CN101750622A - Accelerated degradation test method of multistage separation type dynode electron multiplier - Google Patents

Abstract

The invention discloses an accelerated degradation test method of a multistage separation type dynode electron multiplier, which comprises the following steps: 1) placing at least five electron multiplier samples in a sealed container with binding posts, connecting electrodes of the electron multipliers with the corresponding binding posts, pumping the sealed container and maintaining vacuum; 2) respectively imposing at least three groups of incident particle flow strengths and working voltage values with different levels but higher than the normal using level on all the electron multiplier samples; 3) utilizing a milli-ampere current meter for carrying out continuous monitoring on the output current of all the electron multipliers; dividing the output current by the incident particle flow strength, converting into gain data and recording; and 4) utilizing a computer for processing the recorded gain data of the electron multipliers, and obtaining the predicted result of the service life.

Description

The accelerated degradation test method of multistage separation type dynode electron multiplier

Technical field

The invention belongs to electron tube accelerated test technical field, specifically, relate to a kind of by monitoring and analyze the gain data information of multistage separation type dynode electron multiplier (hereinafter to be referred as electron-multiplier) under acceleration environment, the accelerated test method of the life time of evaluation electron-multiplier under actual service conditions.

Background technology

Electron-multiplier belongs to vacuum electron device, is widely used in fields such as atomic frequency standard, lll night vision, nuclear detection, mass spectrophotometry, medical X imagings, is the key foundation device of restriction related-art technology development.The electron-multiplier life-span is normally defined the working time that its gain in normal operation drops to a certain threshold value, is a typical performance degradation life problems.

For the performance degradation life appraisal, utilize degradation experiment to obtain product performance degradation data under regular service condition usually, it reaches the degeneration time of thresholding by performance degradation characteristics modeling and forecasting.The defective of this method is that the test period is long, and test cost height is for some long-term degradation problems even can't implement.Accelerated degradation test is collected the performance degradation data of product under high stress level by improving the performance degradation process that stress level comes expedite product, utilizes these data to realize the long-term degradation characteristic modeling of product, thereby predicts its performance degradation life-span.The advantage of this method is to have shortened the test period, has reduced the test cost, can study the long-term behaviour degenerate problem in the feasible time.

The research of accelerated degradation test is mainly laid particular emphasis on the theoretical method of general character both at home and abroad, comprise aspects such as acceleration model, degradation model, statistical study, scheme optimization design.The theoretical method of these general character also needs to expand targetedly when using at specific product performance degradation problem, and the research of general character method mainly concentrates on the single stress accelerated degradation test at present, and many stress accelerated degradation test method is still immature.Accelerated degradation test has obtained application in performance degradation life predictions such as light emitting diode, logical integrated circuit, power supply, insulator, medicine at present, yet there are no the research report of electron-multiplier accelerated degradation test method.

Summary of the invention

The objective of the invention is, a kind of accelerated degradation test method of multistage separation type dynode electron multiplier is provided, can and quicken stress and the incidence relation between the time by accelerated test degraded data electron gain multiplier performance in short-term, and predict its serviceable life thus, and reduce the electrovacuum tested number of wasting time and energy.

Method provided by the invention may further comprise the steps:

Step 1, at least 5 electron-multiplier samples of general are put into the airtight container of band binding post, connect the electrode and the corresponding binding post of electron-multiplier, airtight container are pumped into and are kept vacuum;

Step 2, to each electron-multiplier sample apply at least 3 group varying levels respectively but be higher than the incident particle intensity of flow and the operating voltage numerical value of normal usage level;

Step 3, utilize milliampere reometer that the output current of each electron-multiplier is carried out continuous monitoring, and with output current divided by the incident particle intensity of flow, be converted into gain data and note;

Step 4, utilize computing machine the gain data of electron-multiplier of record to be handled, obtain its life prediction result by following flow process:

(1) described gain data is carried out pre-service, reject the singular point of gain data, also need where necessary gain data is carried out synchronous processing (such as utilizing the secondary method for resampling);

(2) each monitors t constantly down to utilize the fitting of distribution method to judge stress level combination i _IjThe distributional class that Shi Zengyi obeyed, calculated gains distribution parameter θ _IjPoint estimation

Wherein, i=1,2 ..., M, M are the stress level number of combinations; J=1,2 ..., l _i, l _iBe the monitoring number of times under the stress level combination i; θ _IjBe vectorial θ _Ij=[θ _Ij1θ _Ij2θ _Ijm] ', m is θ _IjDimension, such as for normal distribution θ _Ij=[θ _Ij1θ _Ij2] ', m=2, θ _Ij1=μ _IjBe average, θ _Ij2=σ _IjBe standard deviation;

(3) according to data

Make up gain profiles parameter θ under the stress level combination i _iAnd the relation between the time t, i.e. distribution parameter curve, its equation is:

lnθ _ik＝a _ik-b _ik?lnt，k＝1，2，…m

In the formula, θ _IkBe θ _iK component, a _Ik, b _IkBe the fitting coefficient of corresponding distribution parameter curve, t is the time;

