0.485 0.391 0.995 2.643 0.232 1.593 40 10.223 GISR 2.745 1.58 1.274 3.257 - 6.051 1.58 1.274 3.239 8,607 0.755 5.189 100 35.551 GM 0.454 | 0.261 0.211 0.538 0.165 - 0.261 0.211 0.535 1.423 0.125 0.858 10 5.042 GPA 1.737 1 0.806 2.061 0.633 3.83 - 0.806 2.05 5.448 0.478 3.284 60 22.133 NDO 2.155 1.24 1 2.557 0.785 4.75 1.24 - 2.543 6,757 0.592 4.074 SO 27.693 > &T 0.847 0.488 0.393 1.005 0.309 1.868 0.488 0.393 - 2.657 0.233 1.602 30 10.283 PR 0.319 0.184 0.148 0.378 0.116 0.703 0.184 0.148 0.376 - 0.088 0.603 0 3.247 SO 3.638 2.094 1.688 4.316 1.325 8.018 2.094 1.688 4.292 11.406 - 6,876 110 47.435 SS 0.529 0.304 0.245 0.628 0.193 1.166 0.304 0.245 0.624 1.659 0.145 - 20 6,042 Considered Statistically Different Figure 12: SCF OR Comparison with Significance Indicators 11 Figure 12’s results reveal the Global Mobility, Personnel Recovery and Space Superiority SCFs have statistically different manning levels as it relates to being fully manned or not. Relative Risk Relative risk ratios (RRR) which are comparative ratios of the probabilities of success (i.e. a given SCF and FE being fully manned) is another quantitative way to compare categories. As the number of categorical levels increases, the number of relative comparisons grows quite large. For example, 12 SCF and FE RRR one-way comparisons is 4,224 P (12 2 combinations *32 FEs) possibilities. In this instance, we will only explore relative comparisons to the ACS SCF. The probabilities of success are taken from the joint model results depicted in Figure 9. If the RRR is equal to 1, we conclude independence or FEi with respect to a given SCF is neither more likely nor less likely of occurring than FE 2 with respect to the same SCF. If the RRR is less than 1, we conclude FEi with respect to a given SCF is less likely of occurring than FE 2 with respect to the same SCF. If the RRR is greater than 1, we conclude FEi with respect to a given SCF is more likely of occurring than FE 2 with respect to the same SCF. The RRRs are computed and shown in Figure 13. ACS AS C2 CS GISR GM GPA NDO | 1 P&T 1 PR | 1 SO SS Acquisition 1 1.43 1.67 0.31 2.01 0.63 1.43 1.67 0.31 - 2.53 0.73 Airfield Operations 1.63 1.55 1.36 0.33 2.3 0.53 1.55 1.36 0.33 0.43 2.36 0.65 C2 Systems Ops 1.13 1.48 1.75 0.3 2.13 0.65 1.43 1.75 0.3 0.56 2.71 0.7 CE 1.13 1.48 1.75 0.3 2.13 0.65 1.43 1.75 0.3 0.56 2.71 0.7 Chaplaincy 2.03 1.53 1.32 0.33 2.33 0.57 1.53 1.32 0.33 - 3.03 0.63 Combat Systems (12X) 2 53 1.62 1.36 0.37 2.46 0.54 1.82 1.36 0.37 0.43 3.2 0.61 CC/SL 0.53 1.2 1.32 0.36 1.43 0.35 1.2 1.32 0.36 0.31 1.73 0.37 Contracting 0.33 1.41 1.64 0.31 1.38 0.7 1.41 1.64 0.32 0.82 2.45 0.74 Distribution 0.33 1.41 1.64 0.31 1.38 0.7 1.41 1.64 0.32 0.82 2.45 0.74 Finance 5.3 1.68 2.06 0.36 2.81 0.5 1.83 2.06 0.36 0.37 3.43 0.57 Force Support 2.53 1.62 1.36 0.37 2.46 0.54 1.82 1.36 0.37 0.43 3.2 0.61 Health Services 253 1.62 1.36 0.37 2.46 0.54 1.62 1.36 0.37 0.43 3.2 0.61 Historian 1 1.43 1.67 0.31 2.01 0.63 1.43 1.67 0.31 - 2.53 0.73 Inspections 5.3 1.68 2.06 0.36 2.61 0.5 1.63 2.06 0.36 0.37 3.43 0.57 Intelligence 0.33 1.41 1.64 0.31 1.36 0.7 1.41 1.64 0.32 0.62 2.45 0.74 Legal 2 53 1.62 1.36 0.37 2.46 0.54 1.82 1.36 0.37 0.43 3.2 0.61 Logistics Plans 5.3 1.68 2.06 0.36 2.61 0.5 1.63 2.06 0.36 0.37 3.43 0.57 Maintenance 1.13 1.43 