Downloaded from https://www.everyspec.com AMCP 706,196 2.11 ACCEPT/REJECT TESTS-NON- any unit from the other population. ObRAMETRIC Both the rankasum test and the run teort Nonparametric tests can be used to evalu- require waiting for all items in both samples ate many properties of a distribution or to fail The next test pertits test truncaton make comparisons, Ref, 25. The tests in and a shorter test time. this paragraph deal with the following kind of experiment (Refs. 16 and 25). A sample 2.11.3 MAXIMUM-DEVIATION of N Items is life tested in the usual (u) environment. Times to failure are noted.
A The maximum-deviation test is a truncated similar set of N Items i3 simultaneously sub- test (Ref. 16), In this test, a value Is pro- jected to a more severe (s) environment. asaalned to r, where r refers to the rth order The statistical analysis determines If exposure statistic. For example, r = 2. Then examine to "s" changes the life of the units in u the data to establish the time (either u 2 or s-significant sense. sl) at which at least two failures have oc- curred In both samples.
From the test data, % The null hypothesis (no difference in the the time corresponding to r w 2 is u2 - 7.5, quality that the statistical test measures) is at which time two failures have occurred in tested against the alternative that thoee is a the "usual" sample and three failures have difference, Engineers need not concern occurred in the "severe" sample, themselves about the technical details of such Define a quantity Mr as the absolute dlf- hptee.ference between the number of failures in Three test procedures will be described in the u and s samples calculated after each these paragraphs: (I) rank-sum, (2) run, failure.
Two other required parameters, m, (3) maximum-deviation-Example Noe. 16, and p,, are tabulated in Table 2-32 for 17, 18, and 19, They will be described for r aI, 3, 6, 10, and for samples of size 10. the same basic set of data. The successful (An expanded version of this table is avail- application of these tests depends on the able in Ref. 16.) For any r, t, a max ur, sr . fact that life-test data can be put lit time Proceed as follows. If Mr - m, + I at any order. time up to and Including t,, stop the test 2.11.1 RANK-SUM and reject No. If Mr Ј (mi, - 1) up to and Including t,, accept HN. If the teot is con. tinued to t.
and M, a m, at least once and Also known as the Mann-Whitney or otherwise M, (m,, - 1), perform a ;, WVlcoxon test. See Sec. 5.3, Ref. 25, and oernole Mi w(ich w ret p e a Exampe No 17.Bernoulli trial which will reject Ho with probability p,. See Example No. 19. 2-11.2 RUNS 2-12 SYSTEM RELIABILITY ESTIMATION ¶ Also known as the Wald-Wolfowitz test. FROM SUBSYSTEM DATA See Ref. 16 or Sec. 7.3 of Ref. 25, and Ex- Many weapon systems are extremely com- ample No. 18. plex and consist of large numbers of sub- If the smaller of the rank sums is greater systems and components.
During a consider- than the critical number in the body of the able portion of the system development table, accept the null hypothesis that the cycle, only component and subsystem failure chances are 50%-50% that any unit from data are available for reliability analyses. The onu population ,will have a shorter life than amount of data often varies considerably [text continues on pale 2-114.]