(4) make up acceleration model according to the fitting coefficient of distribution parameter curve and the relation of quickening between the stress level, its equation is:

$\ln a_k={\mathrm{\&gamma;}}_{a_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">k</figure-callout>}}0}+{\mathrm{\&gamma;}}_{a_{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">k</figure-callout>}}1}\ln U+{\mathrm{\&gamma;}}_{a_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">k</figure-callout>}}2}\ln D+{\mathrm{\&gamma;}}_{a_{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="H2009102267497E00012.png,H2009102267497E00021.png"\; state="\{\{state\}\}">k</figure-callout>}}3}\ln U\&CenterDot;\ln D$

$\ln b_k={\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="0"\; label="b\; k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{k}0}+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="1"\; label="b\; k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{k}1}\ln U+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="2"\; label="b\; k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{k}2}\ln D+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="3"\; label="b\; k"\; filenames="H2009102267497E00012.png,H2009102267497E00021.png"\; state="\{\{state\}\}">b</figure-callout>}}_{k}3}\ln U\&CenterDot;\ln D$

In the formula, a _k, b _k(k=1,2) are the fitting coefficient function of distribution parameter curve,

Be the acceleration model coefficient, U is an operating voltage, and D is the incident particle intensity of flow;

(5) with the horizontal D of the normal applied stress of electron-multiplier ₀And U ₀The acceleration model that substitution (4) is drawn calculates the fitting coefficient a of the gain profiles parameter under the normal applied stress level _0k, b _0k, promptly

$\ln a_{0k}={\mathrm{\&gamma;}}_{a_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">k</figure-callout>}}0}+{\mathrm{\&gamma;}}_{a_{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">k</figure-callout>}}1}\mathrm{<figure-callout\; id="0"\; label="ln\; U"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}{U}_{}{}_0+{\mathrm{\&gamma;}}_{a_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">k</figure-callout>}}2}\mathrm{<figure-callout\; id="0"\; label="ln\; D"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}{D}_{}{}_0+{\mathrm{\&gamma;}}_{a_{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="H2009102267497E00012.png,H2009102267497E00021.png"\; state="\{\{state\}\}">k</figure-callout>}}3}\mathrm{<figure-callout\; id="0"\; label="ln\; U"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}{U}_{}{}_0\&CenterDot;\mathrm{<figure-callout\; id="0"\; label="ln\; D"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}{D}_{}{}_0$

$\ln b_{0k}={\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="0"\; label="b\; k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{k}0}+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="1"\; label="b\; k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{k}1}\mathrm{<figure-callout\; id="0"\; label="ln\; U"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}{U}_{}{}_0+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="2"\; label="b\; k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{k}2}\mathrm{<figure-callout\; id="0"\; label="ln\; D"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}{D}_{}{}_0+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="3"\; label="b\; k"\; filenames="H2009102267497E00012.png,H2009102267497E00021.png"\; state="\{\{state\}\}">b</figure-callout>}}_{k}3}\mathrm{<figure-callout\; id="0"\; label="ln\; U"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}{U}_{}{}_0\&CenterDot;\mathrm{<figure-callout\; id="0"\; label="ln\; D"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}{D}_{}{}_0$

(6) with (5) gained coefficient a _0kAnd b _0kThe listed equation of substitution (3) calculates gain profiles parameter under the normal applied stress level and the relation between the time,

lnθ _0k＝a _0k-b _0k?lnt

In the formula, θ _0kBe the gain profiles parameter θ under the normal applied stress level ₀K parameter;

(7) carry out model checking by steps such as residual analysis, model comptibility test, model accuracy analysis, Akaike's Information Criterion analyses, quicken the correctness of degradation model with check gained electron-multiplier;

(8) according to the given electron-multiplier gain degradation failure threshold value D of actual request for utilization _f, utilize the gain profiles parameter θ under (6) resulting normal applied stress level ₀Calculate the Q-percentile life of electron-multiplier, process is as follows:

1. the t that derives is the Reliability Function of electron-multiplier constantly:

R(t)＝P{G _t＞D _f}＝1-P{G _t＜D _f}＝1-F(D _f；θ ₀(t))

In the formula: R (t) is a Reliability Function, and P is a probability, G _tBe the t gain of electron-multiplier constantly; The distribution function that F () is obeyed for gain; θ ₀Parameter for t moment distribution function F ();

2. calculate given reliability R _τQ-percentile life τ under the condition:

τ＝R ^-1(R _τ)

In the formula: R ^-1() is the inverse function of Reliability Function R ().

In above-mentioned steps 1, the airtight container that a plurality of electron-multiplier samples are put into a plurality of correspondences is tested simultaneously, can control by handled easily, shorten test period greatly.

In above-mentioned steps 2, the highest level setting of adopting the test of knowing the real situation to obtain incident particle intensity of flow and operating voltage, this is provided with the consistance that can guarantee under electron-multiplier degradation mechanism and the regular service condition.

In above-mentioned steps 2, adopt the fractional factorial experiment method for designing can reduce the stress level combination, and corresponding tested number.