1.75 0.3 2.13 0.65 1.43 1.75 0.3 0.56 2.71 0.7 Materiel 2.53 1.62 1.36 0.37 2.46 0.54 1.82 1.36 0.37 0.43 3.2 0.61 Mission Assurance 1.13 1.48 1.75 0.3 2.13 0.65 1.43 1.75 0.3 0.56 2.71 0.7 Munitions 1.13 1.43 1.75 0.3 2.13 0.65 1.43 1.75 0.3 0.56 2.71 0.7 Ops Mgt 1.63 1.55 1.36 0.33 2.3 0.53 1.55 1.36 0.33 0.43 2.36 0.65 Ops Planning 0.33 1.41 1.64 0.31 1.36 0.7 1.41 1.64 0.32 0.62 2.45 0.74 Pilot 1.06 1.45 1.7 " 2.06 0.67 1.45 1.7 0.31 0.53 2.6 0.72 PA 0.77 1.34 1.53 0.33 1.3 0.75 1.34 1.53 0.33 0.63 2.2 0.73 RPA 0.7 1.23 1.46 _ 1.63 0.73 1.23 1.46 0.34 0.73 2.05 0.31 S&T 1E+07 1.74 2.16 0.34 2.75 0.45 1.74 2.16 0.35 0.32 3.64 0.53 Safety 1 1.43 1.67 0.31 2.01 0.83 1.43 1.67 0.31 - 2.53 0.73 SF 1E+07 1.74 2.16 0.34 2.75 0.45 1.74 2.16 0.35 0.32 3.64 0.53 Space/Nuke/Missile Ops 1.63 1.55 1.36 0.33 2.3 0.53 1.55 1.36 0.33 0.43 2.36 0.65 Special Invest/ 1.06 1.45 1.7 - 2.06 0.67 1.45 1.7 0.31 0.53 2.6 0.72 Weather 0.33 1.33 1.61 - 1.32 0.71 1.33 1.61 0.32 - 2.33 0.75 Figure 13: SCF/FE Relative Risk Ratio table 12 In the ACS column of Figure 13, the Acquisition FE is held fixed compared to the other FEs within the ACS SCF. If we refer to the Airfield Operations and Acquisition FEs within the ACS SCF, we see a RRR of 1.63. The interpretation is within the ACS SCF, the Acquisition FE is 1.63 times likely of being 100% or more manned than Airfield Operations. For the rest of the columns (AS-SS), the RRRs are compared within each row or the FE is held fixed relative to the ACS SCF. For example, the 1.43 RRR at the intersection of the Acquisition FE and AS SCF, infers within the Acquisitions FE, the Air Combat Support SCF is 1.43 times likely of being 100% or more manned than the Air Superiority SCF. Similarly, at the intersection of the Acquisition FE and C2 SCF, infers within the Acquisitions FE, the Air Combat Support SCF is 1.67 times likely of being 100% or more manned than the Command and Control SCF. A takeaway from Figure 13 is ACS has a relative moderate risk to the other SCFs with regards to being 100% or more manned. SCF and FE Prioritization Strategic Decision Makers need a concise way to prioritize SCF and FE manning groups. One way is to rank them by level of manning deficiencies. Computing the odds ratios from the logits and examining the odds between SCFs and FEs affords a quantitative opportunity to assess, compare and establish a ranking. There are several methods. The first ranking method is to compare the values of the ORs of a given SCF to all of the other SCF ORs in the population. For example, ACS’ ORs would be compared to the other 11 SCF ORs. We compare them by summing the count of all ACS ORs not greater than the other 11 SCF ORs. From the computed analysis, we know this value to be 61. This means out of the 121 possibilities for ACS ORs to be less than the other SCFs, ACS has lesser manning odds than about half of the other SCFs. We apply this technique across all SCFs and obtain a list ranked from least to greatest. The SCF with the greatest number of counts is ranked last. From Figure 12, Special Ops (SO) is ranked last and Personnel Recovery is ranked first. The same technique is applied to the FEs. The second ranking method is to simply compare the size or magnitude of the OR of a given SCF to all of the other SCF ORs in the