# Average Total Inspection (ATI) Calculator > Source: https://netray.co/tools/average-total-inspection-ati-calculator > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer Estimate how many pieces you actually inspect per lot, and what it costs, when rejected lots are screened 100 percent. ## Category quality ## Industry Discrete Manufacturing ## Audience - Quality manager - Incoming inspector - Cost accountant ## Tool **Kind:** calculator **Currency:** $ **Inputs:** #### Lot size N **Key:** lot_size **Type:** number **Default:** 1200 **Min:** 2 **Step:** 50 **Unit:** units #### Sample size n **Key:** n **Type:** number **Default:** 125 **Min:** 1 **Step:** 1 **Unit:** units #### Acceptance number c **Key:** c **Type:** select **Default:** 3 **Options:** ##### 0 **Value:** 0 ##### 1 **Value:** 1 ##### 2 **Value:** 2 ##### 3 **Value:** 3 #### Incoming percent defective p **Key:** p **Type:** slider **Default:** 3 **Min:** 0.1 **Max:** 15 **Step:** 0.1 **Unit:** % #### Inspection cost per piece **Key:** unit_cost **Type:** number **Default:** 0.6 **Min:** 0 **Step:** 0.05 **Unit:** $/unit **Help:** Labor plus gauge time per piece. #### Lots received per year **Key:** lots_year **Type:** number **Default:** 200 **Min:** 1 **Step:** 10 **Unit:** lots **Outputs:** #### Expected defectives in sample **Key:** m **Expr:** n * p / 100 **Format:** decimal #### Probability of acceptance (fraction) **Key:** pa_frac **Expr:** exp(0 - m) * (1 + if(gte(c,1), m, 0) + if(gte(c,2), m*m/2, 0) + if(gte(c,3), m*m*m/6, 0)) **Format:** decimal #### Probability of acceptance **Key:** pa **Expr:** pa_frac * 100 **Format:** percent #### Average total inspection ATI **Key:** ati **Expr:** n + (1 - pa_frac) * (lot_size - n) **Format:** number **Primary:** true **Description:** Average pieces inspected per lot. #### Share of lot inspected **Key:** ati_pct **Expr:** ati / lot_size * 100 **Format:** percent #### Inspection cost per lot **Key:** cost_lot **Expr:** ati * unit_cost **Format:** currency #### Annual inspection cost **Key:** cost_year **Expr:** cost_lot * lots_year **Format:** currency **Primary:** true **Chart:** #### Pieces inspected per lot (ATI) vs incoming defect rate **Type:** line **X:** p **From:** 0.2 **To:** 12 **Steps:** 40 **Series:** - ati **Disclaimer:** Poisson approximation. Assumes every rejected lot is inspected 100 percent and that sampling is representative. ## Content **Intro:** A sampling plan looks cheap on paper because you only inspect n pieces. When a lot fails, though, you screen all of it, and that is where the labor goes. ATI tells you the real average workload, which is what you need to size the inspector headcount and quote inspection cost. **Sections:** #### How to use it **Body:** Enter lot size, the sample size and acceptance number, and the incoming percent defective you expect. Add the cost to inspect one piece and how many lots arrive each year. The tool returns the probability a lot passes, the average pieces inspected per lot, and the annual cost. The chart shows ATI as incoming quality worsens, which is the what-if that matters when a supplier slips. **Bullets:** - Use supplier history from your ERP for p, not a hopeful target. - Cost per piece should include setup and handling, not just gauge time. - Compare two plans by running them one after the other. #### The ATI formula **Body:** ATI = n + (1 - Pa) x (N - n). Every lot gets the sample of n. The share of lots that are rejected, 1 - Pa, also gets the remaining N - n pieces screened. Pa is the probability of finding c or fewer defectives in the sample, computed here from the Poisson sum with m = n x p / 100. At very low p, ATI is almost exactly n. At high p, ATI approaches N and your sampling plan has turned into 100 percent inspection. #### Reading the result **Body:** With N = 1200, n = 125, c = 3 and p = 3 percent, the sample is expected to hold about 3.75 defectives, so a lot passes only around half the time and ATI is roughly 700 pieces. That is far above 125. The chart shows why: workload rises quickly once p passes the plan's AQL. If annual cost looks too high, the fix is usually supplier quality, not a looser plan. #### Common mistakes **Body:** People budget inspection labor as n times lots and are surprised in the first bad month. Another mistake is ignoring that screening a rejected lot is often slower per piece than sampling, because it is a rework-style activity. Add a loading factor to the cost per piece for screened lots if that applies to you. **Cta:** Our team can connect this to your inspection lot and receipts data so staffing and cost are forecast from live supplier performance. Ask for a short review. **Faq:** #### What does ATI measure? **Answer:** Average total inspection is the average number of pieces inspected per lot, counting the sample on every lot plus the full screening of the remainder on lots that are rejected. It is the best single number for sizing inspection labor. #### Why is ATI higher than my sample size? **Answer:** Because rejected lots are screened. Every lot that fails the plan adds N minus n extra pieces. As incoming quality worsens, more lots fail, and ATI climbs toward the full lot size. #### Should I use this for destructive tests? **Answer:** No. Screening a rejected lot is not possible when testing destroys the part. In that case lots are returned or scrapped, and a different cost model applies. #### How do I choose p? **Answer:** Use the average percent defective from your last 6 to 12 months of supplier receipts. Also run the worst realistic month, since staffing has to survive the bad periods as well as the average ones. ## Search terms average total inspection calculator, ATI acceptance sampling, inspection cost per lot, rectifying inspection workload, sampling plan inspection effort, how many parts will we inspect, incoming inspection cost, ATI formula --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json