Estimate the cycle service level implied by a safety-stock quantity when lead-time demand is approximately normal. The calculator converts the buffer into a z-score using demand variability and lead time, then reports the probability of completing a replenishment cycle without a stockout.
The result estimates the probability that demand during a replenishment lead time will not exceed expected demand plus the safety buffer. It is a cycle service level, not a unit fill rate.
This estimate assumes independent daily demand, constant lead time, and approximately normal lead-time demand. Correlated demand or variable lead time requires a different variability model.
With 300 safety units, daily demand standard deviation of 35 units, and a 10-day lead time, lead-time deviation is 110.68 units and z is 2.71. The estimated cycle service level is about 99.66%, with roughly 0.08 stockout cycles across 24 cycles.
No. Cycle service level is the probability of no stockout in a cycle; fill rate measures the share of unit demand supplied immediately.
Under the independence assumption, daily demand variances add across days, so standard deviation scales with the square root of time.
Not directly. The formula assumes constant lead time; variable lead time adds uncertainty that must be modeled separately.
It uses the standard normal cumulative distribution for lead-time demand.
It is a long-run expectation: per-cycle stockout probability multiplied by the number of annual replenishment cycles.
| Input | Unit | Role |
|---|---|---|
| Safety inventory | units | Buffer stock above expected lead-time demand. |
| Daily demand standard deviation | units | Historical standard deviation of demand per day. |
| Lead time | days | Replenishment lead time assumed constant. |
| Annual replenishment cycles | cycles | Used to estimate cycles with at least one stockout. |