KEVOS® MAKEOS · Quality
Lot Acceptance from Process Capability (Fraction Defective, Sampling Plan Risk)
Given how capable my process is, what fraction of parts fall outside tolerance, and how often will my customer’s sampling plan reject a lot?
Link between process capability and incoming inspection: z-values, Cpk and the fraction of parts outside the limits for a normal process (as the parts out of tolerance tool), then the probability that a lot with that fraction defective is accepted by a single sampling plan of n parts with acceptance number c (as the sampling plan operating characteristic tool), the share of lots rejected and the average outgoing quality, against the acceptance probability you need.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Process mean | Mean of the process. | |
| Standard deviation | Standard deviation of the process. | |
| Lower specification limit | Lower specification limit. | |
| Upper specification limit | Upper specification limit. | |
| Sampling plan | ||
| Sample size | items | Parts sampled from each lot. |
| Acceptance number | defects | Largest number of defectives in the sample for the lot to pass. |
| Least probability of acceptance wanted | % | Probability of a lot passing that you want to reach. |
Method and formulas
- z to each limit = distance ÷ σ; Cpk = smaller z ÷ 3; fraction defective from the normal distribution (as the parts out of tolerance tool).
- Probability of acceptance = Σ (k = 0 … c) C(n, k) p^k (1 − p)^(n − k) (as the sampling plan operating characteristic tool).
- Lots rejected = 1 − Pa; average outgoing quality ≈ p × Pa.
- Example: Cpk 0.88889 gives 3,862.1 ppm out of tolerance; the n = 50, c = 1 plan accepts 98.384% of lots.
Limitations
- Stable normal process; tails of real processes are often heavier.
- Binomial sampling from large lots.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Predict how often lots will be rejected at goods-in
- Set a capability target to keep lots passing
- Show the cost of an off-centre process
Who it is for
- Quality engineers
- Supplier quality engineers
- Production managers
What you get
- z-values, Cpk and fraction outside tolerance
- Probability of acceptance and lots rejected
- Average outgoing quality
Interpreting the result
- Centring the process usually cuts rejected lots faster than tightening the spread.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 128–133. Topic reference; no source tables or recommended settings are reproduced.
- ISO 2859-1 Sampling procedures for inspection by attributes
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Lot Acceptance from Process Capability (Fraction Defective, Sampling Plan Risk) calculator
