# P Chart Control Limits Calculator

> Source: https://netray.co/tools/p-chart-control-limits-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Enter total defectives, total inspected and subgroup size to get the p-bar centerline and control limits for a fraction defective chart.

## Category

quality

## Industry

Manufacturing

## Audience

- Quality engineer
- Incoming inspection lead
- Six Sigma Green Belt

## Tool

**Kind:** calculator

**Inputs:**

#### Total defective units found

**Key:** defective

**Type:** number

**Default:** 96

**Min:** 0

**Step:** 1

**Unit:** units

**Help:** Sum across all subgroups in the baseline period.

#### Total units inspected

**Key:** inspected

**Type:** number

**Default:** 4000

**Min:** 1

**Step:** 50

**Unit:** units

#### Typical subgroup size

**Key:** n

**Type:** number

**Default:** 200

**Min:** 1

**Step:** 10

**Unit:** units

**Help:** Average units inspected per subgroup. Limits vary if size varies a lot.

#### Limit width

**Key:** k

**Type:** select

**Default:** 3

**Options:**

##### 3 sigma (standard control limits)

**Value:** 3

##### 2 sigma (warning limits)

**Value:** 2

**Outputs:**

#### Centerline p-bar

**Key:** pbar

**Expr:** defective / inspected * 100

**Format:** percent

**Primary:** true

**Description:** Average fraction defective.

#### Standard error of p

**Key:** sp

**Expr:** sqrt((defective / inspected) * (1 - defective / inspected) / n) * 100

**Format:** percent

#### Upper control limit

**Key:** ucl

**Expr:** pbar + k * sp

**Format:** percent

**Primary:** true

#### Lower control limit

**Key:** lcl

**Expr:** max(0, pbar - k * sp)

**Format:** percent

#### Expected defectives per subgroup (n times p-bar)

**Key:** npbar

**Expr:** n * defective / inspected

**Format:** decimal

**Description:** Should be at least about 5 for the normal approximation to hold.

**Chart:**

#### Control limits vs subgroup size

**Type:** line

**X:** n

**From:** 20

**To:** 600

**Steps:** 30

**Series:**

- ucl
- lcl

**Disclaimer:** Uses the normal approximation to the binomial. If n times p-bar is under 5, use exact binomial limits or a different chart.

## Content

**Intro:** A p chart tracks the fraction of units that fail inspection, such as rejected incoming lots, failed final tests or invoices with errors. This calculator gives you the centerline and limits so you can tell normal fluctuation from a real change.

**Sections:**

#### How to use the calculator

**Body:** Enter the total number of defective units and the total number inspected across a baseline period of at least 20 to 25 subgroups, then the typical subgroup size. The calculator returns the average fraction defective, the standard error, and the upper and lower control limits. Plot each subgroup's fraction defective against them. If your subgroup size varies a lot, recompute the limits for each subgroup using that subgroup's own n.

**Bullets:**

- Defective means the unit failed, however many defects it had.
- Use a c or u chart if you count defects rather than defective units.
- Select 2 sigma only for warning lines, not for action limits.

#### Formulas

**Body:** The centerline is p-bar, equal to total defectives divided by total inspected. The standard error of a proportion for subgroup size n is the square root of p-bar times (1 minus p-bar) divided by n. The upper control limit is p-bar plus three standard errors, and the lower control limit is p-bar minus three standard errors, set to zero if negative. This relies on the normal approximation, which is acceptable when n times p-bar is at least about 5 and preferably more.

#### Worked example

**Body:** An incoming inspection team checks 4,000 connectors in 20 lots of 200 and finds 96 defective. P-bar is 2.4 percent. The standard error is the square root of (0.024 times 0.976 divided by 200), about 1.08 percent. The UCL is 2.4 plus 3.24, about 5.6 percent, and the LCL is zero because the calculated value is negative. A lot with 13 defective out of 200, which is 6.5 percent, is therefore a signal worth investigating.

#### Common mistakes

**Body:** Using too small a subgroup so the expected number of defectives is near zero makes the chart useless, since most points will sit on the axis. Mixing different defect types in one chart hides which one is moving, so chart the vital few separately. Do not reset limits after every signal, and do not use p charts when the opportunities for defects per unit vary. Always investigate points below the lower limit too, because they may reflect inspector error rather than real improvement.

**Cta:** If inspection results are recorded in your ERP quality module, we can help you build a private report that charts fraction defective by supplier, part and period.

**Faq:**

#### What is the difference between p chart and np chart?

**Answer:** A p chart plots the fraction defective and allows the subgroup size to vary. An np chart plots the count of defective units and requires a constant subgroup size. Both rely on the binomial model, so they signal the same events.

#### When do I use a c or u chart instead?

**Answer:** Use c and u charts when counting defects, where one unit can have several. Use p and np charts when each unit is simply good or bad. A c chart needs constant area of opportunity and a u chart allows it to vary.

#### Why is my lower control limit zero?

**Answer:** When p-bar is small and the subgroup is modest, the calculated lower limit goes negative and is set to zero. Increase the subgroup size so that the lower limit becomes positive if you want to detect improvements.

#### What if my subgroup sizes vary?

**Answer:** Recalculate the limits for each subgroup using its own n, which gives stepped limits, or use a standardized z-score p chart. If sizes differ by less than about 25 percent from the average, a single set of limits is usually acceptable.

## Search terms

p chart calculator, p chart control limits formula, p chart ucl lcl calculator, fraction defective control chart, attribute control chart calculator, p chart example, np chart vs p chart, proportion defective control limits

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