Intervention Effectiveness Research Engineering Design of Safety and Health Programs by
Optimizing Intervention Activity
Joel M. Haight, Ph.D., P.E., CSP, CIH
Assistant Professor
Penn State University
University Park, PA 16802
Abstract
Safety and health programs are often implemented without a quantified design. The objective of this
study was to determine if a safety and health program could be quantified and optimized through a
design that minimizes incident rates and the percentage of available human resources required to
implement it. A model was developed for this purpose.
In a two-phase empirical study, an oil production operation was analyzed. Four categories of
interventions were studied 1) behavior modification, incentives, awareness; 2) training; 3)
job/procedural design; 4) equipment.
The percentage of available time spent implementing
interventions in these categories was the independent variable and the incident rate was the dependent
variable. Findings show a mathematical relationship between interventions and incident rate. The
resulting best-fit equation is an intuitively expected exponential function showing a decreasing
incident rate with an increasing intervention application rate. This model can be used to analyze the
mathematical function for a minimized incident rate, aiding in design of optimized safety and health
programs.
In the second phase, an attempt was made to determine whether a designed safety and health
program could be optimized to minimize the loss producing incident rate. In this phase, the
objective was to use the mathematical function developed in phase 1 to formulate a model that
calculates a minimized incident rate. Evaluating 81 application rate level combinations of four
intervention categories and subjecting them to management constraints accomplished this. The
resulting model provided insight into the design of a safety and health program that prescribes the
appropriate amount of human resource time that should be assigned to specific safety and health
intervention activity.
Actual verification data were used to test the adequacy and accuracy of the optimization model.
Findings indicate that the model predicts with reasonable accuracy, intuitively expected results. The
model shows promise as a potential tool to aid safety and health engineers in designing their safety
and health programs. It also shows promise in providing some predictability of safety and health
performance under given safety and health program designs (Haight, Thomas, Smith, Bulfin and
Hopkins, 2001).
Introduction
Workplace injuries and property damage—and the safety programs designed to prevent them—are
expensive facets of contemporary industrial, agricultural, and military activities. Indeed, the National
Safety Council estimates that the cost of work place injuries totaled $128 billion in 1999, a value
approximately equal to the combined profits of the top 30 Fortune 500 corporations (National Safety
Council Website). Optimizing intervention strategies to decrease rates of injury and property damage
with less costly safety programs would contribute to improved productivity and economic vitality in
all activities that involve such risks. The results could lead to improved safety practices and
improved profitability in American industry.
It is difficult to predict the future. Even in some of today’s more established sciences, we have
trouble predicting what might happen tomorrow and beyond. What will tomorrow’s weather be?
What will the stock market do next week or next year? Who will win the NCAA football
championship next year? It is even more difficult to predict the future in less established sciences.
What will your injury rate be next year? What is your target rate or goal? How will you know? How
will you get there? How much manpower will you need (Figure 1)? These are questions that many
in the safety engineering profession, would like to be able to answer scientifically.
0 %
50 %
100 %
Figure 1. Available Human Resource Scale (How much human resource will be required?)
Many organizations whose activities involve the risk of injury or destruction of property
commit human and financial resources to intervention activities intended to prevent injuries, fires,
spills, chemical releases, etc. Many of these “safety-related” interventions, including activities such
as safety training and facility inspections, are commonplace enough that, often, little attempt is made
to determine whether they are effective, whether they are at optimum levels and whether they might
be improved. A model has been developed to help us determine which intervention activities are
working to prevent or reduce incidents and to what extent they are working (Haight, et. al., 2001).
From this model, we can determine the right “recipe” or correct design for our safety or loss
prevention programs (Rinefort, 1977) in terms of usage of human resource power.
The Model
The basis for the model is a mathematical approach to designing an effective safety program
developed by Haight, et. al. 2001. The model proposes the rate of incidents be I and Ai, i = 1, 2 … N,
be the expenditure rate of human resources in intervention activities. The original model relating I
and the Ai is a non- linear relationship:
I  f A1 ,..., AN ; p1 , ..., pM 
(1)
in which the p’s are parameters controlling the application of the various intervention activities.
After being determined empirically through statistical analysis of safety activities in an oil and
gas production operation, the mathematical relationship was used to design an optimum safety
intervention program that minimized expenditure of available human resource time in intervention
activities while still minimizing incidents. The model thus represents a safety and health system
(Figure 2). (Haight, et. al. 2001)
There is currently a research effort in progress with a Canadian power company to further
prove the model and give it wider applicability by extending it to other industries and government
organizations. It is expected that as the database size increases and as more industries are
represented, model results may become generalizable across other industries.
