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1 American Institute of Aeronautics and Astronautics

Practical Problems and Solutions in Age Trend-Line

Analyses for Energetic Components

Lien C. Yang*

La Canada Flintridge, CA 91011

∗ A normalization methodology for test temperature and input stimulus level used in energetic components tests is formulated and applied to function time, using a hypothetical electro-explosive device as an example. This approach enables the consolidation of multiple small and statistically insufficient test sample sizes, as used in many test subgroups, into a larger single population. Quantitative performance of the function time can then be evaluated as a function of age via trend line analysis, from which additional shelf life or service life can be assigned with confidence based on age surveillance testing results. The impact of incremental age surveillance testing of small sized samples on tolerance bounds is evaluated. It is found that a superficial rapid divergence of the bounds as a function of age results from this analysis. However, the exaggerated artifact can be offset by allocating additional tolerances in relation to the specification limits. Trend line analysis using these modified theoretical limits can provide useful shelf life extension information.

Nomenclature – Statistical

ave = Average value of a ECS performance parameter in a single sample selection aveR = Average value of a ECS performance parameter in the reference sample database b = Intercept of the trend line in linear regression analysis C = Confidence level in percentage or probability f = Frequency of occurrence in a histogram bin interval LBave = 1% lower bound of ave in physical units for statistics of small sample sizes LLp = Allowable lower bound of ave - 3.09*std in physical units for statistics of small sample sizes m = Slope of the trend line in linear regression analysis N = Sample size or number of units tested NR = Sample size of reference sample database, usually the qualification or lot acceptance test data p-value = Significance probability in regression analysis. In TALE or TLA, p < 0.05 indicates a strong

trend and p > 0.05 indicates no significant trend P = Normalized probability distribution

Where σ is the standard deviation, same as “std” used in this paper, and μ is the mean, used interchangeably with “ave” used in this paper

R2 = Coefficient of determination in a curve fit based on least square formulation std = Standard deviation [1/ (N-1) based] in N samples of a ECS performance parameter TALE = Trend analysis life estimate (employing the same methods as TLA) TLA = Trend line analysis TOLL = Lower tolerance bound in TALE TOLU = Upper tolerance bound in TALE UBave = 99% upper bound of ave in physical units for statistics of small sample sizes ULp = Allowable upper bound of ave + 3.09*std in physical units for statistics of small sample sizes

∗ Senior Member, AIAA Copyright © 2007 by L. C. Yang, Published by the American Institute of Aeronautics and Astronautics, Inc., with permission

( ) ( ) ( )22 2/

21 σμ

πσ−−= xexP

43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit 8 - 11 July 2007, Cincinnati, OH

AIAA 2007-5135

Copyright © 2007 by L.C. Yang. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


Nomenclature - ECS

AAT = Accelerated aging test which includes a high temperature storage test, other required environmental tests and function test

all-fire = Initiation stimulus level for an EED based on threshold sensitivity test which provides a statistical reliability of 0.999 at 95% confidence for successfully firing of the device

Amb. T = Ambient temperature used for EED function test A/S = Aging surveillance, or age surveillance delta qualification = Partial qualification testing for verification of minor ECS design changes, environmental

condition changes, and change of production facility location or configuration ECS = Energetic components and systems EED = Electroexplosive device, including mainly hot bridgewire based initiators and detonators, and

can be generalized to include exploding bridgewire initiators and exploding foil initiators H-Amp = High firing current, the predicted operating current HT = High temperature used for EED function test I = Firing current LAT = Lot acceptance test in which a proportion of the lot is randomly selected and tested L-Amp = Low firing current, the sure fire current, i.e., the current level for an EED which provides a

statistical reliability of 0.999 at 95% confidence for meeting all functional and environmental requirements for all different lots

LT = Low temperature used for EED function test lot = Energetic components manufactured by the same materials in a single production run LSL = Lower specification limit for a ECS performance parameter no-fire = Initiation stimulus level for an EED based on a threshold sensitivity test which provides a

statistical reliability of 0.999 at 95% confidence for not firing of the device NSI = NASA Standard Initiator QTP = Qualification test, a test verification of performance and reliability for a newly designed

energetic component t = Function time, the time from application of a constant firing current to full output is observed t1 = t normalized to Amb.T t2 = t normalized to Amb.T and L-Amp USL = Upper specification limit for a ECS performance parameter

