SPCR — System Performance Analysis Calculator

API-driven: Failure date parsing and all Crow-AMSAA calculations run on the Edge4AssetIQ backend. Your data is sent only for the duration of the request and is not stored.

System / Asset Group Name Date format Failure event dates

At least two failure events on different dates are required.

Rating bands

SPCR	p-value range (when beta > 1)	Narrative
1	p ≥ 0.20, or beta ≤ 1	No significant evidence or improving / stable.
2	0.10 ≤ p < 0.20	Weak evidence.
3	0.05 ≤ p < 0.10	Some evidence.
4	0.02 ≤ p < 0.05	Evidence.
5	p < 0.02	Strong evidence.

T is the span from first to last recorded failure. The first event is the origin (t=0, excluded — ln(T/0) undefined). The last event contributes ln(T/T)=0. Failure-terminated MLE: β = (m−1)/Σln, η = (m−1)/T^β, df = 2(m−1).

Calculation methodology

Model — Crow-AMSAA power-law NHPP

The Non-Homogeneous Poisson Process (NHPP) power-law model describes how the expected cumulative number of failures grows over time. When β > 1 the failure intensity is increasing (degradation); when β < 1 it is decreasing (improvement); β = 1 is a constant-rate HPP.

MCF(t) = η · t^β

MCF(t) = expected cumulative failures by time t from the first observed failure. η is the scale parameter; β (shape / trend parameter) drives the curvature.

Step 1 — Collect and sort failure dates

Record the calendar date of every functional failure event for the asset group. Sort all m dates in ascending order: t₁ ≤ t₂ ≤ … ≤ t_m.

Step 2 — Define the observation period T

T is the total span from the first recorded failure to the last. It is measured in days.

T = t_m − t₁ (days)

Re-index so that t₁ = 0 (the origin). All subsequent failure ages tᵢ are then days elapsed since that first failure. T = t_m in this reference frame.

Step 3 — Compute ln(T / tᵢ) for each event

For every event after the first, compute the log ratio of the total span to the event age:

ln(T / tᵢ) for i = 2, 3, …, m

First event (i = 1, t = 0): excluded — ln(T/0) is undefined.
Last event (i = m, t = T): included but contributes ln(T/T) = ln(1) = 0.
Events on the same calendar date as the first failure also have t = 0 and are excluded.

Step 4 — Sum the log ratios

Σ ln(T/tᵢ) = ln(T/t₂) + ln(T/t₃) + … + ln(T/t_m)

n = m − 1 effective observations (the m − 1 events that contribute to this sum, including the last which adds 0).

Step 5 — Estimate β (failure-terminated MLE)

The maximum-likelihood estimator for the failure-terminated Crow-AMSAA model:

β̂ = (m − 1) / Σ ln(T/tᵢ)

If β̂ ≤ 1 the system is improving or stable — set SPCR = 1 and stop. No chi-squared test is needed.

Step 6 — Estimate η (MCF scale parameter)

η̂ = (m − 1) / T^β̂

η is in units of failures · day^−β. Together with β it fully defines the fitted power-law MCF.

Step 7 — 90% confidence interval on β

Under the failure-terminated model, 2n · β_true / β̂ ~ χ²(2n). Inverting this pivot:

β_lower = β̂ · χ²_0.05(2n) / (2n)

β_upper = β̂ · χ²_0.95(2n) / (2n)

A CI that straddles 1.0 means the data are consistent with a stable system despite β̂ > 1.

Step 8 — Chi-squared trend test statistic

Under H₀ (β = 1, homogeneous Poisson process), the test statistic follows a chi-squared distribution:

χ² = 2 × Σ ln(T/tᵢ) ~ χ²( 2(m−1) ) under H₀

Step 9 — Two-sided p-value

CDF = P( χ²(2n) ≤ χ²_observed )

p = 2 × min( CDF, 1 − CDF )

Step 10 — Assign SPCR

β̂ ≤ 1 → SPCR 1 regardless of p. Otherwise band on the two-sided p as per the table above.

Step 11 — Project future failures (informational)

E[failures in Δ] = η̂ × [ (T + Δ)^β̂ − T^β̂ ]

This extrapolates the fitted trend forward. Planning aid only — not a precision forecast.