Reliability Prediction (217F)

Reliability Prediction

Parts Count and Part Stress Methods, List Syntax, Part Type Keys and Limits of the Handbook

What the handbook predicts

MIL-HDBK-217F, Reliability Prediction of Electronic Equipment, gives a failure rate for each electronic part as a base rate multiplied by factors for temperature, electrical stress, quality and operating environment. The parts of an equipment are taken to be in series and to fail at constant rates, so the equipment failure rate is the sum of the part failure rates, the mean time between failures is its reciprocal and the reliability over a mission of t hours is R = e^−λt. All failure rates are in failures per 10⁶ hours. The tool follows the handbook as amended by Notice 1 (10 July 1992) and Notice 2 (28 February 1995), which replaced the resistor, capacitor, connector, circuit board and connection sections and the whole of Appendix A.

The fourteen environments are those of the handbook's Table 3-2: G_B ground benign, G_F ground fixed, G_M ground mobile, N_S naval sheltered, N_U naval unsheltered, A_IC and A_IF airborne inhabited (cargo, fighter), A_UC and A_UF airborne uninhabited (cargo, fighter), A_RW rotary winged, S_F space flight, M_F missile flight, M_L missile launch and C_L cannon launch. The same list can be evaluated in two environments at once.

Parts count (Appendix A)

For bids and early design, when only the kinds and numbers of parts are known: λ_EQUIP = Σ N_i (λ_g π_Q)_i. The generic failure rate λ_g of a part type in an environment is read from the Appendix A tables, which the handbook computed from its own part stress models at default conditions stated with each table: a junction temperature of 50 to 90 °C or a component ambient of 30 to 70 °C depending on the environment, a power stress of 0.5 for resistors, a voltage stress of 0.4 for capacitors, 0.7 for diodes and 0.5 for small transistors, hermetic packages with the pin counts shown. π_Q is the quality factor of Appendix A, which is not always the part stress value. A microcircuit in production for less than two years also takes the learning factor π_L = 0.01 e^{5.35 − 0.35 Y}.

The tool ships the Appendix A rows of 174 part types exactly as printed in Notice 2 (pages A-2, A-3, A-5 to A-10): gate and logic arrays, linear circuits, programmable logic and microprocessors, memories, low-frequency diodes, thyristors, bipolar, field-effect and unijunction transistors, opto-electronic devices, every resistor and capacitor style, transformers and coils, relays, switches and circuit breakers, connectors and sockets, plated-through-hole boards, single connections, quartz crystals and fuses. Not shipped, and entered with the key custom and a rate when needed: hybrids (the handbook gives none), VHSIC and GaAs microcircuits, microwave diodes and transistors, laser diodes, tubes, lasers, rotating devices, elapsed time meters, surface-mount boards, meters, lamps and filters.

A parts count line is reference, part type key, quantity, quality, for example U4-U9, ic_mos_dig_100, 6, B. The quality is a level of the part's family or the factor itself as a number; left blank it is the level whose factor is 1 (MIL-SPEC 1.5 for mechanical relays, lower 1.0 for sockets). A fifth field lg=0.05 replaces the generic rate (it is then used in both environments), and y=1 gives the years in production of a microcircuit. The plated-through-hole board row assumes 1,000 wave-soldered holes on three circuit planes; scale it with lg= or use the part stress method for the board. Text after # is a comment.

Part stress (Sections 5 to 19)

When the design is known, each part is given the temperature and stress it actually sees. A part stress line is reference, family, key=value key=value ...; qty=N repeats identical parts. The families and their keys:

Temperatures. The form gives the air temperature around the parts in each environment. A resistor, capacitor or connector is at that ambient plus its own rise dT, or at an absolute temperature T. A semiconductor's case is at the ambient plus dTc, or at an absolute Tc, and its junction is at T_J = T_C + θ_JC P (Sections 5.11 and 6.14); TJ sets the junction temperature directly. Parts given an absolute temperature do not move when the ambient is changed.

