Total dose lot acceptance analysis
Paste each parameter's readings, units down the side and dose steps across the top, set the limits and the P and confidence pair, and get the one sided tolerance bound x̄ + KTL s at every step, a pass or fail call per step and for the lot, and a report to print or download.
Acceptance criterion
Parameter data
One table per parameter. First row: a unit label header (optional) then the dose steps in krad(Si); non numeric headers such as "RT anneal" or "100C anneal" are plotted after the last dose step. Following rows: one unit per row. Paste straight from a spreadsheet (tab separated) or type comma separated values.
Each parameter card has its own limits, an optional log transform for parameters that are lognormal (leakage currents, bias currents), and a choice of evaluating the measured values or the shifts from pre irradiation against delta limits. Blank cells are missing measurements; F marks a functional failure and removes the unit from that step and the later ones.
Test identification, for the report
Does the lot pass?
Report
How it works
Evaluating lot acceptance from measured data
Paste the readings
One table per parameter, units down the side and dose steps across the top. A blank cell is a missing measurement; F marks a functional failure and takes the unit out from that step on.
Compute the bound at each step
At every step the tool takes the mean and standard deviation of the units measured there, and the exact KTL for that sample size, P and γ, from the noncentral t.
Compare it with the limit
A step passes when x̄ + KTL s stays at or below the upper limit, and x̄ − KTL s at or above a lower one. The lot passes when every irradiation step of every parameter with a limit does.
The acceptance criterion in brief what the report states, and why small lots are hard
Paste the parameter readings from a total dose test, one table per parameter with the units down the side and the dose steps across the top, set the limits, and get the report: every unit plotted against dose, the sample mean, and the one sided tolerance bounds x̄ ± KTL s at each step, with the pass or fail call against the limit. KTL is computed exactly from the noncentral t for the sample size at each step (units that failed functionally drop out and the factor grows). The default criterion is the usual space pairing, 99 percent of the lot with 90 percent confidence; change it to what your program calls for.
The criterion. With n units measured at a dose step, sample mean x̄ and standard deviation s, the lot is accepted at that step when x̄ + KTL(n, P, γ) s ≤ upper limit and, for a parameter with a lower limit, x̄ − KTL s is at or above it. The statement this supports is: with confidence γ, at least a fraction P of the lot is inside the limit at that dose. For n = 10, P = 0.99 and γ = 0.90, KTL = 3.53, so the mean must sit three and a half sample standard deviations inside the limit. This statistical margin can make acceptance difficult for small samples when a parameter drifts toward its limit, as the plots illustrate.
Methodology: how the report is computed the factor, the steps, the assumptions
What the report computes, where the factor comes from, and what the method assumes about your data.
The one sided tolerance limit
Assume a parameter x at a given dose step is normally distributed across the lot with unknown mean and standard deviation. From n units we have x̄ and s. We want to claim, with confidence γ, that at least a fraction P of the lot has x inside the limit. The claim is supported when
KTL is the one sided normal tolerance factor. It is larger than the normal quantile zP because x̄ and s are themselves uncertain: for n = 10, P = 0.99, γ = 0.90 it is 3.53 against z0.99 = 2.33, and at n = 100 it is still 2.60. It depends only on n, P and γ, never on the parameter or the technology, which is why MIL-HDBK-814 [1] and Method 1019 [2] can carry it as a table. This tool computes it rather than looking it up, so any sample size and any P, γ pair work, including the reduced sample sizes that appear after a functional failure.
Computing K exactly
If T' is a noncentral t variable with ν = n − 1 degrees of freedom and noncentrality δ = zP√n, then KTL = t'γ(ν, δ)/√n with t'γ the γ quantile. The distribution function is evaluated by writing T' = (Z + δ)/S with S = √(V/ν), V chi square, so that P(T' ≤ t) is the expectation over S of Φ(tS − δ); that is a one dimensional integral against the density of S, done by Simpson's rule on 4000 points, and the quantile is found by bisection. Results agree with the Odeh and Owen tables [3] to the third decimal for n from 3 to 100 and were checked by Monte Carlo (two million simulated samples reproduce the stated coverage at n = 2, 3, 5, 10, 20). The n = 2 value for P = 0.99, γ = 0.90 is 18.50; some older tables print a different figure.
