DASO 28. Trident II D5 Reliability

DASO 28 Trident II D5

DASO 28 Operation

The Ohio-class ballistic missile submarine USS Nebraska (SSBN 739) along with the U.S. Navy’s Strategic Systems Programs (SSP) conducted successful test flights of two Trident II D5 Missiles as part of Demonstration and Shakedown Operation (DASO) 28 in the Pacific Test Range off the coast of Southern California, March 26.

For more see: http://www.navy.mil/submit/display.asp?story_id=104916

Trident II D5 Reliability

We discussed D5 reliability in the previous topics.

For more see: https://rpubs.com/alex-lev/275641, https://rpubs.com/alex-lev/260829, https://rpubs.com/alex-lev/257362, https://rpubs.com/alex-lev/243719, https://rpubs.com/alex-lev/200551

Test Flight Program Reliability of Trident II D5

With 27 test flights conducted Trident II D5 SLBM had only 4 failed.

library(ggplot2)
seed=12345
PD50<-rbeta(10000, shape1 = 23, shape2 = 4)
bnt0 <- binom.test(23,27,0.9)
print(bnt0)

## 
##  Exact binomial test
## 
## data:  23 and 27
## number of successes = 23, number of trials = 27, p-value = 0.3403
## alternative hypothesis: true probability of success is not equal to 0.9
## 95 percent confidence interval:
##  0.6626891 0.9581126
## sample estimates:
## probability of success 
##              0.8518519

bnt.low0 <- bnt0$conf.int[1]
bnt.up0 <- bnt0$conf.int[2]
quantile(PD50,probs = c(0.025,0.5,0.975))

##      2.5%       50%     97.5% 
## 0.6995247 0.8601797 0.9551115

ggplot(data=as.data.frame(PD50), aes(PD50)) + 
  geom_histogram(bins = 30,col="black",fill="green") + 
  geom_vline(xintercept = mean(PD50), color = "red") + 
  geom_errorbarh(aes(y=-5, x=mean(PD50), xmin=quantile(PD50,0.025), xmax=quantile(PD50,0.975)), 
                 data=as.data.frame(PD50), col="#0094EA", size=3) +
  ggtitle(label="Probability density of Trident II D5 successful trial after test flight program")

Current Reliability of Trident II D5

Now we want to update our previous estimation results to date, assuming 167 successful and 6 failed historical trials of Trident II D5 SLBM.

seed=12345
PD5<-rbeta(10000, shape1 = 167, shape2 = 6)
bnt <- binom.test(167,173,0.95)
print(bnt)

## 
##  Exact binomial test
## 
## data:  167 and 173
## number of successes = 167, number of trials = 173, p-value = 0.483
## alternative hypothesis: true probability of success is not equal to 0.95
## 95 percent confidence interval:
##  0.9260432 0.9871679
## sample estimates:
## probability of success 
##              0.9653179

bnt.low <- bnt$conf.int[1]
bnt.up <- bnt$conf.int[2]
quantile(PD5,probs = c(0.025,0.5,0.975))

##      2.5%       50%     97.5% 
## 0.9334319 0.9672138 0.9869855

ggplot(data=as.data.frame(PD5), aes(PD5)) + 
  geom_histogram(bins = 30,col="black",fill="green") + 
  geom_vline(xintercept = mean(PD5), color = "red") + 
  geom_errorbarh(aes(y=-5, x=mean(PD5), xmin=quantile(PD5,0.025), xmax=quantile(PD5,0.975)), 
                 data=as.data.frame(PD5), col="#0094EA", size=3) +
  ggtitle(label="Probability density of Trident II D5 successful trial after DASO 28")

Trident II D5 Reliability Progress

quantile(PD5/PD50,c(0.025,0.5,0.975))

##     2.5%      50%    97.5% 
## 1.005737 1.122762 1.382802

ggplot(data=as.data.frame(PD5/PD50), aes(PD5/PD50)) + 
  geom_histogram(bins = 30,col="black",fill="green") + 
  geom_vline(xintercept = mean(PD5/PD50), color = "red") + 
  geom_errorbarh(aes(y=-5, x=mean(PD5/PD50), xmin=quantile(PD5/PD50,0.025), xmax=quantile(PD5/PD50,0.975)), 
                 data=as.data.frame(PD5/PD50), col="#0094EA", size=3) +
  ggtitle(label="Probability density of Trident II D5 reliability progress")

Conclusion

1.Trident II D5 missile had got 95% confident interval for its test flight program reliability with 27 test events and 4 failures as \(P(0.697\le P_{D50} \le0.956)=0.95\) with the mean value \(P_{D50}=0.860\).

2.Trident II D5 missile has got historical and unprecedented record for SLBM of 167 consecutive successful trials which in spite of 6 failed trials gives 95% confident interval for its reliability as \(P(0.934\le P_{D5} \le0.987)=0.95\) with the mean value \(P_{D5}=0.967\).

3.The overall progress for Trident II D5 reliability gives 95% confident interval as \(P(1.006\le P_{D5,D50} \le1.387)=0.95\) with the mean value \(P_{D5,D50}=1.123\) that is 12% increase.