I. Introduction In the new 2005 AIAA/SMC Ordnance Standard1, a provision was included for using trend line analysis (TLA) of performance parameters acquired from age surveillance (A/S) tests as a means for extending predicted ECS shelf life. More detailed discussions are included in AIAA-2005-40392 in which effective utilization of results acquired by small test sample sizes is illustrated. However, several fundamental problems exist in the current age surveillance testing methodology. The first limitation is that testing and analysis is based on the production lot. The treatment of several lots as one population, in order to increase the sample size and therefore the accuracy, requires careful work due to possible substantial differences in performance from lot-to-lot, and is only done on case-by-case basis. In other words, currently one lot is usually treated as a standalone for both reliability and shelf life considerations. The current accelerated aging test (AAT) consists of 30 days of high temperature (160oF) storage in combination with 50 ± 10% RH. Three years of additional shelf life is granted for successfully passing the AAT, and subsequent environmental tests and function tests. AAT is widely in used as it provides a longer shelf life of 3 years as compared to an ordinary A/S test. By convention, AAT is specified for testing ten (10) units of a lot. In addition, the units are mandated to be function-tested at high (160o – 300oF), ambient and low (-260o to -65o F) temperatures. This reduces the sample sizes of temperature “subgroups” to only three (3) or four (4) units which are too small for reliable statistical evaluations if subgroups are analyzed individually, especially when only limited number of AAT increments is performed (dictated by the ~ten years of required application shelf life). For a one year service life extension, testing of five (5) units is required. The 2/1/2 sample units split for three temperatures renders the standalone subgroup sample size statistically inadequate for TLA reliability. In QTP and LAT of electro-explosive devices (EEDs), function testing at several different firing current levels is also required, (e.g., sure fire level of 3.5 A to 4.5 A; and predicted operating firing level of 5.0 A to 7.0 A). This further reduces subgroup sample sizes. Table 1 summarizes these details for EEDs. QTP is listed because “combined QTP and LAT” is widely practiced for many applications. For ECS other than EED, the methods specified are similar but at still smaller sample sizes.


Table 1 EED Function Test Sample Size per Governmental ECS Specifications

Test Firing Current Temperature

MIL-STD-15763

DoD-E-83578A4

EWR 127-15

AIAA S-113-20051

Total N 90 - 131 94 – 105

H-Amp LT/ Amb. T/ HT 15/15/15

L-Amp LT/ Amb. T/ HT 15/ 15/ 15 11/ 12/ 11 QTP

Others, e.g., 22 A

LT/ Amb. T/ HT 5/ 5/ 5 6/ 8/ 6

Total N ≥ 30*

H-Amp LT/ Amb. T/ HT

≥ 5/ 5/ 5 LAT

L-Amp LT/ Amb. T/ HT

≥ 5/ 5/ 5

Total N 5 LT 0 2

Amb. T 5 1 A/S, 1 yr L-Amp HT 0 2

Total N 10 LT 3 4

Amb. T 4 2 A/S, AAT L-Amp HT 3 4

* 10% of the lot or 30 units whichever is greater Increase of sample size is necessary for alleviating these problems. Instead of proposing testing of more units at high costs, this paper explores techniques for normalizing test data gathered from different temperatures and firing current levels so that all data can be treated as one large-sized sample population rather than small and separate sample subgroups. The resulted sample sizes of ~100 for QTP/LAT and 10 for AAT meet the criteria required for reference database accuracy and small sample group function reliability respectively, as reported in Ref. 2. In an accompanying paper6, it is pointed out that the equivalent shelf life as tested by the AAT actually depends on the ECS storage temperature history. A 30-day AAT may warrant an equivalent shelf life much longer than the currently specified three (3) years. This paper will show that using of actual and longer equivalent life will improve the trend line analysis accuracy and result.