In above-mentioned steps 3, the principle that dredge by principle that equates or earlier close back at the monitoring time interval is provided with, and energy short form test scheme improves estimated accuracy.Monitoring time is arranged to uniformly-spaced, is convenient to the physical record operation; The time interval of being arranged to dredge earlier close back can reduce the monitoring number of times, and optimal design is because the gain decline rate of electron-multiplier first quick and back slow.

The invention provides a cover and realize the method for electron-multiplier performance degradation life prediction based on two stress accelerated degradation tests.This method will gain as the monitoring index of electron-multiplier performance degradation, with incident particle intensity of flow and operating voltage as quickening stress, the gain data that utilization obtains in accelerated test in short-term carries out modeling to electron-multiplier performance degradation process, thus the performance degradation life-span of predict electronic multiplier.This method can truly reflect the normal performance degradation process of using of electron-multiplier, can carry out accelerated test with bigger accelerator coefficient, shortened test period, reduced the test cost, for electron-multiplier long-term behaviour degeneration life search provides a kind of feasible technical method.

Method provided by the invention has been successfully applied to the long-life tackling key problem research of certain multistage separation type dynode electron multiplier at present, and the electron-multiplier performance degradation life-span has been carried out predicting accurately.

Description of drawings

Fig. 1 to Fig. 5 is respectively the gain-time plot of each electron-multiplier sample (#1 to #5) under 5 kinds of varying level operating voltage U and incident particle intensity of flow D condition.

Fig. 6 is the gain degenerated curve figure after resampling.

Fig. 7 is the Parameters of Normal Distribution average-time plot of gain.

Fig. 8 is the Parameters of Normal Distribution standard deviation-time plot of gain.

Fig. 9 is the Parameters of Normal Distribution logarithm average-logarithmic time curve map of gain.

Figure 10 is the Parameters of Normal Distribution logarithm standard deviation-logarithmic time curve map of gain.

Figure 11 to Figure 15 is the Parameters of Normal Distribution average match residual error Normal P-P under 5 kinds of varying level operating voltage U and incident particle intensity of flow D condition.

Figure 16 to Figure 20 is the Parameters of Normal Distribution standard deviation match residual error Normal P-P under 5 kinds of varying level operating voltage U and incident particle intensity of flow D condition.

Figure 21 is coefficient a ₁Acceleration model match residual error Normal P-P.

Figure 22 is coefficient b ₁Acceleration model match residual error Normal P-P.

Figure 23 is coefficient a ₂Acceleration model match residual error Normal P-P.

Figure 24 is coefficient b ₂Acceleration model match residual error Normal P-P.

Figure 25 is an electron-multiplier fiduciary level curve map under the normal applied stress level.

Embodiment

Be the embodiment that example further specifies the method for the invention with certain homemade 9 grades of separate type dynode electron-multiplier below.The negative electrode of this electron-multiplier and each dynode material are the Mg-AgO alloy, adopt CO ₂Active mode, the cesium ion bundle that is used for certain atomic frequency standard system detects and the intensity amplification.It needs to be noted, below implement only to be used to illustrate the present invention, but not be used to limit scope of the present invention.

Embodiment 1, 9 grades of separate type dynode electron-multiplier accelerated degradation tests

Step 1, the electron-multiplier sample is put into airtight container with a plurality of binding posts, connect the electrode and the corresponding binding post of electron-multiplier, airtight container is pumped into and is kept vacuum.Every 5 electron-multiplier samples of test input of taking turns are tested, and each electron-multiplier sample uses an airtight container, therefore needs 5 airtight containers.

Step 2, to each electron-multiplier sample apply 3 groups of varying levels respectively but be higher than the incident particle intensity of flow and the operating voltage numerical value of normal usage level.

Operating voltage U when this electron-multiplier sample normally uses ₀=2400V, cesium ion incident particle intensity of flow D ₀=6 * 10 ^-12A.The highest level that obtains incident particle intensity of flow and operating voltage by the test of knowing the real situation is set to 5 * 10 ^-11A, 2700V, this setting can guarantee the consistance under degradation mechanism and the regular service condition.Therefore the acceleration stress level that provides U and D is respectively:

U ₁＝2500V，U ₂＝2600V，U ₃＝2700V；

D ₁＝0.9×10 ^-11A，D ₂＝2×10 ^-11A，D ₃＝5×10 ^-11A。

The complete combination of above-mentioned acceleration stress level has constituted 3 * 3 grid, and is as shown in table 1, and each grid has been represented an accelerated test condition, therefore need carry out 9 groups of son tests.

The complete combination of table 12 stress 3 levels

	??D 1	??D 2	??D 3
				??U 1	??(U 1，D 1)	??(U 1，D 2)	??(U 1，D 3)
??U 2	??(U 2，D 1)	??(U 2，D 2)	??(U 2，D 3)
				??U 3	??(U 3，D 1)	??(U 3，D 2)	??(U 3，D 3)

In order to reduce tested number, save test sample, use for reference the statistics test design method, adopt the fractional factorial experiment design to carry out accelerated test.Because it is high more to quicken stress level, the deterioration velocity of electron-multiplier is fast more, and the efficient of test is high more, therefore adopts fractional factorial experiment design as shown in table 2, carries out 5 groups of son tests altogether.

