P Chart (Proportion Defective)

Monitor proportion or percentage of defective items in processes with variable sample sizes.

Chart Overview & Key Characteristics

What is a P Chart?

The P chart (proportion chart) is an attribute control chart used to monitor the proportion or percentage of defective items in a process. It tracks the fraction nonconforming over time and is particularly useful when sample sizes vary from subgroup to subgroup. The P chart helps detect changes in the defect rate and overall process quality.

Key Characteristics

• • Purpose: Monitor proportion of defective items over time
• • Data Type: Attribute data (pass/fail, good/bad)
• • Sample Size: Variable sample sizes acceptable
• • Best For: Processes where you want to track defect rates

Typical Applications

• • Manufacturing: Proportion of defective products per batch
• • Healthcare: Infection rates, medication errors per period
• • Service: Customer complaints, order errors, billing mistakes
• • Software: Bug rates, failed tests per release
• • Financial: Transaction errors, loan defaults by period

Control Limits & Statistical Formulas

Subgroup and overall proportion defective

= number defective in subgroup i

= sample size of subgroup i

P chart control limits with variable subgroup size n_i

= overall proportion defective

= sample size for subgroup i

P chart control limits with constant subgroup size n

= constant sample size

Sample Size Requirements

• • Minimum: n × p̄ ≥ 5 and n × (1-p̄) ≥ 5
• • Recommended: n ≥ 50 for low defect rates
• • For very low p̄: may need n ≥ 1000
• • Variable sample sizes should not differ by more than ±25%

Reading the p Chart

Example Chart & Visualization

sixsigmacenter.com Implementation Guide

Example Data Layout for P Chart

Data for P Chart with variable sample sizes. Calculate proportion defective for each period to track defect rates over time. Sample Size Recommendation: Variable sample sizes acceptable but should be large enough that np ≥ 5 and n(1-p) ≥ 5 for each subgroup for normal approximation validity.

This is how your spreadsheet or CSV file should be structured before you upload it. Match the column names, keep one row per observation, and leave the analysis to the platform.

Process in Statistical Control

• • All proportions fall within control limits
• • No systematic patterns or trends
• • Random variation around center line
• • Defect rate is stable and predictable

Out-of-Control Indicators

• • Points beyond control limits (special causes)
• • 8 consecutive points above or below center line
• • Obvious trends or patterns in defect rates
• • Sudden shifts in process defect level

Action Guidelines

• • High proportions: Investigate for root causes
• • Trends upward: Process deterioration, take corrective action
• • Trends downward: Process improvement, identify what changed
• • Stable but high p̄: Process needs fundamental improvement