II. An EED Case Example Out of many measured EED performance parameters, function time provides the most useful data. It is the sum of the times for all EED functional train elements including heating of the bridgewire, heat transfer to the energetic material immediately surrounding the wire, ignition of the material and the propagation within it. The time of propagation is usually on the order of 0.1 ms in initiators and in microseconds in detonators. Thus, it normally has no significant impact on the variation of overall function time in milliseconds regime. Other parameters (e.g., peak pressure measurement of a pyrotechnic initiator in a closed bomb and detonator dent depth measurement by a witness plate) are subjected to the interference of high frequency pressure transients7 created by the resonance in the bomb, and impacted by the plate temperature, plate material and its hardness variability8. Inaccuracies can result. Because of the constraint of the 1 A-1 W no-fire requirement, the design and performance of hot bridgewire-based EEDs are quite similar to each other. Other than the minor differences in the heat sink material, bridgewire material, primer composition and binder in the primer that can affect the function time, the function time of EEDs is generally measured in milliseconds9 for the sure–fire, or the L-Amp firings and approximately 1.0 millisecond or below for operating currents, or H-Amp firings. The effect of test temperature on the function time (and for that matter on the Bruceton all-fire threshold) is usually quite prominent, a fact appreciated by the author at least as far back as 1967 during work on the Apollo Standard Initiator, the developmental version of NSI. The test temperature span of 560oF used there9 was comparable to the ignition temperature of the zirconium potassium perchlorate pyrotechnic primer used in the unit. Quite a few of parameters can contribute to the variability of the function time. To name a few: bridgewire resistance, effective length and diameter tolerances of the bridgewire, contact intimacy


between the bridgewire and the header (heat sink) or the primer, primer particle size and composition (especially the binder), variability in the primer composition, and degradation of primer by 1 A-1 W test, all can affect bridgewire temperature rise or primer ignition temperature, and these can in turn affect the function time. The following hypothetical function time example is formulated for the sole purpose of illustrating the methodology. It incorporates some typical features of 1 A-1 W EED function time including temperature sensitivity and time variability at H-Amp and L-Amp firings. For illustration, in the L-Amp, Amb. T firing, artificial upper and lower specification limits, USL = 5.0 ms and LSL = 3.0 ms are imposed. This mandates that the span between 3.0 ms and 5.0 ms should correspond2 to ~6.18 times of standard deviation (std) of a large sample function time and that its average (ave) be very close2 to 4.0 ms, the center of the span. Note that current 1 A-1 W EEDs commonly adopt USL = 10 ms (based on system requirements rather than statistical considerations) and there is no LSL because the function time for H-Amp firing is below 1.0 ms as noted above. The sample size of LAT and AATs, is 95 and 10 units respectively, in accordance with MIL-STD-1576, as well as the approximate sub-group sizes. The first AAT is performed at the same time as, but separated from the LAT, and the second AAT is performed several years later, as commonly practiced for current EEDs. The seven years shelf life as illustrated is typical for many EED applications. Figures 1 and 2 illustrate the function time statistics for this hypothetical EED at LT, Amb.T and HT for L-Amp

and H-Amp firings, respectively, with the last chart in each figure integrating data for all temperatures. The apparent probability distribution, P, and the associated histogram frequency, f, are plotted. The irregular appearance of f is due to the small sample sizes. It is included in order to illustrate of the drastic improvements in this parameter when compared with that obtained by normalization in the later sections of this paper. The principal feature of these figures is that the std of the distributions are relatively smaller than the temperature induced shifts in the function time so that a temperature trend is seen. Furthermore, the plot combining data from different temperatures results in a larger std. This is not favorable for statistical analyses as can be seen in Fig. 1 in which the ave + 3.09*std value exceeds the 5 ms USL for LT case and ave – 3.09*std value falls below the 3 ms LSL for HT case. The exact values of ave and std are not accurately known due to the small sample size limitation as indicated in Ref. 2. However, the shifts in ave value as a function of test temperature are consistent with the primer ignition temperature characteristic.

