Core Time Definitions
Shift Time
$$\text{Shift Time} = \text{All Time} - \text{Unscheduled Time}$$
Scheduled operational period (All Time = 24/7/365 Calendar Time)
Planned Production Time (PPT)
$$\text{PPT} = \text{Shift Time} - \text{Schedule Loss}$$
Time explicitly scheduled for production with labour present.
Denominator for OEE calculation.
PPT (Plan Layer)
$$\text{PPT}_{\text{plan}} = \text{Run Time}_{\text{planned}} + \text{PDT}_{\text{(planned duration)}}$$
Planning perspective: sum of intended productive time and anticipated downtime durations
PPT (Actual Layer)
$$\text{PPT}_{\text{actual}} = \text{Run Time}_{\text{actual}} + \text{PDT}_{\text{(planned duration, actual events)}}$$
Actual execution: sum of observed productive time and planned duration of
actual PDT events that occurred (not actual event durations)
Potential Time (PT)
$$\text{PT} = \frac{\text{Good Output}}{\text{BNS}}$$
Theoretical minimum time required to produce actual good output at bottleneck
speed (BNS) with zero losses
Lost Time Categories
Lost Time Slow Running (LTSR)
$$\text{LTSR} = (\text{BNS} - \text{Actual Speed}) \times \text{Good Output}$$
Time lost producing at below-theoretical speed whilst making good product
Lost Time Making Waste (LTMW)
$$\text{LTMW} = \frac{\text{Waste Output}}{\text{BNS}}$$
Time consumed producing defective output at bottleneck speed
Planned Downtime (PDT)
$$\text{PDT} = \text{PPT}_{\text{actual}} - \text{Run Time}_{\text{actual}}$$
Scheduled non-productive time within PPT: changeovers, planned maintenance,
meetings, breaks, cleaning
Unplanned Downtime (UPDT)
$$\text{UPDT} = \text{Run Time}_{\text{actual}} - \text{PT} - \text{LTSR} - \text{LTMW}$$
Unscheduled stoppages during intended productive time: breakdowns,
starvation, blockages
Total Lost Time Verification
Total Lost Time (Two Formulations)
$$\text{Total Lost Time} = \text{LTSR} + \text{LTMW} + \text{PDT} + \text{UPDT}$$
$$\text{Total Lost Time} = \text{PPT}_{\text{actual}} - \text{PT}$$
These must be mathematically equivalent. Discrepancy indicates measurement
error in either output data or time allocation.
Efficiency Metrics Hierarchy
| Metric | Formula | Strategic Context | Primary Audience |
|---|---|---|---|
| Run Efficiency | $\frac{\text{Potential Time}}{\text{Run Time}_{\text{actual}}}$ | Universal | Shop floor execution |
| Machine Efficiency | $\frac{\text{Potential Time}}{\text{Shift Time}}$ | Sales-constrained | Production management |
| OEE | $\frac{\text{Potential Time}}{\text{Planned Production Time}}$ | Production-constrained | Production management |
| OOE | $\frac{\text{Potential Time}}{\text{Shift Time}}$ | Production-constrained | Production management |
| TEEP | $\frac{\text{Potential Time}}{\text{Calendar Time}}$ | Production-constrained strategic | Senior leadership |
| Labour Efficiency | $\frac{\text{Potential Labour Hours}}{\text{Actual Labour Hours}}$ | Sales-constrained | Production management |
Note on OOE vs Machine Efficiency
OOE and Machine Efficiency are mathematically identical ($\frac{\text{Potential Time}}{\text{Shift Time}}$). The terminology distinction reflects strategic context:
- Machine Efficiency used in sales-constrained environments (cost optimisation focus)
- OOE used in production-constrained environments (throughput maximisation focus)
Labour Efficiency Framework
Labour Efficiency (Primary)
$$\text{Labour Efficiency} = \frac{\text{Potential Labour Hours}}{\text{Actual Labour Hours}}$$
Measures labour productivity relative to theoretical minimum labour requirement.
