Question 1a: Company That Makes Car Parts And Controls

Question

Question 1a Company That Makes Car Parts The Company Control Its Pro A company that makes car parts monitors its production process by sampling 100 units periodically, inspecting for defects. Control limits are set at three standard deviations from the mean. The last 12 samples recorded defect proportions. Calculate the mean proportion defective, UCL, and LCL. Then, draw a control chart with these samples, and assess if the process is in statistical control.

Dr. Jack HW Helper · Accepted Answer

Introduction Monitoring and controlling manufacturing processes are essential components of quality management. Control charts are fundamental tools used to determine whether a manufacturing process remains in statistical control, based on data collected from samples taken over time. In the context of a company producing car parts, establishing the mean proportion defective, along with upper and lower control limits (UCL and LCL), enables continuous evaluation of process stability. This paper discusses the calculation of these parameters, visualizes the process with a control chart, and assesses the process stability based on the data provided. Calculating the Mean Proportion Defective, UCL, and LCL Given the data from 12 samples, each with recorded defect proportions, the first step involves calculating the average defect proportion (p̄), which indicates the overall process defect rate. The mean proportion defective p̄ is computed as the sum of individual sample proportions divided by the number of samples. For illustration, if the recorded defect proportions are: 0.02, 0.03, 0.01, 0.04, 0.02, 0.03, 0.05, 0.02, 0.03, 0.04, 0.02, 0.03, the calculation proceeds as follows: p̄ = (0.02 + 0.03 + 0.01 + 0.04 + 0.02 + 0.03 + 0.05 + 0.02 + 0.03 + 0.04 + 0.02 + 0.03) / 12 ≈ 0.029 Next, the control limits are calculated using the standard deviation of the proportion defective, considering the sample size (n=100). The standard error (SE) for proportions is: SE = √(p̄(1 - p̄) / n) ≈ √(0.029 * 0.971 / 100) ≈ 0.0168 The control limits are set at three standard deviations: UCL = p̄ + 3 × SE ≈ 0.029 + 3 × 0.0168 ≈ 0.079 LCL = p̄ - 3 × SE ≈ 0.029 - 3 × 0.0168 ≈ -0.022 (since negative defect proportions are impossible, LCL is set to zero) Thus, the process control limits are approximately UCL=0.079 and LCL=0. Control Chart Construction and Assessment Plotting the 12 sample defect proportions on a control chart, with the center line at p̄=0.029 and the control limits at 0 and 0.079,

Question 1a: Company That Makes Car Parts And Controls

Question 1a Company That Makes Car Parts The Company Control Its Pro

Paper For Above instruction

Introduction

Calculating the Mean Proportion Defective, UCL, and LCL

Control Chart Construction and Assessment

Conclusion

References