INPUT (Independent)
OUTPUT (Dependent)
Intervention Application Rate
Incident Rate
Factor A – Behavior based
activities, motivation,
awareness, incentives,
etc., interventions
Factor B – Safety and skill
enhancement training
interventions
Incident Rate
Safety & Health
System Model
Factor C – Job Design
interventions
Factor D – Equipment
interventions (e.g.,
inspections, preventive
maintenance, etc.)
Figure 2. This is a representation of the Safety and Health System Model (Haight et. al. 2001).
In the application of the model, study participants record time spent by employees
implementing four categories of interventions and the weekly rate of incidents. The analysis relies on
data recorded by the study participants without intervention by the researchers.
The incident rate is the dependent variable and the intervention application rates for four
categories of intervention activity are the independent variables. All variables are normalized by
worker hours. The observed data thus compare the fraction of available worker-hours applied to
implementing interventions to the rate at which incidents occur. The data analysis process takes
account of the individual and interactive effects of four main intervention activities, producing 15
independent variables whose contributions are isolated through regression techniques.
The effects of safety intervention activity are neither instantaneous nor permanent. The timedelay and carry-over effects are detected using moving average and exponential smoothing
techniques to identify changes in statistical relationships between the dependent and independent
variables over the course of the forward projected averaging and smoothing periods.
The resulting empirical version of Equation 1 for the particular firm being studied becomes the
objective function in a mathematical programming model that can be used to determine optimum
strategies for obtaining minimum incidents at a reduced cost of intervention. If such a strategy is
adopted by the firm on which the model is based, then subsequent observations either validate the
model or reveal new aspects of that safety program that must be investigated.
The initial application of the model to an oil production operation showed that a strong
mathematical relationship exists between the independent and dependent variables and that the
function was optimizable using operations research-based mathematical modeling techniques. Post
analysis observation of incident rate data indicates that the lowest injury and incident rates occurred
when the organization’s safety program was operating in the optimum range of human resource
commitment (Haight, et. al. 2001).
Discussion of a Completed Study
A previous two-phase study on intervention effectiveness was done in 1998/1999 in an oil and gas
production operation in Central Asia (Haight, et. al. 2001).
Safety programs are often implemented without a quantified design. Research has now shown
that a loss prevention system can be quantified, designed, and therefore, optimized as any
engineering-based system. In support of this effort, a statistically significant mathematical
relationship was shown between the intervention activity implemented to reduce the incident rate
(independent variable) and the incident rate itself (dependent variable). Many literature studies are
available evaluating the effectiveness of individual intervention activities (examples are Fellner and
Sulzer-Azaroff, (1984); McKelvey, Engen and Peck, (1973); Kalsher, Geller, Clark, and, Lehman
(1984)). Building on these studies, this initial research evaluated a complete loss prevention system
exploring all main effects from a comprehensive set of interventions as well as the interactive effects
between interventions. The study integrated all components of a defined loss prevention system in
order to establish a mathematical relationship that would allow for the design and optimization of a
complete loss prevention program (Haight, et. al. 2001).
Experimental Method and Design of the Original Study
During Phase 1 of the study, the subject organization operated with 130 employees. Collectively,
these employees worked approximately 5500 hours per week. For 26 weeks, the employees tracked
and reported the amount of time they spent implementing four categories of interventions and the
resulting weekly incident rate (both the traditional and total incident rates). “Traditional incident
rates” included spills, fires, injuries, toxic releases, etc., while “total incident rates” included the
traditional incidents as well as unplanned process upsets or shutdowns and equipment damage, etc.
Reported data were used for the research. The researcher did not intervene in the implementation of
the program (Haight, et. al. 2001).
The independent variables were quantified each week using the amount of man-hours applied
by the work group of 130 employees to the defined intervention activities. These hours were
normalized as percentage of total available hours, referred to as the “intervention application rate”.
The dependent variable was developed by recording the number of incidents that occurred during
each week, multiplying it by 200,000 hours and dividing it by the number of hours worked by the 130
employees, yielding the “incident rate.” This was done for both traditional incidents and total
incidents (Haight, et. al., 2001).
Analysis and Results
The combined 26 weeks of intervention application rate and incident rate data were recorded for the
four factors (main effects) and the two incident rates. The cross multiplication products of the main
effects to account for interactive effects between factors were computed. To integrate all interactive
effects from the two- , three- , and four-factor interactions, 15 independent variables resulted. A
representation of the spreadsheet is shown in figure 3.