The fractional factorial experiment design of table 22 stress 3 levels

	??D 1	??D 2	??D 3
				??U 1	??-	??-	??(U 1，D 3)
??U 2	??-	??-	??(U 2，D 3)
				??U 3	??(U 3，D 1)	??(U 3，D 2)	??(U 3，D 3)

Every group of son test drops into 5 electron-multiplier samples, and therefore testing total electron-multiplier sample size is 25.

Step 3, a utilization milliampere reometer carry out continuous monitoring to the electron-multiplier sample output current that is under step 1, step 2 environment, test monitoring adopts the monitoring mode of constant duration, every 1 hour the output current of electron-multiplier sample is once monitored, and with output current divided by the incident particle intensity of flow, being converted into gain data notes, as Fig. 1～shown in Figure 5, be respectively that each electron-multiplier sample (#1 to #5) is at (U ₃, D ₁), (U ₁, D ₃), (U ₃, D ₂), (U ₂, D ₃) and (U ₃, D ₃) gain time curve map under the condition.

Step 4, utilize computing machine by following flow process to the record electron-multiplier sample gain data handle, obtain its life prediction result:

(1) will gain-time data carries out pre-service, rejects the singular point of gain data.Asynchronism(-nization) step problem at gain data exists adopts the secondary method for resampling that gain data is carried out synchronous processing, and pretreated gain-time data as shown in Figure 6.

(2) utilize the fitting of distribution method judge stress level combination i (i=1,2 ..., M, M are the stress level number of combinations) each monitoring t constantly down _Ij(j=1,2 ..., l _i, l _iBe stress level combination i monitoring number of times down) time distributional class that gains and obeyed, calculated gains distribution parameter θ _Ij(θ _IjBe vectorial θ _Ij=[θ _Ij1θ _Ij2θ _Ijm] ', m is θ _IjDimension.Such as for normal distribution θ _Ij=[θ _Ij1θ _Ij2] ', m=2, θ _Ij1=μ _IjBe average, θ _Ij2=σ _IjBe standard deviation) point estimation

Data shown in Figure 6 are divided into groups according to each stress level, respectively each gain data constantly that resamples is carried out test of hypothesis, the result shows gain, and Normal Distribution, lognormal distribution, exponential distribution, Weibull distribute simultaneously, therefore further utilize the related coefficient analysis to select optimum distributional class, as calculated respectively to quicken under the stress level related coefficient as shown in table 3.Because the related coefficient average that data obtain when normal distribution and lognormal distribution are carried out match is the most near 1, and the two is comparatively approaching, calculates for the ease of statistical study, this test selects for use normal distribution as the gain profiles function.

Table 3 correlation coefficient charts

Calculated stress horizontal combination i is each monitoring moment t down _IjThe Parameters of Normal Distribution θ of Shi Zengyi _Ij=[θ _Ij1θ _Ij2[the μ of] '= _Ijσ _Ij] ' point estimation ${\widehat{\mathrm{\&theta;}}}_{\mathrm{ij}}={\left[\begin{array}{cc}{\widehat{\mathrm{\&theta;}}}_{\mathrm{<figure-callout\; id="1"\; label="ij"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ij</figure-callout>}1}& {\widehat{\mathrm{\&theta;}}}_{\mathrm{<figure-callout\; id="2"\; label="ij"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ij</figure-callout>}2}\end{array}\right]}^{\&prime;}={\left[\begin{array}{cc}{\widehat{\mathrm{\&mu;}}}_{\mathrm{ij}}& {\widehat{\mathrm{\&sigma;}}}_{\mathrm{ij}}\end{array}\right]}^{\&prime;},$

${\widehat{\mathrm{\&mu;}}}_{\mathrm{ij}}=\frac{1}{n}\underset{h=1}{\overset{n}{\mathrm{\&Sigma;}}}{G}_{\mathrm{ijh}}$

${\widehat{\mathrm{\&sigma;}}}_{\mathrm{ij}}={\left[\frac{1}{n-1}\underset{h=1}{\overset{n}{\mathrm{\&Sigma;}}}{(G_{\mathrm{ijh}}-{\widehat{\mathrm{\&mu;}}}_{\mathrm{ij}})}^2\right]}^{1/2}$

Wherein: i represents a certain stress level combination, i=1,2,3,4,5; N is the electron-multiplier sample number under the stress level combination i, n=5;

Be illustrated respectively under the stress level combination i, n sample is at t _IjThe average of Shi Zengyi and the point estimation of standard deviation; G _IjhUnder the expression stress level combination i, t _IjThe gain of h electron-multiplier constantly.

(3) according to data

Make up gain profiles parameter θ under the stress level combination i _iAnd the relation between the time t, i.e. distribution parameter curve, its equation is:

lnθ _ik＝a _ik-b _ik?lnt，k＝1，2，…m

In the formula, θ _IkBe θ _iK component, a _Ik, b _IkBe the fitting coefficient of corresponding distribution parameter curve, t is the time.