Figure 1 L-Amp Firing Function Time Distribution: P and f


III. Normalization of Temperature Effect Our objective here is simply to translate the function time data measured at HT and LT to its equivalent values at Amb.T. There is precedence for this approach. In solid rocketry, the temperature coefficient of propellant burning rate, a linear factor, is measured and used to normalize the motor ballistics measured at different temperatures to a standard ambient temperature10 for performance evaluation. This procedure is reasonable since the heat transfer for the rather small background temperature range is a linear phenomenon. Unfortunately, this type of data is not available for most explosive material. We will use an alternate approach outlined as follows. Figs. 3 and 4 are the linear plots of the function time versus the test temperature for LAT L-Amp and H-amp firings respectively. Reasonable straight line fits are obtained for determining linear offsetting factors with respect to the Amb.T. A constant offset factor obtained is subtracted from all LT data and another constant offset factor obtained is added to all HT data. The values of ave ± 3.09*std of the new probability distributions for LT and HT cases, in terms of the adjusted function time, t1, are well within the 5 ms USL and 3.0 ms LSL. The probability distribution and histogram of combined results for all temperatures with respect to the adjusted function time, t1, are plotted in Figs. 5. It can be seen that the quality of the distributions has been improved to the extent that the histograms are more “Gaussian” and std comparable to individual temperature values shown in Figs. 1 and 2 are obtained. Normalized function time data, t1 using the same offset factors obtained above, for AAT #1 and AAT #2 are also presented. The hypothetical probability distribution respective to t1 for AAT #1 has values of ave ±3.09*std well enveloped between USL and LSL, and for the distribution of AAT #2, slight excursions are presented (details are summarized in Table 3). Both statistical behaviors are common occurrence for small sample sizes such as that used in AATs. Note that H-Amp firing is not required in AAT, and therefore, only t1 is used in the analysis that follows (i.e., t1 = t2 for these cases).

Figure 2 H-Amp Firing Function Time Distribution: P and f


IV. Normalization of Firing Current

Reference 2 pointed out that the accuracy of statistical analysis depends on sample sizes used in both A/S tests and QTP/LAT, which is used as the reference distribution. Therefore, the normalization of H-Amp firing data to L-Amp firing data is important as it accounts for ~50% of QTP/LAT samples per Table 1. Once again, there is some precedence for this procedure from solid rocketry. It is known that the cross section of the rocket nozzle throat controls the ballistics in the motor firing. Therefore, different ballistic profiles result from throat tolerance or erosion

Figure 5 Temperature Normalized Function Time, t1 Distribution, P and f, for LAT L-Amp

and H-Amp Firings and AAT #1 and AAT #2 L-Amp Firings

Figure 3 LAT L-Amp Function Time, t, versus Temperature

Figure 4 LAT H-Amp Function Time, t, versus Temperature


Figure 6 Temperature Rise in Bridgewire

Region Normalized to Input Electrical Power

Figure 7 LAT t1 versus I-2 with Linear Fit

0 t2 Histogram, LAT, All T & I

0

20

40

3 3.4 3.8 4.2 4.6 5t 2 , ms

f

0

0.8

1.6

P

fP

Figure 8 Fully Normalized LAT Function Time, t2 Distribution: P and f

and need be adjusted via propellant burning rate formulas which provide faster burning at higher chamber pressures (due to smaller throats)10. Caution needs be exercised in this approach as it is also well known that the pressure exponent of the burning rate equation can be nonlinear across large pressure ranges. Therefore, it is important to examine the heat transfer characteristics of the different heating modes in the EED initiation, before proceeding to the normalization procedure. Temperature rise as a function of time in the bridgewire region normalized respective to input electrical power can be conceptually represented by the thermal transient test response as illustrated in Method 105 of Ref. 1. The five different modes are schematically identified in the response curve and showed in Fig. 6. Qualitative remarks for each mode are summarized in Table 2.

