Certified Production & Operations Manager (POM) Practice Exam

What significance does the Central Limit Theorem have for managers in relation to control charts?

1. It allows for unlimited data collection.

2. It allows managers to use the normal distribution as the basis for building some control charts.

3. It guarantees all processes are in control.

4. It indicates sample sizes must be very large.

The correct answer is: It allows managers to use the normal distribution as the basis for building some control charts.

The Central Limit Theorem (CLT) is fundamental for managers using control charts because it explains that, regardless of the distribution of the population, the sampling distribution of the sample mean will approach a normal distribution as the sample size becomes sufficiently large. This characteristic is crucial for managers because control charts are often based on the assumption of normality. By understanding and applying the CLT, managers can confidently use the normal distribution to create and interpret control charts, even when the underlying process data is not normally distributed. The significance here lies in the practical application of the theorem: it allows for effective monitoring and management of processes by ensuring that, as sample sizes grow, so does the reliability of the control chart's indications of process stability and performance. Thus, control charts can be based on sample means that are normally distributed, which supports decision-making and quality control across various operational contexts.