Missing Delivery Proof: Sensitivity Analysis

Missing proof changes what a delivery score can support

A distribution manager may have a clean on-time percentage for shipments with complete proof of delivery and little information about the rest. Excluding the missing records makes calculation easy, but the result can become a measure of the well-documented subset rather than the whole shipment population. This research proposes a sensitivity analysis that shows how unresolved delivery evidence can affect an on-time conclusion.

The immediate question is not whether every missing proof indicates a failed delivery. It does not. The question is how much the performance claim depends on outcomes that have not yet been established. That distinction helps the team prioritize evidence collection without turning uncertainty into either automatic success or automatic blame.

What the primary sources establish

The Census Bureau's Monthly Wholesale Trade Survey estimation procedures (opens in a new tab) discuss coverage, nonresponse, and reporting errors in addition to sampling variability. The statistical setting differs from a shipment ledger, but the distinction matters: a precise calculation does not remove missing-record bias. NIST's confidence limits for proportions (opens in a new tab) describe interval methods for proportion estimates under specified assumptions.

Both publications were checked October 2, 2026. The shipment bounds and workflow below are our analysis. We are not applying Census survey weights to a private operation or claiming that a standard binomial interval captures all uncertainty in carrier evidence. No company results are reported, and the numerical example is hypothetical.

Define the eligible shipment population

Start with the set of shipments whose delivery commitments fall within the review period. Reconcile it against the order and transport records, including cancellations, replacements, split deliveries, and customer changes. State which cases are excluded and why. A shipment should not disappear simply because no proof file was found.

Define an accepted commitment and an accepted completion event. The requested delivery date may differ from a later authorized promise. A document upload time may differ from delivery occurrence. If the team cannot establish those meanings, it cannot reliably classify on-time performance even for records that appear complete.

Use at least three outcome categories: confirmed on time, confirmed late, and unresolved. Add a separate ineligible category outside the performance denominator with a recorded reason. Do not combine unresolved with ineligible. The former belongs to the population but lacks enough evidence; the latter fails an established inclusion rule.

Calculate transparent bounds before a refined estimate

Consider a hypothetical population of one hundred eligible deliveries. Seventy-two are confirmed on time, eight are confirmed late, and twenty remain unresolved. Among the eighty resolved records, the observed on-time share is ninety percent. That is a valid description of the resolved subset, provided the label says so.

For the entire population, a simple lower bound assumes none of the twenty unresolved deliveries was on time: seventy-two percent. A simple upper bound assumes all twenty were on time: ninety-two percent. These are logical bounds given the classifications, not a confidence interval and not predictions of what the missing evidence will show.

The twenty-percentage-point range tells the manager how much uncertainty remains from missing outcomes alone. It does not include incorrect proof, an inaccurate commitment, or a poorly defined delivery event. Those are additional data-quality questions.

Test whether missingness is concentrated

Compare unresolved records by carrier, lane, customer, delivery method, and age. A single portal outage can concentrate missing evidence in one carrier. A difficult delivery type can also have weaker documentation. Either pattern undermines an unexamined assumption that unresolved cases behave like resolved ones.

Do not treat a pattern as proof of misconduct or service failure. The purpose is to identify where targeted evidence collection could change the conclusion. If most missing records come from one lane, request the relevant source records and inspect the handoff for that lane. Randomly chasing easy-to-retrieve files from elsewhere may reduce the count without resolving the important uncertainty.

Keep retrieval effort in the record. Cases requiring several requests may differ from cases resolved by an automatic upload. If a later analysis uses only the quickly retrieved documents, it can recreate the same selection problem in a smaller subset.

Separate population uncertainty from sample uncertainty

If the team reviews every eligible shipment, there is no sampling of that finite population, but unresolved outcomes and record errors still matter. A confidence interval around the resolved proportion does not address those missing outcomes. Reporting such an interval without the unresolved share can create false reassurance.

If the team samples shipments, document the selection design. A convenience sample of readily available proof cannot automatically support a population estimate. A probability sample may support estimation under its design, but clustering by route, customer, or operating day can affect uncertainty. An analyst should choose the estimator and interval appropriate to that design.

The distinction matters operationally. More decimal places cannot repair coverage gaps, and a larger sample of easy cases can still omit the hard ones. The first investment may need to be a reconciled shipment frame rather than a more sophisticated statistical package.

Prioritize evidence by the decision it could change

Suppose an owner must decide whether the population met an internally approved eighty-five-percent threshold. In the illustrative example, the logical range crosses that threshold, so the available evidence does not settle the question. The team needs more resolved outcomes or an explicitly qualified conclusion.

If subsequent retrieval confirms fifteen of the unresolved deliveries on time and five late, the final result becomes eighty-seven percent. If only ten are confirmed on time, it becomes eighty-two percent. These alternative scenarios show why the missing records matter; they are not forecasts. Retain the original report and the later resolution so the change can be explained.

The commercial owner decides what evidence is sufficient for any contractual judgment. A sensitivity table is a reporting aid, not a substitute for the agreement's measurement and dispute terms. Keep internal analytic categories separate from formal liability conclusions.

Keep unresolved evidence visible after the meeting

Assign each unresolved case a next retrieval action and owner, but do not make the analytic category depend on whether someone has acknowledged the task. A proof request sent to a carrier is an action, not an outcome. When evidence arrives, retain the prior category, the new classification, and the reference that justified it.

Also record cases that remain unresolved after the approved follow-up effort. Their persistence may justify a process change, but it does not justify guessing the delivery result. The next report should make that remaining uncertainty easy to find rather than carrying the cases in an unreviewed spreadsheet tab.

Build the review packet and its limits

An assistant can reconcile the shipment list, index proof files, identify missing commitments, and prepare the category counts. The transport owner approves milestone definitions, and the reporting owner signs off on the denominator and exclusions. Where evidence conflicts, preserve both sources for review rather than selecting the one that improves the score.

Record the retrieval cutoff, accepted proof criteria, unresolved count, and reasons for exclusions beside the result. When records arrive later, update a versioned analysis rather than silently overwriting the earlier statement. This makes it possible to assess both the service outcome and the information available at each review.

The method's limit is deliberate: bounds can expose uncertainty without resolving it. They do not prove that the observed subset is representative or that a document accurately describes physical delivery. Use them to decide where additional evidence is worth obtaining and how cautiously to state a performance claim.

For help organizing the proof queue, explore delivery exception support and contact the team. Begin with one reporting period and a reconciled eligible list. A clearly labeled unresolved category gives decision-makers more useful information than a polished percentage that quietly drops the shipments they most need to understand.