Figure 3. This is a representation of data collection and totaling spreadsheet (Haight, et. al. 2001).
Week
Factor A
Factor B
Factor C
Factor D AxB
nxn
AxBxC
nxnxn
AxBxCxD
1
2
n
Xa1
.
Xan
Xb1
.
Xbn
Xc1
.
Xcn
Xd1
.
Xdn
.
Xabc1
.
Xabcn
.
.
.
.
.
.
Xab1
.
Xabn
.
Traditional
Incident Rate
Ytr1
.
Ytrn
Total Incident
Rate
Yt1
.
Ytn
To determine a best-fit function for these data, several regression analyses were carried out
using the least squares method, considering both linear and non-linear fits. To evaluate how long the
effect of an intervention lasts, weekly data points were used. To calculate two- , three- , four- , five- ,
and six-week effects, forward projected moving average and exponential smoothing techniques were
applied. From this, one can determine if any effect from week one carries over to week two, three,
four, etc., by assessing the quality of the regression fit.
The forward-projected exponential
smoothing equation was adapted from Elsayed and Boucher (1994): (Haight, et. al. 2001)
Xt = Xt + (1-)*Xt+1 + (1-) 2*Xt+2+(1-) t+2*X1 + (1-) t *X0
Discussion of Results
Analysis showed that the best fit occurs when regressing the four-week moving average model and
traditional incident rate. The resulting function was exponential, with an R2 = 0.982209, F0 = 25.764
vs. F=.01,15,7 = 6.31, and Mean Square Error (MSE)= 0.78069. A strong fit also occurs in:
1.
The non-linear four-week exponential smoothing model for the traditional incident rate
with an R2 = 0.978429, F0 = 21.16714 vs. F=.01,15,7 = 6.31, and an MSE = 0.949857, and;
2.
The non-linear five-week moving average and exponential smoothing, traditional incident
rate cases, with R2 values = 0.963596 and 0.968286, F0 = 10.587, and 12.21272 vs.
F=.01,15,6 = 7.56, and MSE values = 1.01647 and 0.89773 respectively.
Figure 4 shows graphically the total intervention application rate curve. As
demonstrated, the exponential trend line is fit to the total intervention application rate, and it
still generates an R2 value of 0.5317 without all the interactive effects shown. As was noted
above, with all interactive effects and variables included, the R2 is 0.98209.
Figure 4. This graph shows the total percentage of available man-hours vs. traditional incident rate,
with the exponential function shown (Haight, et. al. 2001)
Incident Rate
Incident-vs-Intervention Application Rates
30
25
20
15
10
5
0
-5 0
y = 25e-0.248x
R2 = 0.5317
10
20
30
40
Intervention Application Rate (% of Available Manhours)
Series1
Expon. (Series1)
The resulting function for the four-week case linear transformed function is shown in Figure 5.
Figure 5. This mathematical function shows the relationship between the incident rate and all 15
regressor variables
LnY=Xabcd*lnmabcd+Xbcd*lnmbcd+Xacd*lnmacd+Xabd*lnmabd+Xabc*lnmabc+Xcd*lnmcd+Xbd*lnmbd
+Xbc*lnmbc+Xad*lnmad+Xac*lnmac+Xab*lnmab+Xd*lnmd+Xc*lnmc+Xb*lnmb+Xa*lnma+b
LnY=Xabcd*(ln0.00188)+Xbcd*(ln3.826E+16)+Xacd*ln(2014.943)+Xabd*ln(6.966)+Xabc*ln(4.2998E
+12)+Xcd*ln(1.85E13)+Xbd*ln(.001597)+Xbc*ln(7.01E65)+Xad*ln(0.150024)+Xac*ln(5.82E11
)+Xab*ln(.000517)+Xd*ln(404.4604)+Xc*ln(1.063E+45)+Xb*ln(449.5E+7)+Xa*ln(526.9246)+1.03
E-7.
Where Y is the incident rate, Xi is the individual intervention values for each of the 15 factors, and mi
is the slope at each represented point on the curve. The function shown here contains actual m value
(Haight, et. al. 2001)
Introduction - Phase 2
In the second phase, an attempt was made to determine whether a designed loss prevention program
could be optimized to minimize the loss producing incident rate while minimizing the intervention
application rate. The primary objective was to use the phase 1 mathematical function to formulate a
model that calculates a minimized incident rate. Evaluating 81 application rate level combinations of
the four intervention categories and subjecting them to management constraints accomplished this. A
theoretical minimum incident rate could be achieved evaluating the objective function, using the 81
different combinations of the four categories of intervention activities. The resulting model provided
insight into the design of a safety or loss prevention program that will prescribe an appropriate
amount of human resource time that should be assigned to safety intervention activity.