Because ${\widehat{\mathrm{\&theta;}}}_{\mathrm{ij}}={\left[\begin{array}{cc}{\widehat{\mathrm{\&mu;}}}_{\mathrm{ij}}& {\widehat{\mathrm{\&sigma;}}}_{\mathrm{ij}}\end{array}\right]}^{\&prime;},$ M=2, k=1,2, so said process can be embodied as: according to data

Make up gain profiles parameter μ under the stress level combination i _iAnd the relation between the time t

lnμ _i＝a _i1-b _i1?lnt

In the formula, μ _iBe the Mean Parameters of the normal distribution of gain under the stress level combination i, a _I1, b _I1Be corresponding fitting coefficient, t is the time.

According to data

Make up gain profiles parameter σ under the stress level combination i _iAnd the relation between the time t

lnσ _i＝a _i2-b _i2?lnt

In the formula, σ _iBe the standard deviation parameter of the normal distribution of gain under the stress level combination i, a _I2, b _I2Be corresponding fitting coefficient, t is the time.

By calculating the average under the different stress levels combination i and the fitting coefficient a of standard deviation curve _I1, b _I1, a _I2, b _I2, as shown in table 4, corresponding distribution parameter curve such as Fig. 7～shown in Figure 10, wherein Fig. 9 and Figure 10 are respectively logarithm average-logarithmic time curve, the logarithm standard deviation-logarithmic time curve after the linearization.

Different average and the variance curve fitting coefficients that quicken under the stress level of table 4

Parameter	??U 3，D 1	??U 3，D 2	??U 1，D 3	??U 2，D 3	??U 3，D 3
						??a i1	??14.356	??14.337	??13.883	??12.84	??12.744
??b i1	??1.1054	??1.0965	??1.0537	??0.8467	??1.0113
						??a i2	??13.815	??13.934	??10.128	??9.4813	??12.47
??b i2	??1.0415	??1.4393	??0.67903	??0.19467	??1.23

(4) make up acceleration model according to the fitting coefficient of distribution parameter curve and the relation of quickening between the stress level, its equation is:

$\ln a_k={\mathrm{\&gamma;}}_{a_{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">k</figure-callout>}}0}+{\mathrm{\&gamma;}}_{a_{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">k</figure-callout>}}1}\ln U+{\mathrm{\&gamma;}}_{a_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">k</figure-callout>}}2}\ln D+{\mathrm{\&gamma;}}_{a_{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="H2009102267497E00012.png,H2009102267497E00021.png"\; state="\{\{state\}\}">k</figure-callout>}}3}\ln U\&CenterDot;\ln D$

$\ln b_k={\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="0"\; label="b\; k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{k}0}+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="1"\; label="b\; k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{k}1}\ln U+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="2"\; label="b\; k"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{k}2}\ln D+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="3"\; label="b\; k"\; filenames="H2009102267497E00012.png,H2009102267497E00021.png"\; state="\{\{state\}\}">b</figure-callout>}}_{k}3}\ln U\&CenterDot;\ln D$

In the formula, a _k, b _k(k=1,2) are the fitting coefficient of distribution parameter curve,

Be the acceleration model coefficient, U is an operating voltage, and D is the incident particle intensity of flow.

Consider to adopt respectively two kinds of acceleration models.The 1st kind of acceleration model considered two kinds of linear coupling terms of quickening between the stress, promptly

$\ln a_1={\mathrm{\&gamma;}}_{a_{1}0}+{\mathrm{\&gamma;}}_{a_{1}1}\ln U+{\mathrm{\&gamma;}}_{a_{1}2}\ln D+{\mathrm{\&gamma;}}_{a_{1}3}\ln U\&CenterDot;\ln D$

$\mathrm{<figure-callout\; id="1"\; label="ln\; b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}{b}_{}{}_1={\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1}0}+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1}1}\ln U+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1}2}\ln D+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1}3}\ln U\&CenterDot;\ln D$

$\ln a_2={\mathrm{\&gamma;}}_{a_{2}0}+{\mathrm{\&gamma;}}_{a_{2}1}\ln U+{\mathrm{\&gamma;}}_{a_{2}2}\ln D+{\mathrm{\&gamma;}}_{a_{2}3}\ln U\&CenterDot;\ln D$

$\mathrm{<figure-callout\; id="2"\; label="ln\; b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}{b}_{}{}_2={\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2}0}+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2}1}\ln U+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2}2}\ln D+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2}3}\ln U\&CenterDot;\ln D$

The 2nd kind of acceleration model equation do not considered two kinds of linear coupling terms of quickening between the stress, promptly

$\ln a_1={\mathrm{\&gamma;}}_{a_{1}0}+{\mathrm{\&gamma;}}_{a_{1}1}\ln U+{\mathrm{\&gamma;}}_{a_{1}2}\ln D$

$\mathrm{<figure-callout\; id="1"\; label="ln\; b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}{b}_{}{}_1={\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1}0}+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1}1}\ln U+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{1}2}\ln D$