Temperature factors. Microcircuits: π_T = 0.1 exp[−(E_a / 8.617 × 10⁻⁵) (1/(T_J + 273) − 1/298)] with E_a = 0.4 eV for bipolar digital logic, 0.35 for digital MOS, 0.65 for linear circuits and 0.6 for memories. Diodes: exp[−3091 (1/(T_J + 273) − 1/298)], with 1925 for voltage regulators and current regulators; bipolar transistors 2114; FETs 1925. Resistors, capacitors and connectors use the Arrhenius form without the 0.1, with E_a = 0.2 or 0.08 (resistor columns 1 and 2), 0.15 or 0.35 (capacitor columns 1 and 2) and 0.14 (connectors, at the ambient plus the insert rise k i^1.85).

Stress factors. Diodes π_S = V_s^2.43 (0.054 at 0.3 or less); bipolar transistors π_S = 0.045 e^{3.1 V_s} and π_R = P_r^0.37; resistors π_P = P^0.39 and π_S = 0.71 e^{1.1 S} or 0.54 e^{2.04 S}; capacitors π_C = C^0.09 or C^0.23 and π_V = (S / 0.6)^m + 1 with m = 5, 10, 3 or 17, or (S / 0.5)³ + 1 for variable capacitors. The handbook's models stop at a stress ratio of 1; a line above it is refused.

One part of the list, chosen by its line number, is printed factor by factor; the table lists the factors of every part.

Contribution, temperature and derating

The failure rate is grouped by part family and the largest lines are charted, which is the use the handbook itself recommends: to show where the failure rate comes from and what a change of part quality, stress or cooling buys. For the part stress method the list is evaluated again from 0 to 100 °C ambient and the MTBF plotted against temperature. The derating table compares each resistor power ratio, capacitor voltage ratio, semiconductor voltage stress and junction temperature with limits typed on the form. The handbook sets no derating limits; the defaults on the form (0.5, 0.6, 0.7 and 110 °C) are illustrative and should be replaced by those of the programme's derating guideline. The default parts lists describe an illustrative digital control board of 42 parts, not a published example.

Checks against the handbook

The tool reproduces the handbook's worked examples that use these models: the CMOS gate array of Section 5.13 (0.15 failures per 10⁶ hours), the die, transistor and diode of the hybrid example (0.038, 0.031, 0.0015, 0.0069), the dual transistor of Section 6.15 (0.011), the capacitor of Section 10.2 and the surface-mount example of Section 16.2 (18,893 cycles, 0.4). Every Appendix A cell of a part type that has a part stress model here (1,964 cells) was recomputed from that model at the appendix's stated defaults; 1,930 agree to the two printed figures and the rest differ by the handbook's own rounding (the film-resistor rows are printed to one figure).

Points where the printed handbook is not consistent with itself, and what the tool does: the capacitor example prints 0.049 from factors rounded to two figures, and the unrounded model gives 0.047; the Appendix A note gives 20 µF as the assumed capacitance of glass and ceramic capacitors, but the printed rows are reproduced with 2.0 µF; the default table for diodes on page A-12 lists a base rate of 0.0031 for transient suppressors where Section 6.1 and the printed row use 0.0013; the MOS programmable-logic table of Section 5.1 jumps from "501 to 1,000" to "2,001 to 5,000" gates where Appendix A prints 501 to 2,000 (the tool uses 2,000); component F of the hybrid example still uses the capacitor model that Notice 2 replaced; the learning-factor equation gives 1.05 at two years where the table gives 1.0 (the tool uses 1.0 from two years).

Limits of the prediction

The models are point estimates fitted to field data gathered before 1995 and the handbook has not been revised since; later part types and packages are extrapolations. Failures are assumed random at a constant rate: wear-out, infant mortality, software, design errors and induced failures are outside the models (the surface-mount model is the one wear-out model, averaged over the design life). The parts are taken in series with no redundancy. The handbook states that a prediction "should never be assumed to represent the expected field reliability" and is a means of comparing designs and locating the main contributors. The equipment failure rate found here is the input of a block in System Reliability and of a basic event in Fault Tree Analysis, where redundancy and repair are treated.

Part type keys of the parts count method

Generic failure rates in ground benign and airborne inhabited cargo are shown for orientation; the tool holds all fourteen environments.