Where: Potential Labour Hours = Potential Time × Potential Crew
Labour Efficiency (Alternative)
$$\text{Labour Efficiency} = \text{Machine Efficiency} \times \frac{\text{Potential Crew}}{\text{Actual Crew}}$$
Decomposition separating equipment effectiveness (Machine Efficiency component)
from labour deployment optimisation (crewing factor)
Packs Per Labour Hour (PPLH)
$$\text{PPLH} = \frac{\text{Total Packs}}{\text{Total Labour Hours}}$$
Absolute labour productivity metric measuring units produced per person-hour
of labour consumed
⚠️ Critical PPLH Formula (from configuration)
$$\text{PPLH} = \frac{v_{\text{theoretical}} \times \text{OOE} \times 60}{\text{FTE}}$$
If only OEE available: $\text{OOE} = \text{OEE} \times \frac{\text{PPT}}{\text{Shift Time}}$
WARNING: Must use OOE (not OEE) because labour is paid for Shift Time
Standard OEE Decomposition
⚠️ OEE Multiplicative Formula
$$\text{OEE} = \text{Availability} \times \text{Performance} \times \text{Quality}$$
Note: OEE and majaco's Lost Time framework use fundamentally different allocation methodologies. These frameworks cannot be mathematically translated bidirectionally.
⚠️ CRITICAL TERMINOLOGY DIFFERENCE
OEE "Run Time" = Time equipment physically running and producing (excludes unplanned downtime)
majaco "Actual Run Time" (Run Timeactual) = OEE Run Time + UPDT
Equivalently: $$\text{Run Time}_{\text{actual}} = \text{PT} + \text{LTSR} + \text{LTMW} + \text{UPDT}$$
These are NOT interchangeable. Using OEE Run Time in majaco formulas will produce incorrect results.
Availability
$$\text{Availability} = \frac{\text{Run Time}}{\text{Planned Production Time}}$$
Proportion of PPT that equipment was actually running (physically operating
and producing output). NOTE: OEE "Run Time" excludes unplanned downtime.
Performance
$$\text{Performance} = \frac{\text{Ideal Cycle Time} \times \text{Total Pieces}}{\text{Run Time}}$$
OR: (Total Pieces/Run Time)/(Ideal Run Rate) | Captures all speed loss
including slow running whilst making waste
Quality
$$\text{Quality} = \frac{\text{Good Pieces}}{\text{Total Pieces}}$$
First-pass yield measuring percentage of production that met quality
standards without rework
Diagnostic Decompositions
Machine Efficiency Decomposition
$$\text{Machine Efficiency} = \text{Run Efficiency} \times \frac{\text{Run Time}_{\text{actual}}}{\text{Shift Time}}$$
Separates shop floor execution quality (Run Efficiency) from planning
effectiveness in maximising operational window (Time Allocation Factor)
TEEP Decomposition
$$\text{TEEP} = \text{OOE} \times \frac{\text{Shift Time}}{\text{Calendar Time}}$$
Isolates operational effectiveness during shifts (OOE) from strategic shift
pattern deployment (Facility Utilisation Factor)
Valuation Formulas
Production-Constrained
Lost Output
$$\text{Lost Output} = \text{Lost Time} \times \text{BNS}$$
Units that could have been produced if the lost time had been productive
at bottleneck speed with no losses
Unit Marginal Profit (UMP)
$$\text{UMP} = \text{Price} - \text{RM Cost} - \text{Processing} - \text{Distribution}$$
Profit per incremental unit. Excludes labour cost because labour is
already paid during Lost Time.
Annual Value (Production-Constrained)
$$\text{Annual Value} = \text{Lost Output} \times \text{UMP} \times \text{Operating Weeks}$$
Financial impact of throughput losses when market demand exceeds production
capacity. Lost Time elimination increases output at full margin.
Sales-Constrained
Annual Value (Sales-Constrained)
$$\text{Annual Value} = \text{Labour Hours Saved} \times \text{Fully Loaded Labour Rate}$$
Cost reduction potential when capacity exceeds demand. Lost Time elimination
enables labour cost reduction while maintaining current output.
Key Relationships
| Relationship | Formula |
|---|---|
| Equipment Time | $\text{Equipment Time} = \text{Time Basis} \times \text{Number of Lines}$ |
| Labour Time | $\text{Labour Time} = \text{Time Basis} \times \text{Number of People}$ |
| Actual Run Time Verification | $\text{Run Time}_{\text{actual}} = \text{PT} + \text{LTSR} + \text{LTMW} + \text{UPDT}$ |
| Planning Rate from BNS | $\text{Planning Rate} = \text{BNS} \times \text{Run Efficiency}_{\text{planned}}$ |