population. We do this by summing the ORs of each SCF by row and obtain a list ranked from least to greatest. For example, the sum of the ACS’ ORs is 12.314. The SCFs with the greatest and least values are ranked last and first respectively. The same technique is applied to the FEs. The third ranking method takes into account the amount of shortages and overages of a given SCF or FE. Table 2 provides a list the overages and shortages by SCF and FE. 13 Table 2: SCF and FE Overages and Shortages (-) □ug^Sht(-) Ovg/ShtH Acquisition Airfield Operations -573 45 ACS -32 C2 Systems Ops 747 AS -2076 CE -374 C2 -674 Chaplaincy Combat Systems (12XJ -34 -250 CS -1136 CC^SL 105 GISR -1363 Contracting -31 Distribution -333 GM 1519 Finance 3 GPA -5320 Force Support 1725 NDQ -1995 Health Services 373 Historian -14 P &T -1323 Inspections -37 PR 23 Intelligence -442 SO -633 Legal -311 SS -11^6 Logistics Flans -71 Maintenance 2133 Materiel -461 Mission Assurance 220 Munitions -1234 Ops Mgt -41 Ops Planning -476 Pilot -373 PA 43 RFA -134 S6tT -550 Safety 44 SF -1363 SpaceHNuke^Missile Ops -73 Special Invest^ -135 Veather -41 The overages/shortages are ranked from greatest to least. For example, the PR SCF is ranked first since it has the highest number of overages. Conversely, Global Precision Attack (GPA) is ranked last because it has the highest number of shortages. The issue with the first three methods is rank ties are common. A way to minimize rank ties is to apply a composition technique. The fourth method is a composite of the first three methods with some additional computations. The composite method involves three components; summing the first three methods’ rankings; computing a dampening factor which takes into account the actual manning rate; and computing a weight by accounting for the number of authorizations per SCF or FE. This method is called the composite value denoted by /? * co * r where /? = 1 + (1 — M) represents the i i* i jt * j i of auths per SCF or FE. . dampening factor which M is the manning rate; co = 1 + (-) and * ’ v Total auths y r = ^ ith Rank(j), where i = SCF or FE and j = 1,. .3. This procedure takes into account the size of the population (SCF or FE), population manning rate, population overage/shortage and population odds of being fully manned. The composite values are then ranked from least to greatest. Figure 14 shows the final ranked SCFs with regards to the least likely to be fully manned. 14 ACS - Agile Combat Support AS - Air Superiority C2 - Co mma nd & Control CS - Cyberspace Superiority GISR-Global ISR GM - Global Mobility GPA - Global Precision Attack NDO - Nuclear Deterrence Ops P & T- Personnel & Training PR - Personnel Recovery SO -Special Ops SS -Space Super' ACS ACS AS C2 cs GISR GM GFA NDO P8T PR SO SS 1.737 2.155 0.343 2.745 0.454 1.737 2.155 0.847 0.319 3.638 0.529 Comp. M Dampen inn cu T Value Ovg/ShtH Manning Faaor Weight Total 23.4647 -32 0 9993 1.0002 138 17.00 27,7906 -2076 0.8972 1.1028 1.05 24.00 23,80 -674 0.9671 1.0329 1.05 22.00 16.8770 -1136 0.9076 1.0924 1.03 15.00 33.6074 -1363 0.9331 1.0669 1.05 30.00 5.42472 1519 1.0313 0.9687 1.12 5.00 31,0992 -5320 0,9063 1.0912 1.14 25,00 32,0128 1995 0,9214 1.0786 106 28.00 20.5377 -1826 0.9236 1.0764 1.06 18.00 4.01738 23 1.0056 0.9944 101 4.00 31.7578 -683 0.9366 1.0632 103 29.00 14.5435 -1146 0.9243 1.0757 104 13.00 AS C2 CS GISR GM GPA NDO P&T PR 50 SS RANK 0.576 0.464 1.136 0.364 2.204 0.576 0.464 1.18 3.135 0.275 1.39 6 - 0.806 2.061 0.633 3.83 1 0.806 2.05 5.448 0.478 3.284 3 1.24 - 2.557 0.785 4.75 1.24 1 2343 6.757 0.592 4.074 7 0.485 0.391 - 0.307 1.858 0.485 0.391 0.995 2.643 0.232 1.593 4 1.58 1.274 3.257 6.051 1.58 1.274 3.239 8.607 0.755 5.189 12 0.261 0.211 0.538 0,165 0.261 0.211 0.535 1.423 0.125 0.853 2 1 0.806 2.061 0,633 3.83 - 0.806 2.05 5.448 0.478 3.284 9 1.24 1 2.557 0785 4.75 1.24 - 2.543 6.757 0.592 4.074 11 0.438 0.393 1.005 0309 1.868 0.483 0.393 - 2.657 0.233 1.602 5 0.184 0.148 0.378 0116 0.703 0.184 0.148 0.376 - 0.088 0.603 1 2.094 1.688 4.316 1.325 8.018 2,094 1.688 4.292 11.406 ■ 6.876 10 0.304 0.24S 0.628 0.193 1.166 0.304 0.245 0.624 1.659 0.145 * 3 Figure 14: SCF Prioritization Technique Results from Figure 13 show the top 3 SCFs with lower odds of not being fully manned are Personnel Recovery, Global Mobility and Space Superiority. Conversely, the bottom 3 SCFs with higher odds of not being fully manned are Global ISR, Nuclear Deterrence Ops and Special Ops. A comparison of the ranking methods is listed in Table 3. 15 Table 3: Ranking methodology Comparison with respect to being not fully manned OR Comp. Sum OR Ovg/Sht Composite Rankl Rank2 Rank3 Rank4 ACS S G 3 G AS 6 7 11 8 C2 9 9 4 7 CS 5 4 G 4 GISR 11 11 8 12 GM 2 2 1 2 GPA 6 7 12 9 NDO 9 9 10 11 P &T 4 5 9 5 PR 1 1 2 1 SO 12 12 5 10 SS 3 3 7 3 Final Remarks This research presents an alternative method of assessing USAF manning by SCF and FE by using logistic regression functions and contingency analyses. Statistically, there is an association between SCFs or FEs and full manning levels. Manning relationships among CFLs or FEs can be rigorously prioritized by OR comparisons. Further, this research can inform Strategic Decision Makers of manning capability gaps and substantiate advocacy for more resources to meet combat and peacetime requirements. There are no SCFs fully manned in the USAF. Overall, across the USAF, ‘commanders or senior leaders’ is the only FE of 32 likely to be fully manned. This methodology enables senior decision makers to better qualify risk and enhance the strategic planning & programming process risk assessment, which enables the CSAF to better substantiate and advocate for personnel resources. 16 References Agresti, Alan (2013). Categorical Data Analysis (3rd ed.). p. 119-122. Hoboken, New Jersey: John Wiley & Sons, Inc. NAP of Science, Eng. & Medicine. (2014). “Development Planning: A Strategic Approach to Future Air Force Capabilities” https://www.nap.edu/read/18971/chapter74. Accessed Feb 2017 -There are no DOIs associated with these references. 17 Appendix I. (Joint Model) 2.00205380064806 + Matchf. SCF, "ACS", -0.169625541949248, "AS", 0.382773594328361, "C2", 0.598187339531182, "CS", -0.340458443926399, "GISR", 0.840216482139152, "GM", -0.959983538960857, "GPA", 0.382773594328361, "NDO", 0.598187339531182, "P & T", -0.335101203204821, "PR", —1.3124077302221, "SO", 1.1217617567933, "SS", -0.806323648388117) + Match (= Functional Equity, "Acquisition", — 1.50895901227517, “Airfield Operations", —0.774050445307, "C2 Systems Ops", -1.22630715465715, "CE", -1.22630715465715, "Chaplaincy", -0.485653424612526, "Combat