$\ln a_2={\mathrm{\&gamma;}}_{a_{2}0}+{\mathrm{\&gamma;}}_{a_{2}1}\ln U+{\mathrm{\&gamma;}}_{a_{2}2}\ln D$

$\mathrm{<figure-callout\; id="2"\; label="ln\; b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">ln</figure-callout>}{b}_{}{}_2={\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2}0}+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2}1}\ln U+{\mathrm{\&gamma;}}_{{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="H2009102267497E00011.png,H2009102267497E00012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{2}2}\ln D$

It is as shown in table 5 to draw acceleration model coefficient and the corresponding model fitting residual sum of squares (RSS) of considering linear coupling terms by model fitting, acceleration model coefficient and the corresponding model fitting residual sum of squares (RSS) of not considering linear coupling terms are as shown in table 6, acceleration model match residual sum of squares (RSS) shown in the table 6 is littler, therefore adopt the acceleration model of not considering linear coupling terms, promptly

lna ₁＝7.5527-0.8729lnU-0.0798lnD

lnb ₁＝0.0923-0.3016lnU-0.0949lnD

lna ₂＝-23.6906+3.0167lnU-0.0988lnD

lnb ₂＝-80.7618+9.478lnU-0.2397lnD

Table 5 is considered the acceleration model coefficient and the residual sum of squares (RSS) of linear coupling terms

Parameter	??γ 0	??γ 1	??γ 2	??γ 3	Residual sum of squares (RSS)
						??a 1	??0.4702	??-0.0183	??-0.3576	??0.039	??5.5826
??b 1	??-1.3833	??-0.114	??-0.1575	??0.0079	??0.02933
						??a 2	??0.0281	??-0.023	??0.9202	??-0.1255	??4.7233
??b 2	??-3.8752	??-0.2387	??2.9949	??-0.4104	??2.253

Table 6 is not considered the acceleration model coefficient and the residual sum of squares (RSS) of linear coupling terms

Parameter	??γ 0	??γ 1	??γ 2	Residual sum of squares (RSS)
					??a 1	??7.5527	??-0.8729	??-0.0798	??0.0032187
??b 1	??0.0923	??-0.3016	??-0.0949	??0.02891
					??a 2	??-23.6906	??3.0167	??-0.0988	??0.024478
??b 2	??-80.7618	??9.478	??-0.2397	??1.7708

γ 0 expression in table 5, the table 6

γ 1 expression

γ 2 expressions

γ ₃Expression

(5) with the horizontal U of the normal applied stress of electron-multiplier sample ₀=2400V, D ₀=6 * 10 ^-12The acceleration model that A substitution (4) is drawn calculates the fitting coefficient a of the gain profiles parameter under the normal applied stress level _0k, b _0k, k=1,2, promptly

lna ₀₁＝7.5527-0.8729lnU ₀-0.0798lnD ₀

lnb ₀₁＝0.0923-0.3016lnU ₀-0.0949lnD ₀

lna ₀₂＝-23.6906+3.0167lnU ₀-0.0988lnD ₀

lnb ₀₂＝-80.7618+9.478lnU ₀-0.2397lnD ₀

Calculate a ₀₁=16.794, b ₀₁=1.2187, a ₀₂=10.391, b ₀₂=0.44969.

(6) with (5) gained coefficient a ₀₁, b ₀₁, a ₀₂, b ₀₂The listed equation of substitution (3) calculates gain profiles parameter under the normal applied stress level and the relation between the time,

lnθ ₀₁＝a ₀₁-b ₀₁lnt

lnθ ₀₂＝a ₀₂-b ₀₂lnt

θ herein ₀=[θ ₀₁θ ₀₂]=[μ ₀σ ₀], so

lnμ ₀＝16.794-1.2187lnt

lnσ ₀＝10.391-0.44969lnt

(7) carry out model checking by steps such as residual analysis, model comptibility test, model accuracy analysis, Akaike's Information Criterion analyses, quicken the correctness of degradation model with check gained electron-multiplier.

(7.1) residual analysis

The match residual analysis result of gain profiles parametric line such as Figure 11～shown in Figure 20, result's approximately linear shows match residual error Normal Distribution among the figure.Acceleration model match residual analysis result such as Figure 21～shown in Figure 24, result's approximately linear shows match residual error Normal Distribution among the figure.

(7.2) model comptibility test

By the distribution parameter curve fitting goodness coefficient of determination R that calculates ²As shown in table 7.

Table 7 goodness of fit coefficient of determination

Remove son test (U ₂, D ₃) owing to pilot system break down shut down midway cause the coefficient of determination value on the low side outside, the coefficient of determination under all the other each stress levels all is in close proximity to 1, curve fitting is more excellent.

(7.3) model accuracy analysis

Owing to judged the match residual error Normal Distribution of gain profiles parametric line and acceleration model, only need further match residual error average to be carried out test of hypothesis, H ₀: μ=0; H ₁: μ ≠ 0.Calculate the gained test statistics $t=\frac{\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}}{S/\sqrt{n-1}}$ Absolute value is listed in table 8 and table 9 respectively.

