An attribute chart is a kind of control chart where you display information on defects and defectives. Helps you visualize the enemy – variation! Follows a philosophy of detection, not prevention; thus it is NOT really, truly part of Six Sigma which focuses on prevention.

There are four types of Attribute Charts:

## p Chart (proportion chart)

### What they do:

- Evaluates the stability of a process when we are evaluating the proportion of defectives vs in good order as a percentage.
- The plot shows the percentage of defectives.

### When to Use:

- Sample sizes are NOT equal.
- Have discrete data.

### Step 1) Measure P-bar:

p bar = the fraction rejected = total defectives / total inspected.

### Step 2) Find Control Limits:

3 SD = 3 (SQRT((pbar * (1-pbar))/n))

N refers to a SINGLE instance of a sample size, not the # of sample sizes (or rows) listed. Since there are multiple sample sizes, we use the largest one on the list – the worst case. (You can establish UCL & LCL with the best case to get a different interpretation.

**Upper control limit** = pbar + 3 SD

**Lower control limit** = pbar – 3 SD

## np Chart

### What they do:

- Evaluates the stability of a process when we are evaluating the proportion of defectives as a raw number.
- The plot shows the # of defectives.

### When to Use:

- Sample sizes are equal.
- Subgroups are the same size.
- Attributes are discrete and binary (ex. yes vs no; up vs down)

### Step 1) Calculate p as above.

### Step 2) Calculate np.

np bar = total # defective / total samples.

The total samples are the # of rows listed.

### Step 3) Calculate the control limits

**UCL** = np bar + 3 * (SQRT(npbar*(1-pbar)))

**LCL** = np bar – 3 * (SQRT(npbar*(1-pbar)))

## C Charts

### What they do:

- Evaluates the stability of counted data
- Measures defects per unit. Helpful if you have a list of # of defects per unit ID.
- The plot shows the # of defectives.

### When to Use:

- Total opportunity population is large compared to # defects.
- When you cannot count “not a defect.”
- Data type is discrete but each count has an equal opportunity of coming up.

c = total # defects / # units

**UCL** = c bar + 3 * (SQRT(c))

**LCL** =c bar – 3 * (SQRT(c))

## u Chart

### What they do:

- Evaluates the stability of counted data
- Measuring variable defects per unit. Helpful for when you have lots of varying sample size.
- The plot shows the # of defectives.

### When to Use:

- Sample size varies – ex. Multiple types of a defect.

### Step 1) Calculate the number of defects per unit in each lot.

u = c / n = number of defects in the lot / # of units in the lot.

Then repeat this for all of the lots.

### Step 2) Calculate u bar

u bar = total defects in all of the lots total / total # units in all of the lots combined.

### Step 3) Calculate UCL & LCL for EACH lot size

Ex. if you have lot sizes of 1, 2, 3, and 4 – you must create an UCL & LCL for each of them!

UCL = ubar + 3* (SQRT(ubar / n)) where n is the # of items in the lot size

LCL = ubar – 3* (SQRT(ubar / n))

This makes the c chart look like a control chart married with a box plot.

## Attribute Chart Videos

## ASQ Six Sigma Black Belt Attribute Chart Questions

**Question:** Which of the following control charts is most appropriate for monitoring the number of defects on different sample sizes?

(A) u

(B) np

(C) c

(D) p

**Answer:** The u chart is the most appropriate because it evaluates the stability of counted data.

## ASQ Six Sigma Green Belt Attribute Chart Questions

Which of the following control charts is used to monitor discrete data?

(A) p

(B) I & mR

(C) X Bar

(D) X Bar – R

**Answer:** p charts are used to monitor discrete data. See the control chart matrix in downloads. Also, review attribute charts.

I & MR charts and X Bar charts are for continuous data and When you have subgroups of size = 1. You use the ImR (XmR) chart only when logistical reasons prevent you from having larger subgroups or when there is no reasonable basis for rational subgroups.

Use X Bar R Control Charts when you have small amounts of constant, continuous data and when you can rationally collect measurements in subgroups of generally between two and 10 observations.

Praful bhusari says

Why sample size held constant for NP chart and varies for People chart?

Six Sigma Study Guide says

No idea what you mean by a people chart.

An NP chart is for samples of varying size and a P chart is for samples of a fixed size if that helps.

Praful bhusari says

Is pre control tool useful for attributes inspection?

Six Sigma Study Guide says

Well, I guess that depends on the precontrol tool you are using. An attribute chart is a kind of control chart where you display information on defects and defectives. This helps you visualize the enemy – variation!

If your pre-control helps you see variation better, then perhaps yes.

Amy says

Under C chart and U chart you have that the purpose is to identify the # of defectives. From my notes, this statement is inaccurate, did you mean to state the # of defects for the C chart and the % of defects for the U chart?

Abd Ahmed says

Hello Could some ONE helping me please, to solve the following Problem

A shop uses a control chart on maintenance workers based on maintenance errors per standard worker-hour. For each worker, a random sample of 5 items is taken daily and the statistic c/n is plotted on the worker’s control chart where c is the count of errors found in 5 assemblies and n is the total worker-hours required for the 5 assemblies.

(a) After the first 4 weeks, the record for one worker is c=22 and n=54. Determine the central line and the 3-sigma control limits.

(b) On a certain day during the 4-week period, the worker makes 2 errors in 4,3 standard worker-hour. Determine if the point for this day falls within control limits.

Six Sigma Study Guide says

This is a nice homework problem. What have you tried so far?