Systems (12 X)", -0.215625028117114, "Commander/SrLeaded', -2.78780240085377, "Contracting", -1.6287434114286, "Distribution", — 1.6287434114286, "Finance", 0.620987265633101, "Force Support", -0.215625028117114, "Health Services", -0.215625028117114, "Historian", -1.50895901227517, "Inspections", 0.620987265633101, "Intelligence", — 1.6287434114286, "Legal", -0.215625028117114, "Logistics Plans", 0.620987265633102, "Maintenance", — 1.22630715465715, "Materiel", —0.215625028117114, "Mission Assurance", -1.22630715465715, "Munitions", -1.22630715465715, "Ops Mpt", -0.774050445307, "Ops Planning", -1.6287434114286, "PA", -2.00975916866181, "Pilot", -1.40608660852006, "RPA", -2.25311850963814, "S&r", 15.3930762469828, "Safety", -1.50895901227517, "SF", 15.3930762472812, "Space/Nuke/Missile Ops", —0.774050445307, "Special Invest. ", —1.40608660852006, "Weather", -1.72694463802467). 18 Appendix II. (SCF and FE Assigned Manning levels by Demographic) Appendix Figure 1 FE Assigned by Demographic ^ %of Total(Sum of Assgncnl) & 2 more vs. Function 40% I % of Tot*l($um of AwgnenQ 1 % of ToUl(Som of Awgnoff) 1 % of ToUl[Sum of Assent rv) % of Total = Sum of Assigned of Demographic Functional Area Total Assigned of Functional Area Appendix Figure 2 19 Appendix III. FE Manning OR Analyses Rank Acq lirfld 0[j2 Sys 0| CE | Chap. | Nays raSL| Contr. □ist. Fin. Dree Sujealth Srj Hist. Insp. | Intel. | le LG PlanJ Mk | | Mat'l | [isnAs^ Muns |Dps Mg|)ps Plar| Pilot | PA | RPA | S&T 1 SE I SF le/NukeJ SI | Vk 19 Acq 0.48 0.754 0.754 0.359 0.274 3.582 1.127 1.127 0.119 0.274 0.274 1 0.118 1.127 0.274 0.118 0.754 0.274 0.754 0.754 0.43 1.127 0.802 1.65 2.105 0 1 0 0.43 0.902 1.244 14 Airfld Ops 2.085 1.572 1.572 0.748 0.572 7.481 2.351 2.351 0.248 0.572 0.572 2.085 0.248 2.351 0.572 0.248 1.572 0.572 1.572 1.572 1 2.351 1.831 3.441 4.338 0 2.035 0 1 1.331 2.583 7 C2 Sys Ops 1.327 0.64 1 0.477 0.364 4.766 1.485 1.485 0.158 0.364 0.364 1.327 0.153 1.485 0.364 0.153 1 0.364 1 1 0.636 1.485 1.187 2.138 2.782 0 1.327 0 0.636 1.187 1.65 21 CE 1.327 0.64 1 0.477 0.364 4.766 1.485 1.485 0.158 0.364 0.364 1.327 0.153 1.485 0.364 0.153 1 0.364 1 1 0.636 1.485 1.187 2.138 2.782 0 1.327 0 0.636 1.187 1.65 25 Chap. 2.782 1.33 2.087 2.087 - 0.763 8.886 3.136 3.136 0.331 0.763 0.763 2.782 0.331 3.136 0.763 0.331 2.087 0.763 2.087 2.087 1.334 3.136 2.51 4.581 5.356 0 2.732 0 1.334 2.51 3.46 26 Navs 3.645 1.75 2.747 2.747 1.31 13.08 4.108 4.108 0.433 1 1 3.645 0.433 4.108 1 0.433 2.747 1 2.747 2.747 1.743 4.108 3.238 6.014 7.671 0 3.645 0 1.743 3.238 4.533 1 CC^SL 0.278 0.13 0.21 0.21 0.1 0.076 ■ 0.314 0.314 0.033 0.076 0.076 0.278 0.033 0.314 0.076 0.033 0.21 0.076 0.21 0.21 0.133 0.314 0.251 0.458 0.536 0 0.273 0 0.133 0.251 0.346 4 Contr. 0.887 0.43 0.668 0.668 0.318 0.243 3.187 - 1 0.105 0.243 0.243 0.387 0.105 1 0.243 0.105 0.668 0.243 0.668 0.668 0.425 1 0.3 1.464 1.367 0 0.337 0 0.425 0.3 1.103 13 □ist. 0.887 0.43 0.668 0.668 0.318 0.243 3.187 1 0.105 0.243 0.243 0.337 0.105 1 0.243 0.105 0.668 0.243 0.668 0.668 0.425 1 0.3 1.464 1.367 0 0.337 0 0.425 0.3 1.103 24 Fin. 8.414 4.04 6.343 6.343 3.024 2.308 30.23 8.485 8.485 2.308 2.308 3.414 1 8.435 2.308 1 6.343 2.308 6.343 6.343 4.035 8.435 7.582 13.83 17.71 0 3.414 0 4.035 7.582 10.46 17 