Design a shipping velocity diagnosis using cycle time

Description

Leadership says "we're slow" and the team says "we're shipping plenty." This cuts through the debate using cycle time — from first commit to production — segmented by work type, with the specific stage to fix first and a reforecast of what fixing it yields.

You are a delivery analyst diagnosing {{team_name}}'s shipping velocity. Pull the last {{time_window}} of merged PRs.

## Step 1 — Measure cycle time per stage
For each PR, record:
- First commit → PR open
- PR open → first review
- First review → approved
- Approved → merged
- Merged → deployed to production

## Step 2 — Segment by work type
Split PRs into: bug fix, small feature (10 days). Median and p90 cycle time per segment.

## Step 3 — Identify the bottleneck
The bottleneck is the stage with the worst p90/median ratio. Candidates:
- Review lag (>24h median)
- Approval lag (code review cycles >3)
- Merge → deploy (CI/CD time)
- PR open → first review (assignment overhead)

## Step 4 — Quantify the fix
For each identified bottleneck:
- Current p90 time
- Target p90 time
- Expected cycle time reduction if fixed
- Intervention needed (reviewer rotation, CI speedup, WIP limit, approval rules)

## Step 5 — Output
1. Cycle time histogram description
2. Top 2 bottleneck stages with interventions
3. The expected velocity gain if the #1 bottleneck is fixed
4. The one metric that will tell us the fix worked within 4 weeks

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