Paper cup production trial randomization prevents treatment order from being confused with time-related change. If every baseline run is made cold and every alternative run follows after warm-up, the observed difference cannot be assigned confidently to the factor under study. Blocking controls known nuisance sources that cannot be ignored.
This guide supports experimental planning. It does not authorize process settings or provide a universal design. A qualified process engineer, statistician and machine supplier must approve safe factor ranges, run order and analysis.
Diagnostic decision table
| Design issue | Planning tool | Risk reduced |
|---|---|---|
| Machine changes over time | Randomized run order | Treatment is confounded with drift |
| Material lots differ | Block or balance lots | Material effect inflates treatment effect |
| Changeover has carryover | Washout or transition plan | Previous setting affects next run |
| Only one run per condition | Replication | Random error cannot be estimated |
Write the decision and experimental unit
State the primary factor, response and decision. Identify the experimental unit: a timed production run, material batch, forming position or another unit receiving a condition independently. Individual cups taken from one run are subsamples, not automatically independent replications.
Define safe settings with HANNAI and site engineering. Select primary and secondary responses before testing, such as defect rate, seal measurement or dimensional outcome. Record material, tooling, operator, environment and warm-up state. A clear unit prevents hundreds of cups from being misreported as hundreds of independent trials.
Identify nuisance factors and possible blocks
List variables expected to affect the response but not central to the decision: board lot, ink or coating lot, operator, shift, day, forming position and machine thermal state. Control them where possible. Use blocks when a nuisance factor must vary and can be grouped into more homogeneous sets.
NIST describes randomized blocks as a way to reduce nuisance-factor contribution while comparing the factor of interest. Do not create so many incomplete blocks that treatment effects become inseparable from block effects. Review feasibility and the analysis model before production starts.
Randomize within safe operating constraints
Generate the treatment order before results are known. Randomize within blocks where unrestricted order is safe and practical. Preserve the generated order, actual order and reasons for deviations. Do not rearrange runs for convenience and retain the label “randomized.”
Some changes require stabilization, cleaning or safe directional progression. Use restricted randomization, planned sequences or split-plot structures when justified by the process. A statistician should model those constraints. Safety and machine protection remain primary; randomization never authorizes abrupt or unapproved setting changes.
Plan replication, transitions and sampling
Include independent replication across the relevant production range. Define stabilization or washout criteria so measurements do not mix transition material with steady-state response. Keep transition waste and time visible as operational outcomes when relevant.
Use a fixed sampling plan within each run and preserve denominators. Balance forming positions and measurement order where possible. Record missing runs, alarms and deviations. Do not replace a failed run silently or pool cups across runs until the independent run identity disappears.
Analyze according to the executed design
Review raw timelines, run order and process events before fitting the planned model. Include blocks and restricted-randomization terms as required. Report uncertainty and interactions supported by the design. A statistically visible difference still needs practical and product-quality interpretation.
Confirm the selected condition in a separate representative run before release. Send HANNAI the executed order, safe factor definitions, material identities and response plots. This evidence makes process recommendations more defensible while avoiding a setting change based on warm-up, lot or operator effects.
Related equipment and next checks
Review the HN-M100 paper cup machine and the related guide to sealing factorial trial plan. The Engineering Notes archive connects these checks with wider machine planning.
Technical reference
- NIST: randomized block designs — general reference; confirm applicability to the installed equipment.
- NIST: design of experiments terminology — general reference; confirm applicability to the installed equipment.
Frequently asked questions
Are many cups from one run independent replications?
Usually they are subsamples unless the condition was independently applied to each unit.
Must every trial be fully randomized?
Use safe randomization or a justified constrained design approved by specialists.
Why block by material lot?
It helps separate known lot variation from the factor being studied.
Can actual run order differ from the plan?
Record every deviation and analyze the experiment as executed.
Review the evidence with HANNAI
Send your machine model, component identification and the observations described in this guide. Include the drawing or material reference and any before-and-after measurements so the required next check can be identified.