Force Supt 3.645 1.75 2.747 2.747 1.31 1 13.08 4.108 4.108 0.433 1 3.645 0.433 4.108 1 0.433 2.747 1 2.747 2.747 1.743 4.108 3.238 6.014 7.671 0 3.645 0 1.743 3.238 4.533 18 Health Srus 3.645 1.75 2.747 2.747 1.31 1 13.08 4.108 4.108 0.433 1 3.645 0.433 4.108 1 0.433 2.747 1 2.747 2.747 1.743 4.108 3.238 6.014 7.671 0 3.645 0 1.743 3.238 4.533 8 Hist. 1 0.48 0.754 0.754 0.358 0.274 3.582 1.127 1.127 0.118 0.274 0.274 0.118 1.127 0.274 0.118 0.754 0.274 0.754 0.754 0.43 1.127 0.802 1.65 2.105 0 1 0 0.43 0.802 1.244 30 Insp. 8.414 4.04 6.343 6.343 3.024 2.308 30.23 8.485 8.485 1 2.308 2.308 3.414 8.435 2.308 1 6.343 2.308 6.343 6.343 4.035 8.435 7.582 13.33 17.71 0 3.414 0 4.035 7.582 10.46 11 Intel. 0.887 0.43 0.668 0.668 0.318 0.243 3.187 1 1 0.105 0.243 0.243 0.337 0.105 0.243 0.105 0.668 0.243 0.668 0.668 0.425 1 0.3 1.464 1.367 0 0.337 0 0.425 0.3 1.103 28 LE 3.645 1.75 2.747 2.747 1.31 1 13.08 4.108 4.108 0.433 1 1 3.645 0.433 4.108 0.433 2.747 1 2.747 2.747 1.743 4.108 3.238 6.014 7.671 0 3.645 0 1.743 3.238 4.533 27 LG Plans 8.414 4.04 6.343 6.343 3.024 2.308 30.23 8.485 8.485 1 2.308 2.308 3.414 1 8.435 2.308 6.343 2.308 6.343 6.343 4.035 8.435 7.582 13.33 17.71 0 3.414 0 4.035 7.582 10.46 8 Mh 1.327 0.64 1 1 0.477 0.364 4.766 1.485 1.485 0.158 0.364 0.364 1.327 0.153 1.485 0.364 0.153 - 0.364 1 1 0.636 1.485 1.187 2.138 2.782 0 1.327 0 0.636 1.187 1.65 28 Mafl 3.645 1.75 2.747 2.747 1.31 1 13.08 4.108 4.108 0.433 1 1 3.645 0.433 4.108 1 0.433 2.747 2.747 2.747 1.743 4.108 3.238 6.014 7.671 0 3.645 0 1.743 3.238 4.533 10 Msn Assr. 1.327 0.64 1 1 0.477 0.364 4.766 1.485 1.485 0.158 0.364 0.364 1.327 0.153 1.485 0.364 0.153 1 0.364 ■ 1 0.636 1.485 1.187 2.138 2.782 0 1.327 0 0.636 1.187 1.65 23 Muns 1.327 0.64 1 1 0.477 0.364 4.766 1.485 1.485 0.158 0.364 0.364 1.327 0.153 1.485 0.364 0.153 1 0.364 1 0.636 1.485 1.187 2.138 2.782 0 1.327 0 0.636 1.187 1.65 20 Ops Mgt 2.085 1 1.572 1.572 0.749 0.572 7.491 2.351 2.351 0.248 0.572 0.572 2.035 0.243 2.351 0.572 0.243 1.572 0.572 1.572 1.572 2.351 1.331 3.441 4.338 0 2.035 0 1 1.331 2.583 12 Ops Plans 0.887 0.43 0.668 0.668 0.318 0.243 3.187 1 1 0.105 0.243 0.243 0.887 0.105 1 0.243 0.105 0.668 0.243 0.668 0.668 0.425 0.3 1.464 1.367 0 0.337 0 0.425 0.3 1.103 15 Pilot 1.108 0.53 0.835 0.835 0.388 0.304 3.882 1.248 1.248 0.132 0.304 0.304 1.103 0.132 1.248 0.304 0.132 0.335 0.304 0.335 0.335 0.532 1.248 1.328 2.333 0 1.103 0 0.532 1 1.373 2 PA 0.606 0.28 0.457 0.457 0.218 0.166 2.177 0.683 0.683 0.072 0.166 0.166 0.606 0.072 0.633 0.166 0.072 0.457 0.166 0.457 0.457 0.281 0.633 0.547 1.276 0 0.606 0 0.281 0.547 0.754 5 RPA 0.475 0.23 0.358 0.358 0.171 0.13 1.707 0.536 0.536 0.056 0.13 0.13 0.475 0.056 0.536 0.13 0.056 0.353 0.13 0.353 0.353 0.223 0.536 0.428 0.734 0 0.475 0 0.228 0.428 0.581 31 S&T 2E+07 1E+07 2E+07 2E+07 8E+06 6E+06 8E+07 2E+07 2E+07 3E+06 6E+06 6E+06 2E+07 3E+06 2E+07 6E+06 3E+06 2E+07 6E+06 2E+07 2E+07 1E+07 2E+07 2E+07 4E+07 5E+07 - 2E+07 1 1E+07 2E+07 3E+07 6 SE 1 0.48 0.754 0.754 0.358 0.274 3.582 1.127 1.127 0.118 0.274 0.274 1 0.118 1.127 0.274 0.118 0.754 0.274 0.754 0.754 0.43 1.127 0.802 1.65 2.105 0 0 0.43 0.802 1.244 32 SF 2E+07 1E+07 2E+07 2E+07 8E+06 6E+06 8E+07 2E+07 2E+07 3E+06 6E+06 6E+06 2E+07 3E+06 2E+07 6E+06 3E+06 2E+07 6E+06 2E+07 2E+07 1E+07 2E+07 2E+07 4E+07 