Predicting Injuries
at Michael D Computer
Company
Tee Welton
6.780 – Semiconductor
Manufacturing
Agenda
“ Background
“ Qualitative
Data Analysis
“ Poisson Regression Model
“ Injury Model Results
“ Sensitivity Analysis
“ Summary
Background
“ Internship
at Michael D Corp
“ Task: To correlate Headcount and
factors of Productivity
“ Concern: Non-Productivity factors such
as Injury Rates and Quality are
important too
Background (2)
“
This Report: Determine how Headcount and
Other factors impact the number of Injuries
seen in the factory
“
Given: Injuries are Poisson distributed with
value of 0, 1,2, or 3
Qualitative Analysis
“ Output
seems to have an impact on Injury
levels (not certain)
“ Shift data shows Shift 2 appears to have
more Injuries (0.96 vs. 0.67 average)
3
First
Second
100
100
N=64 2.5
80
Percent
70
60
50
40
30
20
N=64
90
80
2
70
60
1.5
50
40
1
30
0.5
20
10
10
0
0
0
0
1
2
5000
3000
Total
Factory
Injuries7000
3
0
1
2
17000
15000
9000 11000 13000
Total
Factory
Injuries
RTDB Output
3
Cum Percent
Total Factory Injuries
90
Qualitative Analysis (2)
“ Day
of the Week (hard To determine
trends)
“ Saturday and Monday look significant,
but it is hard to tell.
Pareto Plot
FRI
THU
WED
TUE
MON
SAT
100
100
N=22
N=24
N=26
N=26
N=24
N=6
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
0
0
0
1
2
3
Total Injuries and Near Misses
0
1
2
3
Total Injuries and Near Misses
0
1
2
3
Total Injuries and Near Misses
0
1
2
3
Total Injuries and Near Misses
0
1
2
3
Total Injuries and Near Misses
0
1
2
3
Total Injuries and Near Misses
Cum Percent
Percent
90
Poisson Regression Model
“
Poisson Distribution is described with the
following equation:
“
P(Y=k) = Exp(-µ)*µ n / n!
“
µ can be value or linear equation
“
The Poisson Loss Function guarantees
“
“
“
“
No negative values
No skewness
No growing variability with mean growth
Final Poisson Loss function
“
(3)
Ln(Y) = -(InjuriesAndNearMisses*model- Exp(model))
-Log(Γ(InjuriesAndNearMisses+1))
Poisson Regression Model (2)
“
The model setup included these factors:
Variable
Injuries and Near Misses
Description
This variable is the target of the study. It is a count of
the Injuries that occurred in the factory, as well as
incidents recorded that could have resulted in an injury
on the factory floor, but was avoided. This information
is collected by shift.
S hift
This is the shift of the factory for which the injury data
was collected.
Total Headcount
The total headcount of the TM C factory floor, collected
by the shift.
This is a measure of the total number of hours worked in
each shift.
This measures the total output, as the number of units
Total Output
shipped from the factory, for each shift.
Percent Temporary Employees This measures the number of temporary employees used
in the factory, as a percent of the total workforce. This
would be used to measure the impact of using temporary
employees on the number of injuries seen in the factory.
This is the day of the week for the model.
Day of the Week
Hours in the S hifts
Injury Model Results
Output gives Estimate, Upper and Lower
Limits
“ Confidence Limits test effect significance
“
Param eter
Estim ate
ApproxStdErr Low er CL
Upper CL
Monday
-0.836
0.405
-1.681
-0.072
Tuesday
-0.012
0.292
-0.584
0.566
Friday
-0.032
0.341
-0.716
0.63
Saturday
1.102
0.459
0.152
1.967
Wednesday
-0.422
0.321
-1.066
0.202
Second
1.048
0.385
0.299
1.812
Intercept
-0.125
1.688
-3.36
3.277
rcentTempCo
-7.711
3.65
-14.885
-0.542
rsWorkedCoe
0.068
0.181
-0.3
0.41
HeadcountCoe
0.879
0.439
0.025
1.75
OutputCoeff
-0.008
0.097
-0.187
0.192
Injury Model Results (2)
“ Analysis
of Residuals shows no trends
“ Concern: Unexplained low values
“ Std Dev = MSE = 0.867 for the model
1.5
1
Residuals
0.5
0
-0.5
-1
-1.5
-2
-2.5
-3
07/02
703
07/2
07/25/2
07/23/20
07/20/200
07/18/2002
07/16/2002
07/13/2002
07/11/2002
07/09/2002
07/03/2002
07/01/2002
06/27/2002
06/25/2002
06/21/2002
06/19/2002
06/17/2002
06/13/2002
06/11/2002
06/08/2002
06/06/2002
06/04/2002
05/31/2002
05/29/2002
05/24/2002
05/22/2002
05/20/2002
05/16/2002
05/14/2002
05/10/2002
05/08/2002
05/06/2002
07
07/2
07/26/
022
07/24/2
07/22/200
07/19/2002
07/17/2002
07/15/2002
07/12/2002
07/10/2002
07/08/2002
07/02/2002
06/28/2002
06/26/2002
06/24/2002
06/20/2002
06/18/2002
06/14/2002
06/12/2002
06/10/2002
06/07/2002
06/05/2002
06/03/2002
05/30/2002
05/28/2002
05/23/2002
05/21/2002
05/17/2002
05/15/2002
05/13/2002
05/09/2002
05/07/2002
Actual Date
Sensitivity Analysis
Manager want conservative estimate of Day
and Shift effects.
“ Assume: Model predicts three Injuries for
Wednesday, Second shift.
“ Use average Estimates for all other Factors
“ Sensitivity shows Injury rate could vary
between 1.973 and 4.027 Injuries per Shift.
“
Factor
Wednesday
Second Shift
Total
Avg Case
Best Case Worst Case
Adjustment Adjustment
-0.422
-0.642
0.642
1.048
-0.385
0.385
-1.027
1.027
Conclusion
“
Poisson Regression used to predict Poisson
Distributed output.
“
No skew, negative numbers, or growing variance
Allows for Confidence Intervals to test factor
significance
“ Prediction Equation can be used to estimate
total Injuries.
“ Sensitivity Analysis can be done to get best
and worst case scenarios.
“