Select a chart from the data and sampling plan

Select a chart from the data and sampling plan

Chart selection starts with how data are generated. Measurements taken individually differ from rational subgroups collected under comparable short-term conditions. Nonconforming units differ from nonconformities, because one unit can contain several faults. For attributes, record whether the inspected quantity or exposure changes. These distinctions guide the candidate family: individuals and moving range, subgroup charts, p or np, and c or u. Selection is not complete until independence and model assumptions are considered. Rare events, autocorrelation, changing opportunity and overdispersion may require specialist methods. Choose the sampling plan and interpretation rules before routine monitoring begins.

Follow the method

1. One measurement per observation
2. Small rational measurement subgroups
3. Fraction of nonconforming units
4. Count of nonconforming units at fixed n
5. Nonconformities at fixed exposure
6. Nonconformities per varying exposure

Choose the chart from the observation and its sampling plan

Fictional case: a monitoring workshop receives six records: individual widths, small width subgroups, rejected-unit fractions, fixed-size reject counts, fixed-area blemish counts and varying-area blemish rates. The core chooser retains six distinct routes. Engineer Sal must assign candidates without pretending that a chart name approves the collection plan.

Follow the method

1. A: individual width
2. B: five-unit width subgroup
3. C: pass/fail, varying n
4. D: pass/fail, fixed n = 100
5. E: blemishes, fixed area
6. F: blemishes, varying area

The word defect is not a data model

Select a monitoring candidate from the observation type and sampling design, then identify the assumptions that still need review.

Fictional case: a monitoring workshop receives six records: individual widths, small width subgroups, rejected-unit fractions, fixed-size reject counts, fixed-area blemish counts and varying-area blemish rates. The core chooser retains six distinct routes. Engineer Sal must assign candidates without pretending that a chart name approves the collection plan.

Role: Quality engineer and process record owner

Normal condition

The team knows what one observation means, its time order, subgroup or exposure basis and whether a unit can contribute more than one event.

The gap

Every record has been labelled defects. A proposed p chart would treat multiple blemishes on one sheet as though they were different rejected sheets.

• These are introductory candidates; dependence, overdispersion and rare events can require other methods.
• Control limits describe process behavior under a model, not product specifications.

1. Separate measurements from classifications

   Sal marks A and B as measured variables. C and D classify each unit once. E and F can record several nonconformities within one inspection area.

   Why: The number format alone is insufficient: both widths and defect counts are numbers. The observation definition determines the statistical question.

   Evidence: Each record names its unit and whether multiple events can belong to it.

2. Examine the sampling mechanism

   For A he retains time order and considers I–MR. For B he examines whether five consecutive units are a rational subgroup under comparable conditions and considers Xbar–R.

   Why: A subgroup is an intentional comparison structure, not any five values pooled for convenience. Serial dependence and measurement fitness can invalidate a simple chart choice.

   Evidence: Candidate A is I–MR; B is Xbar–R subject to subgroup and measurement review.

3. Handle unit fractions and fixed-size counts

   C uses a p candidate because each sample has a known denominator that may change. D can use an np candidate for the count because its denominator remains 100.

   Why: A raw count rises when more units are inspected even if the fraction is unchanged. Fixed-n and variable-n displays must retain their intended scale.

   Evidence: The selection record preserves each sample size and binomial-model questions.

4. Handle multiple events and exposure

   E uses a c candidate only with comparable fixed exposure. F uses a u candidate with count divided by known exposure and exposure-dependent limits.

   Why: Counting blemishes is not the same as classifying a sheet once. A larger area provides more opportunity, and count-model assumptions need scrutiny.

   Evidence: The record defines the exposure unit and distinguishes multiple faults from affected items.

5. Qualify the candidate before deployment

   Sal records unresolved dependence, opportunity, measurement and response-plan questions. A chart owner must confirm baseline development and reaction rules before operational use.

   Why: Choosing a plausible chart is a first decision. It does not establish stability, approve product release or authorize automatic adjustments.

   Evidence: Every row has a candidate and at least one explicit qualification check.

The denominator is missing

Record C gives rejected units but omits how many were inspected on two days.

Retrieve the actual denominators before calculating fractions or limits. Mark the missing observations explicitly; do not assume 100 because another row uses 100.

A plausible-looking graph based on invented exposure would communicate false evidence. Another process’s denominator is not a substitute.

The record identifies the two missing sample sizes and their owner.

Run a practice session

Materials

• Six source-record cards
• Blank chooser table
• Changed four-record exercise

1. Define the observation · 5 minutes

   Can one item contribute more than one count?

2. Explain each route · 8 minutes

   What changes when n or exposure changes?

3. Challenge the mixed subgroup · 10 minutes

   What variation would pooling hide?

4. Debrief implementation · 5 minutes

   Who approves the baseline and response?

Debrief

• Do not mark a justified fixed-n p alternative wrong.
• Require an assumption check even for a correctly named chart.

Annotate the sampling mechanism before looking up any chart name.

Transfer into the work

Owner: SPC owner and process measurement lead

Record: Chart-selection, sampling and response-plan record

Review: Before baseline collection and after process/sampling changes

Evidence: A defined observation, defensible model and reviewed reaction plan

Redesign sampling or seek a suitable specialist method instead of forcing a familiar chart.