Table 2 Characteristic of EED Initiation Modes Mode Stimulus Level Approximate Time Heating region Remarks

1 22 A ~0.1 ms Bridgewire Nearly Adiabatically Burned-Out

For Low Voltage Capacitor Firing11

2 H-Amp ≤ 1.0 ms A Thin Layer of Primer ≤ 1 mil 3 L-Amp ≤5 ms A Thick Layer of Primer ~Several mils

4 All-Fire/No-Fire Tens of ms Bulk of the surrounding Primer and Header No Reliable Data

5 1 A - 1 W Seconds to Minutes Heat EED Plus Heat Sink No Data Reported

It is apparent that only modes 2 and 3 can be considered for the firing current normalization. Further precautions are discussed as follows. At first glance, the time for temperature rise of a heating element to a given temperature (in the case of EED, the ignition temperature of the primer) would be inversely proportional to the electrical power. Fig. 7 plots the temperature normalized LAT function time, t1 in Fig. 5 as a function of I-2. Two straight line fits are performed on the data. It can be seen that the line passing through I = ∞, and t1 = 0, does not fit well with the H-Amp data because of the fact that in this mode the heating is more efficient than that in L-Amp mode as there is less primer to be heated (Table 2). Shorter function times result. For

this reason, the line bypassing the origin is adopted for obtaining a single scaling factor (ratio of the times) for normalizing all H-Amp function times (t1) into their equivalent L-Amp function times (t2). The probability distribution and histogram of the fully normalized LAT function time, t2, which includes data for all three temperatures and both firing currents, are summarized in Fig. 8. It should be noted that the ave and std are fairly comparable with the L-Amp plot in Fig. 5, indicating that by addition of the normalized H-Amp data the result is consistent with the real function time statistical distribution.

V. Trend Line Analysis

Table 3 summarizes the normalized function time statistical parameters relevant to the trend line analysis (TLA2), or the trend analysis life estimate (TALE2).


Table 3 Statistic Parameters of Function Time Test Groups

Test Group Parameter N ave, ms std, ms ave + 3.09*std, ms

ave – 3.09*std, ms

LAT t2 95 4.04964 0.2766 4.9044 3.1948 AAT #1 t1 10 3.98044 0.2629 4.7929 3.1679 AAT #2 t1 10 4.13860 0.3889 5.3404 2.9368

Linear regression analyses including the LAT data provide the following regression parameters for AAT #1 (which includes LAT t2, and AAT #1 t1, see Fig. 14) and AAT #2 (which includes LAT t2, AAT #1 t1 and AAT #2 t1, see Fig. 15):

Table 4 Function Time Regression Line Parameters with Respect to LAT t2

End Point Parameter Assigned Age, mon. N Intercept

b, ms

Slope m,

ms/mon. p-value R2

AAT #1 t1 36* 10 4.04964 -0.00192 0.452 0.00551 AAT #2 t1 ~84* 10 4.04434 0.000673 0.533 0.00345

* Shelf Life Equivalence for AAT is 3 yrs in accordance with specifications The fact that p-values are >> 0.05 indicates that there is no significant trend. In this situation, Ref. 2 suggests the use of small sample size statistical criteria to evaluate the age trend in lieu of TALE upper and lower bounds (TOLU and TOLL) in relation to the USL and LSP. Each AAT sample group is treated as a standalone miniature LAT whose statistics are compared with that of the LAT according to the following criteria for small sample size2:

The 99% and 1% bounds for ave, in terms of physical units, at sample size, N, are2:

UBave = USL – (39.71 – 29.58*N-0.5007)* (USL – aveR)/ (39.71 + 29.58* NR-0.5007) (1)

LBave = LSL + (39.71 – 29.58*N-0.5007)* (–LSL + aveR)/ (39.71 + 29.58* NR-0.5007) (2)

The upper and lower allowable 3.09*std limits, in terms of physical units, at sample size, N, are

ULp = USL + 70.478*N-0.4845 * (USL – aveR)/ (39.71 + 29.58* NR-0.5007) (3)

LLp = LSL – 70.478*N-0.4845 * (–LSL + aveR)/ (39.71 + 29.58* NR-0.5007) (4)