5E+07 1 2E+07 1E+07 2E+07 3E+07 22 Space^Nuke^M.O. 2.085 1 1.572 1.572 0.748 0.572 7.481 2.351 2.351 0.248 0.572 0.572 2.035 0.243 2.351 0.572 0.243 1.572 0.572 1.572 1.572 1 2.351 1.331 3.441 4.338 0 2.035 0 1.331 2.583 16 SI 1.108 0.53 0.835 0.835 0.388 0.304 3.882 1.248 1.248 0.132 0.304 0.304 1.103 0.132 1.248 0.304 0.132 0.335 0.304 0.335 0.335 0.532 1.248 1 1.328 2.333 0 1.103 0 0.532 ■ 1.373 3 Vk 0.804 0.38 0.606 0.606 0.288 0.221 2.888 0.806 0.806 0.086 0.221 0.221 0.304 0.086 0.806 0.221 0.086 0.606 0.221 0.606 0.606 0.386 0.806 0.726 1.327 1.682 0 0.304 0 0.336 0.726 FE odds of not being fully manned x>1000 High 1000 > x > 100 Sig 100 > x > 1 Mod 1 > x > 0 Low Appendix Figure 3 20 Appendix IV. FE Significant Difference in Manning OR Analyses Acq lirfld Orf2 Sys Oj CE | Chap. | Naus ICC/SLl Contr. □ist. Fin. Dree Sule-alth Srj Hist. Insp. | | Intel. | LE LG Plan) | Mk | | Mafl I [isn As^ Muns pps Mg[)ps Plar| Pilot | PA | RPA 1 S&T 1 1 SE 1 1 SF 1 eiT.JukeJ SI | Wk Acq 0.40 0.754 0.754 0.359 0.274 3.592 1.127 1.127 0.119 0.274 0.274 1 0.119 1.127 0.274 0.119 0.754 0.274 0.754 0.754 0.46 1.127 0.902 1.65 2.105 0 1 0 0.4@ 0.902 1.244 Airfld Ops 2.035 1.572 1.572 0.749 0.572 7.491 2.351 2.351 0.249 0.572 0.572 2.005 0.249 2.351 0.572 0.249 1.572 0.572 1.572 1.572 1 2.351 1.001 3.441 4.399 0 2.005 0 1 1.001 2.593 C2 Sys Ops 1.327 0.64 1 0.477 0.364 4.766 1.495 1.495 0.150 0.364 0.364 1.327 0.150 1.495 0.364 0.150 1 0.364 1 1 0.636 1.495 1.197 2.109 2.792 non 1.327 0 0.636 1.197 1.65 CE 1.327 0.64 1 0.477 0.364 4.766 1.495 1.495 0.150 0.364 0.364 1.327 0.150 1.495 0.364 0.150 1 0.364 1 1 0.636 1.495 1.197 2.109 2.792 0 1.327 0 0.636 1.197 1.65 Chap. 2.702 1.33 2.097 2.097 0.763 9.996 3.136 3.136 0.331 0.763 0.763 2.702 0.331 3.136 0.763 0.331 2.097 0.763 2.097 2.097 1.334 3.136 2.51 4.591 5.956 0 2.702 0 1.334 2.51 3.46 Naus 3.645 1.75 2.747 2.747 1.31 13.09 4.109 4.109 0.433 1 1 3.645 0.433 4.109 1 0.433 2.747 1 2.747 2.747 1.746 4.109 3.299 6.014 7.671 0 3.645 0 1.746 3.299 4.533 CC/SL 0.270 0.13 0.21 0.21 0.1 0.076 - 0.314 0.314 0.033 0.076 0.076 0.276 0.033 0.314 0.076 0.033 0.21 0.076 0.21 0.21 0.133 0.314 0.251 0.459 0.566 rol 0.276 0 0.133 0.251 0.346 Contr. 0.007 0.43 0.669 0.669 0.319 0.243 3.197 1 0.105 0.243 0.243 0.007 0.105 1 0.243 0.105 0.669 0.243 0.669 0.669 0.425 1 0.0 1.464 1.067 0 0.007 0 0.425 0.0 1.103 □ist. 0.007 0.43 0.669 0.669 0.319 0.243 3.107 1 0.105 0.243 0.243 0.007 0.105 1 0.243 0.105 0.669 0.243 0.669 0.669 0.425 1 0.0 1.464 1.067 0 0.007 0 0.425 0.0 1.103 Fin. 0.414 4.04 6.343 6.343 3.024 2.309 30.23 9.495 9.465 2.309 2.309 0.414 1 9.495 2.309 1 6.343 2.309 6.343 6.343 4.035 9.465 7.592 13.00 17.71 0 0.414 0 4.035 7.592 10.46 Force Supt 3.645 1.75 2.747 2.747 1.31 1 13.09 4.109 4.109 0.433 1 3.645 0.433 4.109 1 0.433 2.747 1 2.747 2.747 1.743 4.109 3.299 6.014 7.671 0 3.645 0 1.743 3.299 4.533 Health Srus 3.645 1.75 2.747 2.747 1.31 1 13.09 4.109 4.109 0.433 1 3.645 0.433 4.109 1 0.433 2.747 1 2.747 2.747 1.740 4.109 3.299 6.014 7.671 0 3.645 0 1.740 3.299 4.533 Hist. 1 0.40 0.754 0.754 0.359 0.274 3.592 1.127 1.127 0.119 0.274 0.274 ■ 0.119 1.127 0.274 0.119 0.754 0.274 0.754 0.754 0.40 1.127 0.902 1.65 2.105 0 1 0 0.40 0.902 1.244 Insp. 0.414 4.04 6.343 6.343 3.024 2.309 30.23 9.495 9.495 1 2.309 2.309 0.414 9.495 2.309 1 6.343 2.309 6.343 6.343 4.035 9.495 7.592 13.00 17.71 0 0.414 0 4.035 7.592 10.46 Intel. 