In Exercises 21–24, a control chart is shown. Each chart has horizontal lines drawn at the mean mu, at mu ±2sigma, and at mu±3sigma. Determine whether the process shown is in control or out of control. Explain.

An engine part has been designed to have a diameter of 55 millimeters. The standard deviation of the process is 0.001 millimeter.

검증된 단계별 안내

Step 1: Understand the control chart. The chart shows the mean (μ = 55 mm), upper control limits (μ + 2σ and μ + 3σ), and lower control limits (μ - 2σ and μ - 3σ). The standard deviation (σ) is given as 0.001 mm.

Step 2: Calculate the control limits. Use the formulas for the upper and lower control limits: μ ± 2σ and μ ± 3σ. For example, μ + 2σ = 55 + (2 × 0.001) = 55.002 mm, and μ - 2σ = 55 - (2 × 0.001) = 54.998 mm. Similarly, calculate μ ± 3σ.

Step 3: Analyze the data points on the control chart. Observe whether the data points fall within the control limits (μ ± 3σ). If all points are within these limits, the process is in control. If any point falls outside these limits, the process is out of control.

Step 4: Check for patterns or trends. Even if all points are within the control limits, look for systematic patterns (e.g., consecutive points above or below the mean) that might indicate a potential issue with the process.

Step 5: Conclude whether the process is in control or out of control. Based on the observations, determine if the process is stable and consistent or if corrective actions are needed.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Control Chart

A control chart is a statistical tool used to monitor the stability of a process over time. It displays data points in time order and includes control limits, typically set at the mean plus or minus two and three standard deviations. This helps identify variations in the process, distinguishing between common cause variation (in control) and special cause variation (out of control).

Mean and Standard Deviation

The mean is the average of a set of values, representing the central tendency of the data. The standard deviation measures the dispersion or variability of the data points around the mean. In the context of control charts, these statistics are crucial for determining the control limits, which help assess whether the process is operating within acceptable parameters.

In Control vs. Out of Control

A process is considered 'in control' if the data points fall within the control limits and show no significant patterns or trends. Conversely, it is 'out of control' if points fall outside the control limits or exhibit non-random patterns, indicating potential issues in the process that require investigation. This distinction is vital for maintaining quality in manufacturing processes.