The first criterion for examination of small sample test data for AAT is that the value of ave shall be within the bounds calculated from Eqs.1 and 2. The second criterion is that the values of ave ± 3.09*std shall be within the limits calculated from Eqs.3 and 4. If both criteria are met, one can conclude that the performance parameter(s) for the AAT samples is statistically close to that in the reference database, i.e., LAT. Therefore, no change is caused by the aging and a conservative additional four (4) years of shelf life can be assigned. The justification for this approach is based more on common sense than analytic consideration: If there is no change in the device performance after four years of aging, it likely will be good for another four years. For the case study example, USL = 5 ms, LSL = 3 ms, NR = 95, N = 10 and aveR = 4.04964 ms, therefore the calculated values of UBave = 4.325 ms; LBave = 3.745 ms; ULp = 5.514 ms; and LLp = 2.433 ms are obtained. It is seen that the values of ave and ave ± 3.09*std for both AAT #1 and AAT #2 meet the criteria. Therefore, an additional 4 years of shelf life can be assigned in addition to the 3 years which already allowed by AATs. This methodology has been successfully used in the A/S testing of decommissioned Minuteman II inter-continental ballistic missile EEDs for service life extension to ~forty years7, 12, 13. In our case of example EED, the additional shelf life (for a total 7 years) acquired by AAT #1 is actually and redundantly verified by the success of AAT #2.

VI. Trend Line Tolerance Bound Analysis Methodology Evaluation

This graphic-aided analysis facilitates the life estimate and is widely in use for age trend data which exhibit a condition of p-value < 0.05. From the intercept of the TOLU with USL, or TOLL with LSL, the life-limiting age can be projected2. When p-value > 0.05, the trend is considered as not significant, therefore the analysis plot is usually not performed. Because the data features adopted in the current EED case are quite different from that used in Ref. 2


(The testing frequencies used there were higher than the current example and the data for the first few tests alone was usually considered as premature and insufficient for trend determination there, due to the small sample size used in each test increment), this philosophy was re-examined and several new findings are obtained: • The term “significant” is a statistical terminology in which the change of the dependent variable due to the slope

of the regression line is comparable to or in excess of the data variation. • In the physical world such as in our study, the trend is constrained by the USL and LSL. Therefore, the TOLU

and TOLL still can provide useful information in relation to USL or LSL, in spite that p>>0.05. • In using small age test frequencies, small A/S or AAT sample sizes can introduce significant biases or artifacts

in the TOLU and TOLL. This feature is traceable to the built-in conservatism in Eqs.20 thru 22 in Ref. 2. • The biases above can be quantitatively offset by referring to an “inflated” or “fictitious” USL or LSL. These findings are illustrated by the following artificially created case studies. Bounds for 99 percentile (99%) at 95% confidence are used for all cases as suggested by Ref. 2. The large sample size used is identical to the fully normalized LAT data used in the EED example. All 95 data points are included. The small sample size used contains only ten data points and has a probability distribution nearly identical to the normalized LAT data. The ages of the samples correspond to time zero (LAT), AAT #1, and AAT #2. The highlights are summarized in Table 5.

Table 5 Trend Line Tolerance Bound Analysis Methodology Evaluation Highlights

Case #

Fig. # Descriptions

TOLU Excurses

USL (5 ms)

TOLU Excurses

ULp (5.51 ms)

TOLL Excurses

LSL (3 ms)

TOLL Excurses

LLp (2.43 ms)

1 9 All large samples No No No No 2 10 All small samples ~120 mon ~400 mon ~120 mon ~400 mon

3 11 One Large sample followed by two small samples ~210 mon No ~190 mon No

4 12 Case # 3 with std in small samples inflated 1.64 times ~100 mon ~320 mon ~180 mon No

5 13 Case #3 with ave in small samples shifted up 0.276 ms ~48 mon ~168 mon No No

Figure 9 Tolerance Bound Evaluation #1 Figure 10 Tolerance Bound Evaluation #2

Figure 11 Tolerance Bound Evaluation #3 Figure 12 Tolerance Bound Evaluation #4


Figure 13 Tolerance Bound Evaluation #5

As expected, the biases introduced by the small sample sizes are predicted by their distribution bound characteristics, namely ULp and LLp which can serve as the effective USL and LSL. By referencing these effective limits, the tolerance bound evaluation of the life limiting age trend can be performed. It can be seen that for Cases 2 and 3, there is essentially no life-limiting age if ULp and LLp are used as the effective USL and LSL. It should also be noted that the biases will not mask the capability for identification of effects of changes in EED performance distribution, e.g., changes in ave and std as illustrated in cases 4 and 5 (Figs. 12 and 13).