0.007 0.43 0.669 0.669 0.319 0.243 3.107 1 1 0.105 0.243 0.243 0.007 0.105 1 - 0.243 0.105 0.669 0.243 0.669 0.669 0.425 1 0.0 1.464 1.067 0 0.007 0 0.425 0.0 1.103 LE 3.645 1.75 2.747 2.747 1.31 1 13.09 4.109 4.109 0.433 1 1 3.645 0.433 4.109 0.433 2.747 1 2.747 2.747 1.740 4.109 3.209 6.014 7.671 0 3.645 0 1.740 3.209 4.533 LG Plans 6.414 4.04 6.343 6.343 3.024 2.309 30.23 9.495 9.495 1 2.309 2.309 0.414 1 9.495 2.309 6.343 2.309 6.343 6.343 4.035 9.495 7.592 13.06 17.71 0 0.414 0 4.035 7.592 10.46 Mh 1.327 0.64 1 1 0.477 0.364 4.766 1.495 1.495 0.150 0.364 0.364 1.327 0.150 1.495 0.364 0.150 0.364 1 1 0.636 1.495 1.197 2.109 2.792 rol 1.327 0 0.636 1.197 1.65 Mat'l 3.645 1.75 2.747 2.747 1.31 1 13.09 4.109 4.109 0.433 1 1 3.645 0.433 4.109 1 0.433 2.747 2.747 2.747 1.746 4.109 3.299 6.014 7.671 0 3.645 0 1.746 3.299 4.533 Msn Assr. 1.327 0.64 1 1 0.477 0.364 4.766 1.495 1.495 0.150 0.364 0.364 1.327 0.150 1.495 0.364 0.150 1 0.364 1 0.636 1.495 1.197 2.199 2.792 0 1.327 0 0.636 1.197 1.65 Muns 1.327 0.64 1 1 0.477 0.364 4.766 1.495 1.495 0.150 0.364 0.364 1.327 0.150 1.495 0.364 0.150 1 0.364 1 0.636 1.495 1.197 2.199 2.792 0 1.327 0 0.636 1.197 1.65 Ops Mqt 2.065 1 1.572 1.572 0.749 0.572 7.491 2.351 2.351 0.240 0.572 0.572 2.005 0.240 2.351 0.572 0.240 1.572 0.572 1.572 1.572 2.351 1.001 3.441 4.399 0 2.005 0 1 1.001 2.593 Ops Plans 0.007 0.43 0.669 0.669 0.319 0.243 3.197 1 1 0.105 0.243 0.243 0.007 0.105 1 0.243 0.105 0.669 0.243 0.669 0.669 0.425 0.0 1.464 1.967 0 0.007 0 0.425 0.0 1.103 Pilot 1.100 0.53 0.035 0.035 0.390 0.304 3.902 1.249 1.249 0.132 0.304 0.304 1.100 0.132 1.249 0.304 0.132 0.035 0.304 0.035 0.035 0.532 1.249 1.029 2.333 0 1.100 0 0.532 1 1.370 PA 0.606 0.29 0.457 0.457 0.210 0.166 2.177 0.603 0.603 0.072 0.166 0.166 0.606 0.072 0.603 0.166 0.072 0.457 0.166 0.457 0.457 0.291 0.603 0.547 1.276 0 0.606 0 0.291 0.547 0.754 RPA 0.475 0.23 0.350 0.350 0.171 0.13 1.707 0.536 0.536 0.056 0.13 0.13 0.475 0.056 0.536 0.13 0.056 0.350 0.13 0.350 0.353 0.226 0.536 0.429 0.794 0 0.475 0 0.229 0.429 0.591 S&T 2E+07 1E+07 2E+07 2E+07 6E*06 6E+06 0E+O7 2E+07 2E+07 3E+06 6E+06 6E+06 2E+07 3E+06 2E+07 6E+06 3E+06 2E+07 6E+06 2E+07 2E+07 1E+07 2E+07 2E+07 4E+07 5E+07 2E+07 1 1E+07 2E+07 3E+07 SE 1 0.46 0.754 0.754 0.359 0.274 3.592 1.127 1.127 0.119 0.274 0.274 1 0.119 1.127 0.274 0.119 0.754 0.274 0.754 0.754 0.40 1.127 0.902 1.65 2.105 0 0 0.40 0.902 1.244 SF 2E+07 1E+07 2E+07 2E+07 0E*O6 6E+06 0E+O7 2E + 07 2E+07 3E+06 6E+06 6E+06 2E+07 3E+06 2E+07 6E+06 3E+06 2E+07 6E+06 2E+07 2E+07 1E+07 2E+07 2E*07 4E+07 5E + 07 1 2E+07 1E+07 2E+07 3E+07 Space^Nuke^M.O. 2.065 1 1.572 1.572 0.749 0.572 7.491 2.351 2.351 0.249 0.572 0.572 2.065 0.249 2.351 0.572 0.249 1.572 0.572 1.572 1.572 1 2.351 1.001 3.441 4.369 0 2.065 0 1.001 2.593 SI 1.100 0.53 0.035 0.035 0.399 0.304 3.992 1.249 1.249 0.132 0.304 0.304 1.100 0.132 1.249 0.304 0.132 0.035 0.304 0.035 0.035 0.532 1.249 1 1.629 2.333 0 1.100 0 0.532 1.370 Wk 0.004 0.39 0.606 0.606 0.209 0.221 2.009 0.906 0.906 0.096 0.221 0.221 0.004 0.096 0.906 0.221 0.096 0.606 0.221 0.606 0.606 0.306 0.906 0.726 1.327 1.692 n o j 0.004 0 0.306 0.726 Appendix Figure 4 Considered statistically different 21