Up-and-down method

UOP FCC unit, 11 700-702 UOP/HYDRO MTO process, 18 568 UOP Olex olefin separation process, 17 724 Up-and-Down Method, 25 217 U/Pb decay schemes, 25 393-394 Updraft sintering, 26 565 Upflow anaerobic sludge blanket (UASB) in biological waste treatment, 25 902 Upgraded slag (UGS), 25 12, 33 Upland Cotton, U.S., 8 13 U-Polymer, 20 189 Upper critical solution temperature (UCST), 20 320, 322 Upper explosive limit (UEL), 22 840 Upper flammability limit, 23 115 Upper flammable limit (UFL), 22 840 Upper Freeport (MVB) coal... 

Brownlee, K., Hodges, J. and Rosenblatt, M. (1953). The up-and-down method with small samples. J. Am. Stat. Assoc. 48 262-277. 

A modification of the method of limits is the up and down method. A stimulus is presented if the response is positive, the next lower stimulus is presented, if it is negative, the next higher is presented and so on. The primary advantage is, that it automatically concentrates near the mean and a considerable number of observations can be saved. 

From these heights the median height is determined by the Braceton Up-and-Down Method (See Vol 3, p C376 for info on Up-and-Down Method). Usually 50 shots containing 0.03cc of expl are used, although up to 200 have been shot. Standard and test expls are fired alternately. M Sc W also replaced PA with RDX as the standard expl. PA was an unsatisfactory standard because it showed day-to-day variations iQ behavior that seemed to be related to the... 

During World War II Dixon and Mood [72] developed a special experimental method for testing the sensitiveness of explosives to impact. The method gave a statistical estimation of the mean value. It became known as the Bruceton up-and-down method. The primary advantage of the method is that it increases the accuracy with which the mean value can be economically determined. The method requires fewer tests than other methods. 

Fig. 153. Determination of incendiveness of a permitted (permissible in the U.S.A.) explosive in a firedamp atmosphere, by the up-and-down method, according to Grant...

Note Accdg to Dr. Van Dolah (Ref 47), the up-and-down method, first developed in 1944, has been most commonly used for the impact sensitivity test of expls, but can be applied to many other test methods, including the gallery tests... 

B4.1 The up and down method B4.1.1 Direct impact method (1) 4-10mg of sample powder are put on the upper surface of a steel roller 12mm high and 12mm in diameter. 

After data are collected via the up and down method 21 , the 50% explosion height (H s o, cm) is determined and the energy (E 5 o, J) of ball dropped at 50% of the explosion height is calculated. Test results should be recorded as in the example in Table 3.6. 

The data treatment for the up and down method is as follows, using the example of data from table 3.6. 

At the 50% explosion height determined via the up and down method, the results are repeated 10 times or 40 times and the sensitivity of the sample is estimated with 0/10, 10/10 or 20/40. 

In the case of the drop hammer test using the up and down method, the drop height is decreased at certain intervals when the sample explodes or correspondingly is increased at certain intervals when the sample dose not explode. This procedure is carried out through several iterations. As the result of these trials, test heights are concentrated near the 50% explosion height, and it becomes possible to estimate the 50% explosion height. 

The method of measuring the 1/6 explosion height suffers from poorer reliability and unknown accuracy when compared with 50% explosion height measurement with the up and down method. 

When the results are analyzed after the trials with the up and down method, it becomes problematical to make the intervals of the fall heights the same size or to make the logarithms of integrals of the fall height the same. Professor Dixon et al. described that, in the case of sensitivity data for explosive substances, the distribution of the probability of explosion becomes closer to a normal distribution when the logarithm of the fall height is used rather than the fall height itself. In the up and down method, the analysis is done under the supposition that the distribution of explosion probability is a normal distribution. 

The standard deviation ( o ) of a normal distribution is also presumed for trials for the 50% explosion height (Hs ) with the up and down method. The 1/6 explosion height can be estimated using these two values. Accordingly it seems better to use the up and down method to find the 1/6 explosion height. 

In the case of the up and down method, the tests are continued by raising... 

Drop ball tests were carried out 20 times using the same steel ball and drop height determined as mentioned above for some typical low sensitivity oxidizers. The results are shown in Table 3.14. In Table 3.14 only judgments from test results of up and down methods previously reported 2 31 (See Table 3.8) are shown. The test results from the 10/20 test method coincided with those from the up and down method. 

NaCIO 3 = KCIO 3 > NaCIO 2 > NaBrO 3 = KBrO 3 > Ba(C10 a ) z H 2 O. The substances for which "go" was recorded more than 10 times were sodium chlorate, potassium chlorate and sodium chlorite. Potassium chlorate was tested at a height of Hso which had been determined with the up and down method, and the ratio of "go" to "no go" events ratio was 13/20 (65%). A variation of about 3 times should be considered. When the test result are considered with those from the up and down method, the impact sensitivity of sodium chlorate may not be less than that of potassium chlorate. Meanwhile a significant difference between sodium chlorite and potassium chlorate is not observed. It is necessary to carry out the test more times to see if there is a significant difference between sodium chlorite and potassium chlorate. 

The up-and-down method, also called the Bruceton or staircase method, is a widely used statistical procedure for the determination of the height at which 50% of the samples detonate or react and its standard deviation [17,18]. The advantages and disadvantages of the method are described elsewhere [18-20] basically the test gives a reliable 50% value but not a reliable standard deviation. The number of tests required at each height also has been investigated [21]. 

With the ball-drop apparatus, two procedures are followed. These are the up-and-down method, where at least 20 drops are made following tire standard procedure, and the group-data procedure where 20 drops are made at five consecutive levels differing by 1 in., one near the 50% point, two above, and two below it. The up-and-down method determines the height required to produce an explosion m 50% of the trials with a 95% confidence interval of 1.4 in., but does not accurately determine the standard deviation or the probability of firing at low stimulus levels. Data from the group-data method are plotted on probability graph paper and values of both the 50% point and the standard deviation... 

The data were gathered using the Picatinny Arsenal apparatus (1-kg weight) and the up-and-down method. The nature of each sample s response was noted as well as the height for which 50% of the samples reacted [54.55]. 

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