VII. Application of Trend Line

Tolerance Bound Analysis to the EED Example

TOLU and TOLL bound curves. are plotted for AAT #1 and AAT #2 in Figs. 14 and 15. The age at the interceptions between the bound curves and ULp or LLp as well as the estimated additional allowable life estimate are summarized in Table 6. The additional life estimate uses a modification of the guideline for the cases in which p-value < 0.05: If there is no interception in the time frame of interest (~400 mon.), four-year is adopted; If interception is established, 20%

of the extra “useful life” defined by the intercept is allowed (Also limited to four years maximum, both are very conservative). It can be seen that the majority of the allowable additional life is four years except that for AAT #1 as determined by LLp, which is 1.9 yrs. This latter inaccuracy is likely caused by the fact that the trend line for AAT #1 analysis uses only two data groups. This inaccuracy is not a concern for two reasons: First of all, as previously stated, there is actually no LSL for the function time as stated previously. Secondly, a better result via LLp interception is obtained in the analysis for AAT #2 in which 4 yrs is verified by no interception. This more accurate result is attributed to the fact that three data groups are used in the analysis. Overall, the results acquired by the tolerance bound method are consistent with that obtained by the direct sample statistic analysis used in Section V.

Table 6 Trend Line Tolerance Bound Analysis for EED Function Time

Case #

Fig. #

TOLU Excurses

USL (5 ms)

TOLU Excurses

ULp (5.51 ms)

Additional Allowable Life per

ULp

TOLL Excurses

LSL (3 ms)

TOLL Excurses

LLp (2.43 ms)

Additional Allowable Life per

LLp AAT

#1 14 144 mon ~350 mon 4 yrs 72 mon 150 mon 1.9 yrs

AAT #2 15 ~120 mon ~380 mon 4 yrs ~340 mon No 4 yrs

Figure 14 99/95 Bounds for AAT #1 Figure 15 99/95 Bounds for AAT #2


Figure 16 99/95 Bounds for AAT #2 with AAT Equivalent Shelf Life

Assigned as 8.76 yrs Instead of 3 yrs

Recently, the equivalent shelf life as defined by AAT has been re-evaluated and there are indications6 that depending on the ECS storage temperature history, the current AAT may warrant shelf life that is much longer than the currently specified 3 yrs, e.g., 8.76 yrs if the storage temperature is maintained at a constant level of 75oF. To explore the impact of this interpretation, Fig. 16 plots the tolerance bounds for AAT #2 with adjusted equivalent ages for the test increments. It can be seen that this change improves the shelf life allowable with no excursion of ULp by the end of an age of 600 months as indicated in the figure. Future applications of this analysis strategy include: 1) To perform similar analyses for other EED performance parameters, e.g., peak pressure measured in the fixed volume pressure bomb and dent depth in the witness plate; 2) To analyze data for multiple lots; and 3) To analyze performance parameters for ECS other than EED. This will be a more difficult task as the LAT sample size is smaller for these components than that for EED and the same testing subgroups at different temperatures are also required.

