Calculator overview

Inputs and outputs

This summary comes from the calculator's published input and output contract.

Inputs

RDT Test Mode: About this input

Choose accumulated operating time under a constant rate or independent binomial pass/fail missions.

Default Exponential time - zero failures Allowed Exponential time - zero failures, Binomial - zero failures
RDT Time Unit Conditional: About this input

Interpretation unit for exponential-mode time and MTBF. Hidden from binomial calculations.

Default Hours Allowed Hours, Days, Cycles
RDT Confidence: About this input

Frequentist one-sided confidence level used in both modes.

Unit fraction Default 0.9 Range 0.5 to 0.999999
RDT Target MTBF Conditional: About this input

MTBF to demonstrate under the exponential zero-failure model.

Unit hours Default 200 Range 1E-09 to 1E+15
RDT Concurrent Units Conditional: About this input

Number of units sharing the required accumulated operating time.

Unit units Default 4 Range 1 to 1000000
RDT Planned Duration Per Unit Conditional: About this input

Planned zero-failure duration for each concurrent unit.

Unit hours Default 100 Range 0 to 1E+15
RDT Target Reliability Conditional: About this input

Per-unit or per-mission reliability to demonstrate in binomial mode.

Unit fraction Default 0.9 Range 1E-06 to 0.999999
RDT Planned Sample Size Conditional: About this input

Planned number of independent zero-failure binomial trials.

Unit missions or units Default 29 Range 1 to 1000000000

Outputs

RDT Significance: About this output

One minus the entered one-sided confidence.

Unit fraction
RDT Required Total Test Time Conditional: About this output

Accumulated zero-failure operating time required to demonstrate the target MTBF.

Unit hours
RDT Required Duration Per Unit Conditional: About this output

Required accumulated time divided across the entered concurrent units.

Unit hours
RDT Planned Total Test Time Conditional: About this output

Concurrent units multiplied by planned duration per unit.

Unit hours
RDT Exponential Achieved Confidence Conditional: About this output

One-sided confidence achieved if the planned accumulated time completes with zero failures.

Unit fraction
RDT MTBF Lower Bound Conditional: About this output

Exact one-sided zero-failure MTBF lower bound from the planned accumulated time.

Unit hours
RDT Raw Required Sample Conditional: About this output

Unrounded log-ratio sample requirement.

Unit missions or units
RDT Required Sample Size Conditional: About this output

Raw exact binomial requirement rounded upward to a whole trial.

Unit missions or units
RDT Binomial Achieved Confidence Conditional: About this output

One minus target reliability raised to planned sample size.

Unit fraction
RDT Reliability Lower Bound Conditional: About this output

Exact one-sided zero-failure binomial reliability lower bound.

Unit fraction
RDT Plan Status: About this output

MEETS when planned resources equal or exceed the exact zero-failure requirement.

No unit declared
Model Status: About this output

CHECK when planned resources are insufficient; NOT VALID for active-domain failures.

No unit declared

Methodology

Purpose and model boundary

This model plans a zero-failure reliability demonstration in either accumulated-time exponential mode or independent binomial pass/fail mode. It reports required resources and compares the entered plan with that requirement. Plans that accept one or more failures require a different design and are outside scope.

Inputs and units

Both modes use one-sided confidence C. Exponential mode also uses a time unit, target MTBF θ_0, integer concurrent units m, and planned duration per unit d. Binomial mode uses target mission reliability R_0 and integer planned sample size n.

Governing relationships

With zero failures in exponential time mode:

required total test time = -θ_0 ln(1-C)

required duration per unit = required total time / m

planned total time = m d

achieved confidence = 1 - exp[-(m d)/θ_0]

MTBF lower bound = (m d) / [-ln(1-C)]

With zero failures in binomial mode:

raw required sample = ln(1-C) / ln(R_0)

required sample = ceil(raw required sample)

achieved confidence = 1 - R_0^n

reliability lower bound = (1-C)^(1/n)

The chart plots achieved confidence against accumulated time or sample size for the selected mode.

Calculation sequence

Validate confidence and only the fields active for the selected test mode.
Calculate exact required resources for the zero-failure acceptance event.
Calculate resources supplied by the entered plan and the confidence they would achieve if completed with zero failures.
Calculate the corresponding one-sided lower bound.
Set RDT_Plan_Status to MEETS or INSUFFICIENT, then derive Model_Status using the precedence below.

Outputs and interpretation

The required time or sample is the minimum exact zero-failure resource at the entered target and confidence. Achieved confidence and lower bounds describe the entered plan only if it completes with zero observed failures. MEETS is a mathematical resource comparison; it does not certify independence, representativeness, test severity, or execution quality.

Validation and status logic

Condition, evaluated in order	Plan status	Returned model status
A mode, confidence, or active exponential/binomial input violates the workbook domain	`NOT VALID`	`NOT VALID`
Exponential planned total time meets or exceeds required total time	`MEETS`	`OK`
Binomial planned sample meets or exceeds the rounded-up required sample	`MEETS`	`OK`
The selected plan is valid but below its requirement	`INSUFFICIENT`	`CHECK`

The workbook calculates plan status first and then applies Validation!B20; invalid inputs have highest precedence.

Assumptions and limitations

The acceptance event is zero observed failures.
Exponential mode assumes constant failure rate and additive independent unit-time.
Binomial mode assumes independent, identically distributed pass/fail trials.
Confidence is a frequentist long-run property, not the probability that the target is true.
No finite-lot correction, degradation evidence, environmental adjustment, or allowed-failures plan is included.

Restrictions and non-computing states

Confidence and target reliability must stay strictly below one. Unit and sample counts must be positive integers. Target MTBF must be positive and planned duration nonnegative. Values for the inactive mode are ignored.

Errors and warnings

NOT VALID blocks interpretation. CHECK means the valid entered plan is insufficient for the exact zero-failure requirement. An observed failure during execution invalidates the zero-failure acceptance premise and requires a different analysis.

References

Both exact demonstration relationships, rounding behavior, plan comparison, named outputs, and status precedence were verified directly against the delivered workbook, its published input rules, tests, and reviewer packet. The workbook identifies these technical sources:

NIST/SEMATECH e-Handbook — Exponential life-test planning — Zero-failure accumulated-time demonstration relationship.
NIST/SEMATECH e-Handbook — Zero-failure MTBF lower bound — Exact one-sided zero-failure MTBF lower bound.
NIST Dataplot — Exact binomial confidence limits — Exact one-sided binomial zero-failure confidence relationship.

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