14.2 Control charts for variables and attributes

Control charts are powerful tools for monitoring process quality. They come in two main types: variables charts for continuous data and attributes charts for discrete data. Each type has unique applications and requirements, helping businesses maintain consistent quality standards.

X-bar and R charts track process means and variability for continuous data. P, np, c, and u charts monitor defects and non-conformities in discrete data. Proper sample sizes and frequencies are crucial for effective control chart implementation, balancing sensitivity and cost-effectiveness in quality control efforts.

Control Charts for Variables and Attributes

Control charts: variables vs attributes

• Variables control charts measure continuous data quantitative characteristics (length, weight, temperature)
• Attributes control charts assess discrete data qualitative characteristics (defects, non-conformities, pass/fail)
• Key differences involve data type (continuous vs discrete), measurement precision (higher for variables, lower for attributes), and sample size requirements (typically smaller for variables)

X-bar and R charts for variables

• X-bar chart monitors process mean calculating control limits (UCL: $\overline{\overline{X}} + A_2\overline{R}$, LCL: $\overline{\overline{X}} - A_2\overline{R}$)
• R chart tracks process variability with control limits (UCL: $D_4\overline{R}$, LCL: $D_3\overline{R}$)
• Construction steps:
  1. Collect data in subgroups
  2. Calculate subgroup means and ranges
  3. Determine overall mean and average range
  4. Calculate control limits
  5. Plot points and control limits
• Interpretation detects shifts in process mean or changes in variability

P, np, c, and u charts for attributes

• p chart monitors proportion of defective items allowing variable sample size (binomial distribution)
• np chart tracks number of defective items requiring fixed sample size (binomial distribution)
• c chart counts number of defects with fixed sample size (Poisson distribution)
• u chart measures number of defects per unit allowing variable sample size (Poisson distribution)
• Analysis involves identifying out-of-control points, spotting trends or patterns, and investigating special causes

Sample sizes in control charts

• Factors influencing sample size include chart type, desired sensitivity, process variability, and sampling costs
• Guidelines suggest 4-6 items per subgroup for variables charts, 20-100 for attributes charts
• Sampling frequency considers production rate, costs, risk of non-conformity, and time for corrective actions
• Balancing act weighs larger samples and higher frequency for sensitivity against smaller samples and lower frequency for cost reduction
• Adaptive strategies increase frequency during instability and decrease when stable