VIII. Summary and Conclusions

Using EED function time as an example, a methodology for normalizing the effects of different test temperatures and firing currents has been successfully explored. This methodology enables all test samples to be presented as a single population from which data from lot acceptance test and age surveillance tests can be evaluated for statistical parameter age trends. Currently, the multiple sub-groups formed by combinations of several test parameters as required by the specifications render the sample size too small for a valid statistical evaluation if each subgroup is treated as a standalone. Two statistical approaches were examined: The first one was to analyze and compare the distribution characteristics including the average and standard deviation of the normal distribution for both the lot acceptance test and age surveillance test results. The second one was to analyze the tolerance bounds in the trend line analysis in relation to the specification limits. It is found that the criteria for the age trend are essentially the same in both methods. The effects of sample size on the tolerance bound divergence was evaluated, interpreted and compensated in a manner which has not previously been performed. In conclusion, if good age trend behavior is established, age surveillance test and accelerated aging test results can support additional shelf life (or service life) allocation of up to four years in addition to that already specified and allowed by passing these tests.

Acknowledgements

The author acknowledges S. Goldstein of the Aerospace Corporation and D.L. Jackson of ATK, Inc. for many helpful discussions on the topic in recent years; D.M. Miller and J.T. Walsh of Northrop Grumman for earlier discussions on statistics and regression; T.L. Graham of Ohio State Univ., E. Yang of Univ. of Pennsylvania and S. Yang of Case Western Reserve Univ. for reviewing this paper.1

References

1 Criteria for Explosive Systems and Device on Space and Launch Vehicles, AIAA S-113-2005, AIAA, 10 Nov. 2005, (p. 38, Paragraph 6.1.2.5, service Life Extension).

2 Yang, L.C. and Miller, D.M., “Advanced applications of Statistical Methods in Testing of Energetic Components and Systems,” 41th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 10-13 July 2005, Tucson, AZ.

3 MIL-STD-1576 (USAF), “Electroexplosive Subsystems Safety Requirements and Test Methods for Space Systems,” 31 July 1984.

4 DoD-E-63578A (USAF), “Explosive Ordnance for Space Vehicles,” October, 1987. 5 Eastern and Western Range Safety Requirement (USAF EWR 127-1), 45th Space Wing and 30th Space Wing, 31 march,

1997.


6 Yang, L.C., AIAA-2007-5138, “Correlation between Accelerated Aging Test (AAT) and Real World Storage Temperature ,” 43th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 8-11 July 2007, Cincinnati, OH. 7 Yang, L.C., Miller, D.M., Riley, J.A, Pham, D.C., Horst, M., Fuentes and A.A., Kuennen, T., AIAA-2006-4811“Testing of Mini-Igniter Containing 35-Year-Old B/KNO3 Pellets,” 42th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 9-12 July 2006, Sacramento, CA. 8 Yang, L.C., Granda, L.J., Riley, J.A., Grajeda, R., Pham, D.C. and Kuennen, T., AIAA-2006-4988, “Methods for Correction of Factors Affecting Dent Depth Measurement in Witness Plates,” 42th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 9-12 July 2006, Sacramento, CA. 9 Yang, L.C., AIAA-98-3911, "Post-Fire Short Circuit Phenomena of 'NSI Equivalents'," 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 12-15 July 1998, Cleveland, OH. The same paper was also published as “Postfire short Circuit Phenomena of Elctroexplosive Initiators,” pp586-590, Journal of Spacecraft and Rockets, Vol. 36, No. 4, July-August, 1999. 10 Barrere, M., Jaumotte, A., De Veubeke, B.F., and Vaqnderckhove, J., Rocket Propulsion, Elsevier Publishing Co., Armsterdam, 1960. 11 Ward, R.D., “Capacitance Discharge System for Ignition of Single Bridge Apollo Standard Initiators (SBASI),” NASA CR-2461, NASA, Langley Research Center, November 1974. 12 Yang, L.C., Dao-Randall, M.T., Pham, D.C., Jones, M. and Kuennen, T., AIAA-2003-5139,“Service Life Extension Of Minuteman II Thrust Termination Ordnance To Forty-Five Years,” 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 20-23 July 2003, Huntsville, AL. 13 Yang, L.C., Dao-Randall, M.T., Pham, D.C., Jones, M. and Kuennen, T., AIAA-2004-3423,” Testing of Minuteman II Safety And Arming Device with Improved Testing Techniques,” 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 11-14 July 2004, Ft Lauderdale, FL.

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