Why depth matters — and why five is not a law
- Depth = number of consecutive answered whys, counted from Why 1 until the first
- blank (0–5)
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The score, and reading the trend
- Audit % = points scored ÷ (questions × 4) × 100
- Average per S = points in that S ÷ questions in that S
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When is a report closed?
- Report closed = all 8 disciplines complete, with D4 and D6 marked
- “Complete & verified” and carrying written evidence
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Gate deliverables
- A phase can close when every gate deliverable in it is complete.
- Non-gate deliverables can be carried into the next phase with an owner and a date; gates cannot.
The formulas
- Phase completion = complete deliverables ÷ deliverables in phase × 100
- A phase can close when every gate deliverable in it is complete
- Days late (complete) = actual finish − planned finish
- Days late (not complete, past its date) = today − planned finish
- Current phase = the lowest-numbered phase that still has an incomplete deliverable
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Effective capacity, not nameplate
- Effective capacity per week = units per hour × available hours × uptime% ÷ 100 × yield% ÷ 100
Effective capacity, not nameplate
- Utilisation % = demand per week ÷ effective capacity × 100
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How the next due date is worked out
- Next due = last calibration date + interval (in whole calendar months)
How the next due date is worked out
- Days to due = next due date − today
How the next due date is worked out
- Overdue when days to due < 0 · Due soon when 0 ≤ days to due ≤ warning window
How the next due date is worked out
- Compliance breach = status is "in service" AND (overdue OR, where the setting is on, no traceable certificate)
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The formulas
- Variance = actual minutes − planned minutes
- Efficiency = planned minutes ÷ actual minutes × 100
- Right-first-time = first-off passes ÷ changeovers × 100
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Special characteristics
- Coverage rule — every special characteristic:
- reaction plan → required, no exceptions
- frequency → every piece, hourly, per shift, per batch or at setup — a weekly or daily check on a
- special characteristic is refused; tighten it, or record the justification in the reaction plan and choose a
- tighter nominal frequency
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The formulas
- Attainment % = actual ÷ plan × 100
- Variance = actual − plan
- First-pass quality % = (actual − rejects) ÷ actual × 100
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From drawing to working register
- Priority score = likelihood (1–5) × evidence weight
- (none = 1, weak = 2, moderate = 3, strong = 4 — so the score runs 1–20)
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RPN, and what it cannot tell you
- RPN = Severity × Occurrence × Detection
- Range 1 to 1000, from 1 × 1 × 1 to 10 × 10 × 10
- RPN cut = RPN before the action − RPN after the action
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The average and range method
- R-bar = mean of the part × appraiser ranges
- EV (repeatability) = R-bar × K1
- K1 = 0.8862 for 2 trials, 0.5908 for 3 trials
- X-diff = largest appraiser mean − smallest appraiser mean
- AV (reproducibility) = √( max(0, (X-diff × K2)² − EV² ÷ (parts × trials)) )
- K2 = 0.7071 for 2 appraisers, 0.5231 for 3 appraisers
- GRR = √( EV² + AV² )
- R-part = largest part average − smallest part average
- PV (part variation) = R-part × K3
- K3 = 0.4030 (5 parts), 0.3742 (6), 0.3534 (7), 0.3375 (8), 0.3249 (9), 0.3146 (10)
- TV (total variation) = √( GRR² + PV² )
- %GRR of study variation = GRR ÷ TV × 100
- %GRR of tolerance = 6 × GRR ÷ tolerance × 100
- ndc = floor( 1.41 × PV ÷ GRR ), reported as at least 1
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The positive ratio
- Positive ratio = positive observations ÷ all observations
Cadence over depth
- Walks completed = distinct combinations of walk date and walker
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Estimating and verifying benefits
- Realisation % = verified benefit ÷ estimated benefit × 100
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The formulas
- Pass rate = passes ÷ (passes + fails) × 100
- Not-applicable results are excluded from both sides of the division
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Line efficiency and the formulas
- Line efficiency = Σ element time ÷ (stations × longest station time) × 100
- Theoretical minimum stations = ⌈Σ element time ÷ takt⌉
- Balance loss = 100 − line efficiency
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Planned against unplanned
- Unplanned share = unplanned downtime hours ÷ total downtime hours × 100
MTBF, and what it needs
- MTBF = operating hours ÷ number of failures
MTBF, and what it needs
- Site MTBF = (operating hours per asset × assets in the filter) ÷ total failures
MTTR
- MTTR = total downtime hours on failures ÷ number of failures
Reading the Pareto
- Share of hours = cause hours ÷ total hours × 100
- Cumulative = running total of the shares, largest cause first
Costing the loss
- Cost of lost production = units lost × value of one unit
- Total cost = cost of lost production + parts cost
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The three factors
- Run time = planned production time − unplanned downtime
- Availability % = run time ÷ planned production time × 100
- Performance % = (ideal cycle time × total units) ÷ (run time × 60) × 100