The match residual test statistic of table 8 distribution parameter curve | t| * 10 ^-12

Distribution parameter	??U 3，D 1	??U 3，D 2	??U 1，D 3	??U 2，D 3	??U 3，D 3
						??μ	??0.9574	??0.9959	??0.9959	??0.8849	??0.9951

Distribution parameter	??U 3，D 1	??U 3，D 2	??U 1，D 3	??U 2，D 3	??U 3，D 3
						??σ	??0.52607	??1.9976	??0.3976	??0.081	??1.2652

Table 9 acceleration model match residual test statistic

The fitting coefficient of distribution parameter curve	??a μ	??b μ	??a σ	??b σ
					Test statistics | t| * 10 -8	??0.1697	??0.0024	??0.0602	??0.0012

His-and-hers watches 8 data are got confidence alpha=0.05, because in all checks | and t|＜t _1-α/2So the fitting coefficient predicted value of distribution parameter curve does not depart from actual value.His-and-hers watches 9 data are got confidence alpha=0.05, same because | t|＜t _1-α/2So the acceleration model predicted value does not depart from actual value.

(7.4) Akaike's Information Criterion analysis

By said process electron-multiplier being carried out life appraisal needs match two class models, and a class is the match that the gain profiles parametric line is carried out, and a class is the acceleration model match that the fitting coefficient to the distribution parameter curve carries out.Summation obtains total residual sum of squares (RSS) SSE to two class match residual errors _T=107.9559.The variable number q of above-mentioned model _T=18, therefore

AIC _T＝log(SSE _T)+2q _T＝38.0332

The AIC value and two alternative approach of said method gained are analyzed, and the result is as shown in table 10.As can be known, above-mentioned model has less AIC value.Therefore, its fitting result is more excellent under the goodness of fit and the comprehensive balance of model complexity.

Table 10, acceleration model match residual test statistic

The AIC analysis result	This method	Alternative approach 1	Alternative approach 2
				?AIC	??38.0332	??57.7165	??51.9005

(8) according to the given electron-multiplier gain degradation failure threshold value D of actual request for utilization _f, utilize the gain profiles parameter θ under (6) resulting normal applied stress level ₀Calculate the Q-percentile life of electron-multiplier, process is as follows:

1. the t that derives is the Reliability Function of electron-multiplier constantly: the Reliability Function of electron-multiplier is the probability of gain greater than the degradation failure threshold value, owing to the normal distribution that is distributed as of a certain moment electron-multiplier gain, so

$R\left(t\right)=P\{G_t>D_f\}$

$=1-P\{G_t<D_f\}$

$=1-\mathrm{\&Phi;}\left(\frac{D_f-{\mathrm{\&mu;}}_0}{{\mathrm{\&sigma;}}_0}\right)$

$=1-\mathrm{\&Phi;}\left(\frac{D_f-\exp (16.794-1.2187\ln t)}{\exp (10.391-0.44969\ln t)}\right)$

In the formula, R (t) represents Reliability Function, and P represents probability, G _tExpression t gain constantly, D _f=10 ³Be failure threshold, Φ () represents Standard Normal Distribution, θ ₀=[μ ₀σ ₀] for the distribution parameter of Φ () be average and standard deviation.The fiduciary level curve that is obtained by following formula as shown in figure 25.

2. calculate given reliability R _τQ-percentile life τ under the condition: τ=R ^-1(R _τ).By the definite inverse function τ=R of following formula ^-1(R _τ) analytical form be difficult to obtain, below utilize numerical method to find the solution Q-percentile life τ.Given reliability R _τ=0.5 o'clock, with its substitution

1. the Reliability Function in

$0.5=1-\mathrm{\&Phi;}\left(\frac{{10}^3-\exp (16.794-1.2187\ln \mathrm{\&tau;})}{\exp (10.391-0.44969\ln \mathrm{\&tau;})}\right)$

Utilize numerical method (as utilizing the fzero function in the Matlab7 software) to separate above-mentioned equation, obtaining working as fiduciary level is R _τ=0.5 o'clock, corresponding median life was τ=3335 hour.

In sum, above-mentioned example utilizes accelerated test method only to use test less than 240 hours, dope 3335 hours life-span of electron-multiplier, realized long-term behaviour degeneration life prediction by the accelerated test in the short time, reduced experimentation cost, saved test period, in the life search of electron-multiplier performance degradation, had important use and be worth.

In above-mentioned example of the present invention, though used 25 groups of data (every group is 5 samples) under 5 stress levels, use more multi-group data, the result of acquisition will be better.