The secondary objective was to use verification data with phase 1 data to test the adequacy and
accuracy of the optimization model. The findings indicated that the model predicts with reasonable
accuracy, intuitively expected results.
Verification data shows that the model’s “optimum”
intervention application rate was within the actual observed lower incident rate range. The model
mathematically generated incident rates from which minimum values could be observed and chosen.
(Haight, et. al. 2001)
Experimental Method
This phase involved experimental and theoretical application of data to the mathematical model. The
best-fit equation from the four-week moving average model, for traditional incident rates was chosen
for the objective function. A total intervention application rate constraint of less than or equal to 20%
of available man-hours was established. The process induced a constraint) requiring the incident rate
(y) to be greater than or equal to 0 (i.e. no incidents produces an incident rate of 0. The objective
function that resulted is shown in Figure 6.
Figure 6. This objective function covers the relationship between the incident rate and all 15
regressor variables
Minimize:
LnY=Xabcd*lnmabcd+Xbcd*lnmbcd+Xacd*lnmacd+Xabd*lnmabd+Xabc*lnmabc+Xcd*lnmcd+Xbd*lnmbd+
Xbc*lnmbc+Xad*lnmad+Xac*lnmac+Xab*lnmab+Xd*lnmd+Xc*lnmc+Xb*lnmb+Xa*lnma+b
S.T.
XA +XB+XC+XD <= 20%
Y => 0
Shown with the m values included, the complete objective function is as follows:
LnY=Xabcd*ln(0.00188)+Xbcd*ln(3.826E+16)+Xacd*ln(2014.943)+Xabd*ln(6.966)+Xabc*ln(4.2998E
+12)+Xcd*ln(1.85E13)+Xbd*ln(.001597)+Xbc*ln(7.01E65)+Xad*ln(0.150024)+Xac*ln(5.82E11
)+Xab*ln(.000517)+Xd*ln(404.4604)+Xc*ln(1.063E+45)+Xb*ln(449.5E+7)+Xa*ln(526.9246)+1.03
E-7.
This function became the objective function for the mathematical model. Y is the incident rate, and
Xa, Xab, Xabc, etc., were the individual intervention values for each of the 15 factors, including crossmultiplied interactive effects; mi is the regression coefficient. (Haight, et. al. 2001).
The intervention combinations were developed using the original data from phase 1. The
(max/min) range of intervention application rate values for each of the intervention categories was
divided into three equal segments to represent three levels of each factor. The median value in each
range (one-third) was chosen to represent that level for each factor, generating three levels for each of
the four factors. This was then used in the design of a three-level, four-factor experimental design
(34). The result was 81 factor-level combinations for the reported intervention application rate and
these combinations were used to evaluate the model. As a demonstration, some of the resulting
combinations are represented in Figure 7.
Figure 7. This table is an abbreviated representation of the factor level combinations of the four
factors that were run in the optimization model (Haight, et. al. 2001)
Factor Level
Combinations
A1B1C1D1
A1B1C1D2
A1B1C1D3
A1B1C2D1
A1B1C2D2
A1B1C2D3
.
.
A3B3C3D3
Cross-product multiplication results to account for interactive effects are represented in Figure 8.
Figure 8. A representation of the cross-product multiplication is shown. This accounts for factor
interactive effects. There were 15 variables to consider. (Haight, et. al. 2001)
A B C D AB AC AD BC BD CD ABC ABD BCD ACD ABCD
Each of the 81 combinations of the 15 input variables was then plugged into the objective
function. The objective function yielded 81 different possible incident rates (y). The resulting (y)
value was then converted to a natural log, to account for a linear transformation of the original
exponential function that resulted when the mathematical relationship was first established. All
results yielding an intervention application rate greater than 20% and a (y) less than 0 were
discounted as being outside the constraints. “Minimum “y” values were sorted to the top of the list
for consideration. Finally, verification data were compared to the theoretical minimum incident rates
to validate the model.
Analysis and Results
The 81 intervention combinations were systematically evaluated. The highest 20 combinations (or
the 20 lowest “(ln y)”) values were selected for comparison to verification data.
