P Chart (Proportion Defective)
Monitor the proportion of defective units over time when your sample size varies from one subgroup to the next. The P chart plots the fraction defective and adjusts its control limits to each subgroup's size.
Create P Chart →What is a P Chart?
A P chart is an attribute control chart that monitors the proportion of defective units in a process over time. Each unit is classified as either conforming or defective, and the chart plots the fraction defective in each subgroup, tracking whether that proportion is stable.
Its defining feature is that it handles variable sample sizes. Because the sample size can differ between subgroups, the control limits are recalculated for each subgroup, wider for smaller samples and narrower for larger ones. This gives the P chart its characteristic stepped or varying limits.
The P chart is based on the binomial distribution, which applies because each unit is a pass or fail outcome. It answers whether the defective rate is in statistical control, distinguishing real changes in quality from the ordinary variation expected when sampling a stable process.
In plain terms: When you inspect batches and count how many units are defective, and the batch sizes vary, the P chart tracks the defective rate over time. Because sample sizes change, the control limits move, tighter for big samples, looser for small ones. It tells you if your defect rate is genuinely changing or just wobbling.
Key Points
Proportion Defective
Plots the fraction of units that are defective in each subgroup. Each unit is classified pass or fail.
Variable Sample Size
Handles changing sample sizes by recalculating control limits for each subgroup, giving stepped limits.
Binomial Basis
Based on the binomial distribution, appropriate for pass/fail (defective/non-defective) classification of units.
Key Formulas
Reading the Chart
Because the control limits vary with sample size, they step in and out along the chart. A point beyond its own subgroup's limits, or a non-random pattern, signals a special cause affecting the defective rate.
Distinguish a defective from a defect: the P chart counts defective units (a unit is either defective or not), regardless of how many flaws each has. If you need to count multiple defects per unit, a C or U chart is the correct choice instead.
Assumptions & Validation
Binary Classification
Each unit is classified as defective or not.
If violated: To count multiple defects per unit, use a C or U chart.
Independent Units
Units are independent, so the binomial model applies.
If violated: Address dependence between units.
Adequate Sample Sizes
Samples are large enough that expected defectives are not tiny.
If violated: Increase sample size; very low counts make limits unstable.
⚠️ Check assumptions first
The key distinction for attribute charts is defectives versus defects. A P chart counts defective units, each unit either passes or fails, and tracks the proportion; it is based on the binomial distribution. If a single unit can have several defects and you want to count them, a P chart is the wrong tool, use a C or U chart. And with variable sample sizes, the control limits must be recalculated per subgroup.
When NOT to Use P Chart
Constant Sample Size
If the sample size is constant, the NP chart (count of defectives) is often simpler to interpret.
Counting Defects
To count multiple defects per unit, use a C chart (constant area) or U chart (variable area).
Continuous Data
For measured variable data, use an X-bar R, X-bar S or XmR chart.
Industry Applications
Inspection Yield
Monitor the fraction of units failing inspection when lot sizes vary.
Service Defect Rates
Track the proportion of transactions with an error across varying volumes.
Process Control
Detect shifts in the defective rate of a stable process.
Supplier Quality
Monitor the proportion defective in incoming lots of differing sizes.
Frequently Asked Questions
What is a P chart used for?
A P chart monitors the proportion of defective units in a process over time when each unit is classified as either conforming or defective. It plots the fraction defective in each subgroup and is designed to handle variable sample sizes by adjusting the control limits for each subgroup. It answers whether the defective rate is in statistical control or has changed due to a special cause.
What is the difference between a P chart and an NP chart?
Both track defective units, but a P chart plots the proportion defective and handles variable sample sizes by recalculating limits for each subgroup, while an NP chart plots the raw count of defectives and requires a constant sample size. When sample sizes vary, the P chart is necessary; when they are constant, the NP chart is often simpler because it uses counts directly.
What is the difference between a defective and a defect?
A defective is a unit that fails to conform, classified as either defective or not regardless of how many flaws it has. A defect is a single nonconformity, and one unit can have several defects. P and NP charts count defective units and use the binomial distribution, while C and U charts count defects and use the Poisson distribution. Choosing the right chart depends on which you are counting.
Why do the control limits vary on a P chart?
The control limits of a P chart depend on the subgroup sample size, because the variability of a proportion depends on how many units were inspected. Larger samples give a more precise estimate, so the limits are narrower, while smaller samples give wider limits. When sample sizes differ between subgroups, the limits are recalculated for each, producing the characteristic stepped appearance.
What distribution is the P chart based on?
The P chart is based on the binomial distribution, which models the number of successes, here defective units, in a fixed number of independent pass or fail trials. This is appropriate because each unit is classified into one of two categories. The binomial basis is also why the P chart requires units to be independent and the classification to be genuinely binary.
What if my sample size is constant?
If the sample size is the same for every subgroup, you can use either a P chart or an NP chart. The NP chart is often preferred in that case because it plots the actual count of defectives, which some find more intuitive than a proportion, and its control limits are constant. The P chart still works with constant sample sizes, but the NP chart's simplicity is an advantage.
Monitor Defective Rate With Varying Samples
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