Each day, a manufacturing company producing circuit boards will randomly sample 60 circuit boards for a period of 25 days and then determine and plot the number of defects contained in each of these boards. The appropriate control chart is a(n)

Question

BlackTom AI · Accepted Answer

Because the measurement is a count of nonconformities (defects) per inspection unit (a circuit board) and the unit/inspection area is constant, a c-chart is the appropriate control chart.

1. Relevant knowledge points and concepts
- c-chart: used to monitor the count of defects (nonconformities) per inspection unit when the inspection unit size is constant.  
- u-chart: used to monitor defects per unit when the number of units inspected (or unit size) varies from sample to sample.  
- p-chart: used to monitor the proportion (fraction) of defective items (binary: defective vs. good).  
- np-chart: used to monitor the number of defective items (count of defectives) when sample size is constant.

2. Step-by-step reasoning
- The company inspects circuit boards (each board is an inspection unit) and records the number of defects contained in each board. That is a count of nonconformities per unit, not a binary defective/good classification.  
- The inspection unit (a circuit board) is constant in size for every observation. Even though 60 boards are sampled each day, the characteristic measured for control monitoring is “defects per board,” which is a count per constant unit. Thus the c-chart applies.

3. Calculational framework (intermediate steps)
- Compute c̄ = (total number of defects observed across all boards) / (number of boards inspected).  
- Control limits: UCL = c̄ + 3·sqrt(c̄); LCL = max(0, c̄ − 3·sqrt(c̄)).  
- These formulas assume each board is an identical inspection unit and model counts by a Poisson-like distribution, appropriate for c-charts.

4. Why the correct answer is correct
- The c-chart directly monitors counts of defects per constant inspection unit; that matches the scenario exactly.

5. Why the other options are incorrect
- u-chart: used when unit size (or number of items per sample) varies; not needed here.  
- p-chart and np-chart: both monitor defective items (proportion or count of items that are defective), not the number of defects per item. They are inappropriate when multiple defects can occur on a single board.

Conclusion: The appropriate control chart is a c-chart, which matches the provided answer.

Each day, a manufacturing company producing circuit boards will randomly sample 60 circuit boards for a period of 25 days and then determine and plot the number of defects contained in each of these boards. The appropriate control chart is a(n)Single choice

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