The relationship between one reading and the next matters when an analysis assumes independent observations.
Compare neighbours without losing their order
A lag-one plot pairs each observation with its immediate predecessor. A visible structure can prompt investigation of serial dependence or a repeating pattern. It is an exploratory diagnostic, not a physical fault identifier. Preserve the original sampling order; sorting by magnitude creates an artificial relationship that was not present in time.
A hypothetical slowly changing response
Imagine a sequence that rises gradually over an illustrative run. Adjacent readings will often be similar because both occur near the same point in the trend. A lag plot may show a line-like pattern, while a shuffled table obscures the sequence. The pattern alone cannot distinguish a process change from a measurement-system change.
Also preserve elapsed times. Consecutive rows separated by one second and by one hour are not necessarily the same sampling situation. Record gaps and intentional interruptions. These illustrations do not establish the time behaviour of any HM machine.
Connect the diagnostic with the planned analysis
Send the run-sequence plot and lag plot together, with sampling times and observed operating events. Ask whether the intended statistical method remains appropriate for the dependence and any trend present. Increasing the row count does not automatically restore independence.
Do not discard or randomly reorder observations merely to make a diagnostic plot look unstructured. If a different collection design or time-series model is required, document that decision and its scope. A reader should be able to distinguish raw sequential evidence from a model-adjusted result.
Trial discussion worksheet
This blank worksheet is for your own project. It contains no H M machine trial result.
| Review question | Reference or observation to retain |
|---|---|
| What does one lag mean? | Time interval and row order |
| Are there gaps or transitions? | Recorded timestamps |
| Which analysis assumes independence? | Named method and rationale |
Customer Questions
May values be sorted before a lag plot?
Use collection order when examining temporal dependence.
Does a pattern identify the machine cause?
No. Process, sampling and measurement context must be investigated.
Do more rows guarantee independent evidence?
No. Dependence concerns the relationship between observations.
Primary References
These references support the technical principles discussed in this guide. The worked examples and review questions are educational.
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