- Quality % = good units ÷ total units × 100
- OEE % = Availability × Performance × Quality ÷ 10000
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How the analysis works
- Share = category total ÷ grand total × 100
- Cumulative % = running sum of shares, largest category first
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The formulas
- Readiness = required elements that are complete, submitted or approved ÷ required
- elements × 100
- Elements with required unticked are excluded from both sides of the division
- Blocking = required elements that are not started, in progress or rejected
- Overdue = due date in the past and the element is not complete, submitted or approved
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How the due date is worked out
- Next due date = last completed date + interval (days)
How the due date is worked out
- Days to due = next due date − today's date
- Overdue when days to due is negative; days overdue = today's date − next due date
Hours-based tasks
- Next due at hours = reading at last completion + interval (hours)
PPM compliance, done honestly
- PPM compliance % = tasks completed on or before their due date ÷ tasks that fell due in the period × 100
PPM compliance, done honestly
- Period = (today − N days) up to and including yesterday, where N is the compliance window
How compliance figures get inflated
- Wrong: completed on time ÷ completed × 100
- Wrong: completed ÷ completed × 100 = 100 % always
The outstanding workload
- Work outstanding (hours) = sum of estimated minutes for tasks overdue or due inside the window ÷ 60
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Every formula
- mean (x̄) = Σx ÷ n
- sigma (s) = √( Σ(x − x̄)² ÷ (n − 1) ) — sample standard deviation
- Cp = (USL − LSL) ÷ 6s
- Cpu = (USL − x̄) ÷ 3s
- Cpl = (x̄ − LSL) ÷ 3s
- Cpk = lower of Cpu and Cpl
- Pp and Ppk = the same two formulas, evaluated with the overall sigma s
- Within-subgroup sigma = R̄ ÷ d2, with d2 = 1.128 (n 2), 1.693 (n 3), 2.059 (n 4), 2.326 (n 5)
- Estimated defects = [ 1 − ((USL − x̄) ÷ s) + ((LSL − x̄) ÷ s) ] × 1,000,000 ppm
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First-pass and final yield
- First-pass yield (FPY) = good first time ÷ quantity started × 100
First-pass and final yield
- Final yield = (good first time + reworked to good) ÷ quantity started × 100
First-pass and final yield
- Scrap rate = scrapped ÷ quantity started × 100
Why totals, not averaged percentages
- Overall FPY = (sum of good first time across the runs) ÷ (sum of quantity started) × 100
Scrap and rework cost
- Scrap cost = units scrapped × unit material cost
Scrap and rework cost
- Rework cost = units reworked × rework cost per unit (from Settings)
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What the tool calculates
- Acknowledgement rate = acknowledged items ÷ all items × 100
- Days open = days from the handover date to today, for items not done or closed
- Handovers logged = distinct combinations of date, shift and area
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The formulas
- Potential saving = observed minutes − streamlined minutes
- Projected changeover = Σ remaining internal time, i.e. for each internal task: 0 if it moves external,
- otherwise its streamlined minutes (or its observed minutes if no streamlined time is entered)
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The formulae and the constants
- Subgroup mean = (sum of the readings) ÷ n
- Subgroup range R = largest reading − smallest reading
- X̿ = mean of the subgroup means
- R̄ = mean of the subgroup ranges
- Mean chart: UCL = X̿ + A₂R̄
- centre = X̿
- LCL = X̿ − A₂R̄
- Range chart: UCL = D₄R̄
- centre = R̄
- LCL = D₃R̄
- Estimated process sigma = R̄ ÷ d₂
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How the green rate is calculated
- Green rate = green entries ÷ all entries × 100
The gap column
- Gap = measured value − target value
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The parallel-time rule
- Operator cycle for an element = manual time + walk time
- Machine time is not added — it runs in parallel
The formulas
- Element cycle = manual time + walk time
- Total element time = manual + machine + walk (reference only — never the operator's cycle)
- Operator cycle = Σ (manual + walk) for that operator's elements
- Operators needed = ⌈ Σ operator cycle across the cell ÷ takt time ⌉
- Walk and wait = Σ walk time + Σ machine time on wait elements
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What takt time is
- Takt time = available production time ÷ customer demand
- (both over the same period, in the same units)
- Here: Takt (seconds) = (available minutes per shift × shifts per day × 60) ÷ demand per day
The coefficient of variation
- CV % = (standard deviation ÷ mean) × 100
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The formulas
- Change % (higher is better) = (trial value − baseline value) ÷ |baseline value| × 100
- Change % (lower is better) = (baseline value − trial value) ÷ |baseline value| × 100
- Target met = trial value at or beyond the target, in the improving direction
- Evidence = Underpowered if either sample size is missing or below the minimum;
- otherwise Confounded if an adoption has confounders recorded; otherwise Reasonable
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Process-cycle efficiency — the lean number
- PCE = total process time ÷ total lead time × 100
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Quantifying honestly
- Weekly minutes = time per occurrence × occurrences per week
- Annual cost = weekly minutes ÷ 60 × hourly rate × weeks per year
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