Choosing P and gamma
P = 0.99 with γ = 0.90 is the pairing most often quoted for space parts and is the default. 0.90/0.90 is used for non critical applications, 0.99/0.95 or 0.999/0.90 for critical ones. The choice belongs to the program, not to the test, and the report states the pair used. Note what P means: it is the fraction of the lot inside the limit at that dose, not a probability the mission survives; a P = 0.99 part in a box with 50 of them has about a 40 percent chance that at least one is outside the limit at the end of dose.
Dose steps, anneal steps and failures
Each column of a data table is a step and gets its own statistics, factor and verdict; the anneal columns (non numeric headers) are evaluated the same way and plotted after the last dose step, since the Method 1019 room temperature and rebound anneal measurements are part of the acceptance sequence. A unit marked F at a step has failed functionally: it is removed from that step and every later one, the sample size falls, KTL rises for the remaining units, and the step is marked FAIL regardless of the parametric result, because a functional failure in the sample is a failure of the lot criterion. A blank cell is a missing measurement and reduces n at that step only. The report's dose step verdicts are read from the plotted bounds; the "bound crosses the limit at" figure is the first dose step where it does, not an interpolation between steps.
Lognormal parameters and shifts
Leakage and bias currents are typically lognormal across a lot; applying a normal tolerance limit to them overstates the upper bound and can produce a negative lower bound. The log option computes x̄ and s on log10 of the values and transforms the bounds back, which is the tolerance limit for a lognormal population. Shift mode subtracts each unit's own pre irradiation value before computing statistics, for SMDs and program specifications that limit the post irradiation delta rather than the absolute value; the delta limit is entered on the card. Shift mode does not combine with the log option because a shift can be negative.
Reading the plot
Gray lines are the units. The gold line is the sample mean at each step. The dashed blue lines are x̄ + KTL s and x̄ − KTL s; the band between them is the region that, with confidence γ, holds a fraction P of the lot. The red line is the limit. The step fails when the relevant dashed line crosses the red one. The common surprise is a step where every unit is comfortably inside the limit and the bound is outside: that is the sample scatter multiplied by a K of 3.5 or more, and it is the criterion working as designed. The remedies are a bigger sample (K falls slowly past n = 20), a derated limit in the application, or a lower P, none of which the test itself can supply after the fact.
How lot tests go wrong
The statistics assume one normal population per step. The failures that actually occur are elsewhere. A bimodal lot (two wafers or two die revisions under one date code) inflates s and fails a bound that either mode would pass alone; the unit lines on the plot show it. Control units that drift show the measurement moved, not the parts. A bias condition that is not worst case makes every bound optimistic, and for bipolar linear parts the worst case has been the unbiased condition often enough that both should be run. Meter repeatability that is a significant fraction of s is counted as part scatter and makes the bound conservative for the parts.
Limits
The tool evaluates the criterion at the steps you measured and says nothing about the dose between them. It does not know the contract's referenced revision of Method 1019 or ESCC 22900, does not apply overtest factors, and does not handle enhanced low dose rate sensitivity; the dose rate goes on the report as you entered it and the interpretation is yours. Everything is computed in the browser from the pasted data; nothing is uploaded.
References
[1] MIL-HDBK-814, Ionizing Dose and Neutron Hardness Assurance Guidelines for Microcircuits and Semiconductor Devices, US Department of Defense, 1994.
[2] MIL-STD-883, Test Method 1019, Ionizing Radiation (Total Dose) Test Procedure, current revision in MIL-STD-883-1. ESCC Basic Specification 22900 is the European equivalent.
[3] Odeh, R. E. and Owen, D. B., Tables for Normal Tolerance Limits, Sampling Plans and Screening, Marcel Dekker, 1980.
[4] Natrella, M. G., Experimental Statistics, National Bureau of Standards Handbook 91, 1963, Section 2-5, one sided tolerance limits.
[5] Ladbury, R. and Gorelick, J. L., Statistical Methods for Large Flight Lots and Ultra-High Reliability Applications, IEEE Transactions on Nuclear Science 52(6), 2630, 2005.