A c-chart is based on which type of statistical distribution?

• A. Erlang distribution
• B. Binomial distribution
• C. Poisson distribution
• D. Normal distribution

Answer: (C)

The c-chart is specifically designed to monitor the count of nonconformities or defects in a process, where the total area is constant, making it applicable in quality control scenarios. It is fundamentally based on the Poisson distribution, which models the number of events occurring in a fixed interval of time or space, under the condition that these events happen with a known constant mean rate and independently of the time since the last event.

In the context of the c-chart, this means that the number of defects can be treated as a Poisson process, where the mean (or expected value) of the count of defects is known. The characteristics of the Poisson distribution, such as the property that the variance equals the mean, align perfectly with the needs of a c-chart, allowing for effective monitoring and analysis of quality control data.

In contrast, the other distributions mentioned are not applicable for the c-chart's purpose: the Erlang distribution is used for process times, the Binomial distribution deals with a fixed number of trials under two outcomes, and the Normal distribution is typically used when dealing with measurements rather than counts of discrete defects. Therefore, the foundation of the c-chart on the Poisson distribution is what makes it the correct choice in this context