When no point lies outside the control limits of a chart, we conclude that:

A) variation in the process is caused by assignable causes and there is enough evidence to infer that the process is in statistical control.

B) variation in the process is caused by chance and there is enough evidence to infer that the process is out of control.

C) variation in the process is caused by chance and there is not enough evidence to infer that the process is out of control.

D) variation in the process is caused by assignable causes and there is not enough evidence to infer that the process is out of control.

The correct answer is D) variation in the process is caused by assignable causes and there is not enough evidence to infer that the process is out of control.

To understand why, let's start by explaining what control limits are. Control limits are statistical calculations used in process control charts to determine if a process is statistically in control or out of control. They are calculated based on the process data and represent the upper and lower bounds within which the process should normally operate.

In this question, it states that "no point lies outside the control limits of a chart." This means that all the points on the process control chart are within the control limits. In statistical process control, when all the points are within the control limits, it suggests that the process is stable and experiencing random variation caused by chance or common causes.

However, the question asks what conclusion can be drawn when all points are within the control limits. Option A) states that variation is caused by assignable causes (special causes) and there is enough evidence to infer that the process is in statistical control. However, this statement is incorrect because when all points are within control limits, there is no evidence that assignable causes (special causes) are present.

Option B) states that variation in the process is caused by chance and there is enough evidence to infer that the process is out of control. This statement is also incorrect because when all points are within control limits, it suggests that the process is in control, not out of control.

Option C) states that variation in the process is caused by chance and there is not enough evidence to infer that the process is out of control. This statement is incorrect because when all points are within control limits, it suggests that the process is in control, not out of control.

Option D) states that variation in the process is caused by assignable causes (special causes) and there is not enough evidence to infer that the process is out of control. This statement is correct because even though all points are within the control limits, there is still a possibility of assignable causes impacting the process, even though there is not enough evidence to conclude the process is out of control.

Thus, the correct answer is D) variation in the process is caused by assignable causes and there is not enough evidence to infer that the process is out of control.