gen-define-statistical-process-control-and-give-one-short-worked-5170

Define statistical process control and give one short worked example.

# Statistical Process Control (SPC) ## Definition Statistical Process Control is a method of quality control that uses statistical techniques to monitor and control a process. It helps determine whether a process is operating consistently (in control) or if variation is due to special causes that need correction. SPC typically uses control charts to track process performance over time. ## Worked Example **Scenario:** A bottling company fills water bottles with a target of 500ml. **Data collected:** 10 samples of bottle volumes (in ml): ``` 501, 499, 502, 500, 498, 501, 499, 503, 500, 497 ``` **Step 1: Calculate the mean (X̄)** - X̄ = (501+499+502+500+498+501+499+503+500+497) ÷ 10 = **500 ml** **Step 2: Calculate standard deviation (σ)** - σ = 2.0 ml (using standard formula) **Step 3: Set control limits (using ±3σ)** - Upper Control Limit (UCL) = 500 + (3 × 2.0) = **506 ml** - Lower Control Limit (LCL) = 500 - (3 × 2.0) = **494 ml** **Interpretation:** All 10 measurements fall within the control limits (494-506 ml), indicating the process is **in statistical control**. If any point fell outside these limits, it would signal a special cause requiring investigation.