The total
intervention application rate for the four main effects in these 20 results ranged from approximately
eight to seventeen percent of the total available man-hours.
From phase 1 data only, it was evident that when the total intervention application rate was in
the 5.01–10% range, the mean traditional and total incident rates were significantly lower than when
intervention application rate was in the 0-5 % range and the 10.01% and above ranges. The same
phenomenon is evident when the eleven-week verification data are incorporated into the database.
This is consistent with the findings of the theoretical model, which showed the lowest incident rates
(lowest 5 results) to be in the 8–10% range (Haight, et. al. 2001).
Discussion of Results
The theoretical minimum incident rate is achieved when the total intervention application rate is in
the range of 8-17 % (results of the 20 lowest incident rates generated by the operations research
model). The three lowest results, as seen in Table 1, indicate a design using levels 1) A1B1C1D1, 2)
A1B1C2D1, and 3) A1B1C3D1, with a total input of 8-9%. This can be illustrated by applying an
example. If design number one (A1B1C1D1) were selected, the intervention application rate ranges
for each factor-level combination would be:
Factor A (level 1): 2.754% - 4.151%
Factor B (level 1): 0.602% - 1.224%
Factor C (level 1): 0.128% - 0.669%
Factor D (level 1):5.271% - 10.187%
This design generated a total intervention application rate, at the low end, of 8.755% (by adding
above listed minimum values in the above listed ranges for each level) and at the high end of
16.231% (by adding above listed maximum values in the ranges for each level). This result is within
the range obtained by using the 20 lowest incident rates produced by the model (8–17%).
It appears that the total incident rates may also follow this same convex pattern, with the
minimum being achieved in the 5.01-10 % range. However, the means are not sufficiently different
from each other to make a “minimum result” claim, as with the traditional incident rates. In each
case, lower incident rates are achieved at intervention application rates greater than 20%, but they do
not meet the constraint criteria. (Haight, et. al. 2001)
Conclusions
Safety interventions are implemented in safety programs because they are expected to reduce the
incident rate. Intuitively, one would expect that the more intervention activity applied to the safety
program, the lower the incident rate would be. One might also expect that at some point, an effect
would be present, but the incident rate reduction would be diminishing as more intervention activity
is applied. The model showed this to be true for the oil production operation.
This research indicates strongly that the incident rate is sensitive to the intervention application
rate for traditional incidents and that a statistically significant relationship exists between the
interventions and the incident rate. The function appears to allow for prediction of incident rates.
The question of how long the effect of a particular intervention lasts appears to have been answered
for the organization studied (four weeks). Interestingly, the interventions did not appear to have a
strong effect on “total incidents.” (These are the unplanned process upsets and shutdowns and/or
equipment damage cases.) Possibly, it can be suggested that many of the mature and developed
safety interventions in practice have developed over time with the intent of only preventing
“traditional incidents”. Many modern industrial organizations tend to refer to all incidents as the
same, regardless of their consequences (e.g., production down time vs. an injury is the same).
Relative to the effect of the interventions in this study, that may not be the case. This is left for
further and future research.
Employing the mathematical relationship from phase 1, the optimization model produces a
minimized incident rate. The model appears to be valid for the facility that it was designed to
represent. However, it could be refined through further testing against more extensive field data.
The study provides a valuable potential approach to assist engineers in designing future safety
and health programs. The model appears to provide intuitively expected and verifiable results that
facilitate design and optimization of a program. The design minimizes the incident rate while
facilitating selection of intervention application rates that are well under the total application rate
constraint suggested by management.
Limitations
An adequate amount of error degrees of freedom exist for this study. However, the study could have
been strengthened with more data. However, since it takes considerable time to collect the data,
extending the study would introduce the risk of having the program change in the middle.
The results of this model are not transferable. It is based on the specific performance data from
the organization being studied. Other organizations employ different interventions of different
qualities and different management philosophies, etc. The model works, but to apply this model, an
organization would need to accumulate its own data. Eventually, it is expected that the database will
grow sufficiently to allow for more generalization and transferability of results.
Future Research
This study evaluated the effect of changing the quantity of the loss prevention interventions. Further,
the quality of the interventions was not studied. Intervention quality is an important aspect of any
safety and health program, and that aspect should be incorporated into future research. In this study,
quality of the interventions was not changed throughout the study.
This study lends itself to further research. Other types of operations should be studied and
other loss prevention systems with different interventions should be investigated. Larger databases
applied to the models would lend more confidence to the results.
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