Project: qualify a pouch-filling line against fixed weight limits

Last updated: 7 Oct 20265 min read

project

Audit process stability, measurement repeatability and population-tail evidence before recommending a line release.

Freeze specifications and collection

A food-packaging plant requires sealed pouches within 247 to 253 grams and considers a line upgrade. Record the product specification, target fill, line identity, scale calibration, production shifts and ingredient batches before collecting measurements. Sample across ordinary operating conditions and retain chronological order. A calibration change during the study defines a new measurement regime, not just another value in the same distribution. The repeatability lesson helps quantify scale noise.

Check the process before the index

Plot fill weight by time, shift and batch; investigate drifts, steps and outlying periods. Only after a defensible stable window is identified should a normal-model Cpk be interpreted for that window. Compare observed lower- and upper-limit failures with the model’s tail expectation. The capability lesson shows what the index means; the monitoring lesson supports an ongoing alarm rule after release. Do not choose a stable-looking window solely because it produces a favorable index.

Ask for individual-outcome evidence

If the decision requires a stated share of future pouches below the upper engineering limit, use a tolerance-bound design or another justified population-tail method. The maximum-based construction requires independent samples from one stable process and has its own required sample size. The tolerance lesson gives that tradeoff. Neither a small standard error for the mean nor an attractive point Cpk removes uncertainty about rare underfill or overfill.

Ship a reviewable qualification

The packet contains fixed limits, target, full time trace, line and batch coverage, missing readings, calibration ledger, distribution diagnostics, capability estimate and its basis, and the tail claim with confidence. The gate below refuses qualification if stability or independent sampling has not been established. Passing sends the packet for operations review; it does not replace line monitoring after production restarts.

Implementation

def fill_line_gate(packet):
    if not packet["specifications_frozen"]:
        return "hold:engineering-limits"
    if not packet["measurement_system_checked"]:
        return "hold:scale"
    if not packet["stable_window_justified"]:
        return "hold:process-stability"
    if packet["tail_claim"] and not packet["independent_tail_sample"]:
        return "hold:tail-sample"
    return "review:fill-line"

packet = {"specifications_frozen": True, "measurement_system_checked": True,
          "stable_window_justified": True, "tail_claim": True,
          "independent_tail_sample": False}
assert fill_line_gate(packet) == "hold:tail-sample"
assert fill_line_gate({**packet, "independent_tail_sample": True}) == "review:fill-line"

Performance and operating cost

The gate is O(1); checking n measurements in time and by batch is O(n) expected time, while storage of the trace is O(n). Additional independent batches cost production time. Reducing code cannot replace observing the conditions the line will actually face.

Common Mistakes

Replacing engineering limits with limits estimated from the same sample.
Selecting only the most stable-looking hours for the capability report.
Using average-weight precision to claim individual pouches meet limits.
Stopping monitoring because an initial qualification passed.