Claims (2)

1. the accelerated degradation test method of a multistage separation type dynode electron multiplier is characterized in that may further comprise the steps:

Step 1, at least 5 electron-multiplier samples of general are put into the airtight container of band binding post, connect the electrode and the corresponding binding post of electron-multiplier, airtight container are pumped into and are kept vacuum;

Step 2, to each electron-multiplier sample apply at least 3 group varying levels respectively but be higher than the incident particle intensity of flow and the operating voltage numerical value of normal usage level;

Step 3, utilize milliampere reometer that the output current of each electron-multiplier is carried out continuous monitoring, and with output current divided by the incident particle intensity of flow, be converted into gain data and note;

Step 4, utilize computing machine the gain data of electron-multiplier of record to be handled, obtain its life prediction result by following flow process:

(1) described gain data is carried out pre-service, reject the singular point of gain data, also need where necessary gain data is carried out synchronous processing;

(2) each monitors t constantly down to utilize the fitting of distribution method to judge stress level combination i _IjThe distributional class that Shi Zengyi obeyed, calculated gains distribution parameter θ _IjPoint estimation

Wherein, i=1,2 ..., M, M are the stress level number of combinations; J=1,2 ..., l _i, l _iBe the monitoring number of times under the stress level combination i; θ _IjBe vectorial θ _Ij=[θ _Ij1θ _Ij2θ _Ijm] ', m is θ _IjDimension, such as for normal distribution θ _Ij=[θ _Ij1θ _Ij2] ', m=2, θ _Ij1=μ _IjBe average, θ _Ij2=σ _IjBe standard deviation;

(3) according to data

Make up gain profiles parameter θ under the stress level combination i _iAnd the relation between the time t, i.e. distribution parameter curve, its equation is:

lnθ _ik＝a _ik-b _iklnt，k＝1，2，…m

In the formula, θ _IkBe θ _iK component, a _Ik, b _IkBe the fitting coefficient of corresponding distribution parameter curve, t is the time;

(4) make up acceleration model according to the fitting coefficient of distribution parameter curve and the relation of quickening between the stress level, its equation is:

$\ln a_k={\mathrm{\&gamma;}}_{a_{k}0}+{\mathrm{\&gamma;}}_{a_{k}1}\ln U+{\mathrm{\&gamma;}}_{a_{k}2}\ln D+{\mathrm{\&gamma;}}_{a_{k}3}\ln U\&CenterDot;\ln D$

$\ln b_k={\mathrm{\&gamma;}}_{b_{k}0}+{\mathrm{\&gamma;}}_{b_{k}1}\ln U+{\mathrm{\&gamma;}}_{b_{k}2}\ln D+{\mathrm{\&gamma;}}_{b_{k}3}\ln U\&CenterDot;\ln D$

In the formula, a _k, b _k(k=1,2) are the fitting coefficient function of distribution parameter curve,

Be the acceleration model coefficient, U is an operating voltage, and D is the incident particle intensity of flow;

(5) with the horizontal D of the normal applied stress of electron-multiplier ₀And U ₀The acceleration model that substitution (4) is drawn calculates the fitting coefficient a of the gain profiles parameter under the normal applied stress level _0k, b _0k, promptly

$\ln a_{0k}={\mathrm{\&gamma;}}_{a_{k}0}+{\mathrm{\&gamma;}}_{a_{k}1}\ln U_0+{\mathrm{\&gamma;}}_{a_{k}2}\ln D_0+{\mathrm{\&gamma;}}_{a_{k}3}\ln U_0\&CenterDot;\ln D_0$

$\ln b_{0k}={\mathrm{\&gamma;}}_{b_{k}0}+{\mathrm{\&gamma;}}_{b_{k}1}\ln U_0+{\mathrm{\&gamma;}}_{b_{k}2}\ln D_0+{\mathrm{\&gamma;}}_{b_{k}3}\ln U_0\&CenterDot;\ln D_0$

(6) with (5) gained coefficient a _0kAnd b _0kThe listed equation of substitution (3) calculates gain profiles parameter under the normal applied stress level and the relation between the time,

lnθ _0k＝a _0k-b _0klnt

In the formula, θ _0kBe the gain profiles parameter θ under the normal applied stress level ₀K parameter;

(7) carry out model checking by steps such as residual analysis, model comptibility test, model accuracy analysis, Akaike's Information Criterion analyses, quicken the correctness of degradation model with check gained electron-multiplier;

(8) according to the given electron-multiplier gain degradation failure threshold value D of actual request for utilization _f, utilize the gain profiles parameter θ under (6) resulting normal applied stress level ₀Calculate the Q-percentile life of electron-multiplier, process is as follows:

1. the t that derives is the Reliability Function of electron-multiplier constantly:

R(t)＝P{G _t＞D _f}＝1-P{G _t＜D _f}＝1-F(D _f；θ ₀(t))

In the formula: R (t) is a Reliability Function, and P is a probability, G _tBe the t gain of electron-multiplier constantly; The distribution function that F () is obeyed for gain; θ ₀Parameter for t moment distribution function F ();

2. calculate given reliability R _τQ-percentile life τ under the condition:

τ＝R ^-1(R _τ)

In the formula: R ^-1() is the inverse function of Reliability Function R ().

2. the accelerated degradation test method of multistage separation type dynode electron multiplier according to claim 1 is characterized in that in the above-mentioned steps 3, and monitoring time is provided with by the principle that dredge principle that equates or earlier close back at interval.

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