1. **Problem Statement:** (b) Determine if the process is in statistical control. (c) Given the estimate of process standard deviation using the range method is 23.3, and specifications are nominal ±100, calculate the process capability ratio $C_p$ and interpret the capability. 2. **Statistical Control (b):** A process is in statistical control if all points on the control chart lie within control limits and show no non-random patterns. 3. **Process Capability Ratio (c):** The formula for $C_p$ is: $$C_p = \frac{USL - LSL}{6\sigma}$$ where $USL$ and $LSL$ are the upper and lower specification limits, and $\sigma$ is the process standard deviation. 4. **Given Data:** - $\sigma = 23.3$ - $USL = 100$ - $LSL = -100$ 5. **Calculate $C_p$:** $$C_p = \frac{100 - (-100)}{6 \times 23.3} = \frac{200}{139.8} \approx 1.43$$ 6. **Interpretation:** A $C_p$ value greater than 1 indicates the process spread is within specification limits and the process is capable. 7. **Conclusion:** - (b) To confirm statistical control, check control charts for points outside limits or patterns; if none, process is in control. - (c) With $C_p \approx 1.43$, the process is capable of meeting specifications comfortably.