JOTP-011
5 December 2014
APPENDIX G. MARGIN OF SAFETY CALCULATIONS FOR PRESSURE VESSELS
G.1. GENERAL.
This Appendix provides a statistical procedure to determine, at a suitable level of confidence, that
the probability of the motor case rupturing is less than some predetermined small value. The
probability of case rupture is determined from two measured parameters, the maximum operating
pressure of the motor, and the pressure required to rupture the motor case. The reliability of the
motor case is estimated by determining the probability that the strength of the motor case exceeds
the stresses exerted on the motor case.
G.2. CONFIDENCE COEFFICIENT.
An estimate of the probability of motor case rupture is determined from a relatively small sample
size, which is assumed to be randomly selected from the total population. A confidence interval
with an associated confidence coefficient must be defined. The probability of motor case rupture
for this document has been set at a "one-sided" confidence interval of 10-5 with a confidence
coefficient of 90 percent (U.S. requirement).
G.3. TOLERANCE LIMIT PROCEDURE.
The Tolerance Limit Procedure discussed in Appendix I, Reference 31 (US) is used to determine
that at a 90 percent level of confidence, the probability of motor case rupture is better than one in
100,000 (the "one-sided" confidence interval of 10-5). This means that the motor case rupture
pressure must be much better than the motor operating pressure. The following procedure is based
upon the assumptions of independence and normality of the data. The normality of the rupture
and operating pressure data can be checked by calculating the skewness and kurtosis values.
G.4. DEFINITIONS.
X
- burst pressure
Y
- maximum operating pressure
μx
- mean of the population for X
μy
- mean of the population for Y
σx
- standard deviation of the population for X
σy
- standard deviation of the population for Y
_
- average dynamic burst pressure (estimate of μx)
X
- standard deviation of burst pressure (estimate of σx)
Sx
nx
- burst pressure sample size
fx
- degrees of freedom of estimate Sx
_
G-1
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