## P-chart vs Np-chart in Lean Six Sigma. All You Need to Know

Quality monitoring relies partly on attribute charts like P chart and NP chart.

P charts gauge proportions defective when test bunch sizes stay steady. NP charts instead track non-compliant units directly when batch quantities fluctuate.

Both adhere to the binomial distribution modeling independent trials’ success/failure probabilities—the essential attributes a binary nature.

P chart and NP chart statistically set control boundaries before graphing stats for ease of digestion.

Proper utilization proves pivotal for enterprises optimizing quality systems through refining defect occurrences, minimizing costs, and cultivating buyer fidelity.

## Key Highlights

- Companies utilize P chart vs NP chart control charts as quality administration tools tracking defect fractions or amounts.
- P charts serve consistent batches. NP charts handle erratic subgroup quantities.
- Both models attribute binarily: to compliant products/errors. Tracking attribute data concerning flaws, errors, or nonconforming units.
- Correct chart electing and leveraging illuminates processes recognizes glitches, and stimulates refinement. Quality thereby gains through defects truncated.
- Familiarization covers boundaries statistical calculations dictate, desirable readings, and pros/cons guiding apt chart deployment enhancing analysis precision.

## Introduction to P Chart vs NP Charts

When tracking whether work hits its marks, control charts like P Chart vs NP Chart track tasks in manufacturing or services.

P Charts (“Proportion Charts”) monitor error rates during regular-sized tests.

NP Charts (“Non-Compliant Counts”) follow actual glitch amounts with constant subgroup sizes.

Both root in binomial distribution modeling individual trial outcomes – whether it misses standards or not.

Key divergence exists in how data appears – P Charts use percentages, and NP Charts display counts.

This distinction proves key when reading control borders and pinpointing potential problems within procedures.

Using P/NP Charts, businesses track processes detect unexpected changes early, fix issues, and stay quality-consistent.

Crucial for Six Sigma and management systems, these charts let places achieve higher client trust and efficient operations.

## Data Requirements and Assumptions

Both the p chart and the np chart are used to monitor attribute data, which deals with defective or non-defective items. Some specific data requirements and assumptions must be met to use these charts effectively.

### Data Requirements

- The data must consist of defective or non-defective units (attribute data).
- The data should be obtained from a repetitive process or operation.
- For the p chart, the data is in the form of the fraction or proportion of defective items in each subgroup.
- For the np chart, the data is in the form of the actual number of defective items in each subgroup.

### Key Assumptions

- The process being monitored is in statistical control. Any shifts or trends in the control charts may indicate assignable causes that need investigation.
- The probability of a defective item is constant from subgroup to subgroup when the process is in control.
- Within each subgroup, the defective items follow a binomial distribution.
- The subgroup samples are randomly selected from the process output.
- The subgroup sizes are constant for np charts. For p charts, subgroup sizes can vary.

It’s crucial to ensure these data requirements and assumptions are reasonably satisfied. Violating assumptions can lead to invalid control limits and misleading interpretations of the control charts.

Proper data collection, subgroup formation, and understanding of the process being monitored are essential for meaningful attribute control chart analysis.

## Calculating Control Limits

One of the key steps in constructing p chart vs np chart is calculating the control limits that will be used to determine if the process is in control or not.

The control limits are statistically derived from the data itself and provide a baseline for separating common cause variation from special cause variation.

### For p Charts:

The center line (CL) is the average fraction nonconforming across all subgroups. It is calculated as:

CL = Sum of nonconforming units / Total units inspected

**The upper control limit (UCL) and lower control limit (LCL) are calculated as:**

UCL = CL + 3 * sqrt(CL * (1 – CL) / n)

LCL = CL – 3 * sqrt(CL * (1 – CL) / n)

Where n is the subgroup size.

### For np Charts:

The center line (CL) is the average number of nonconforming units per subgroup. It is calculated as:

CL = Total nonconforming units / Number of subgroups

**The upper control limit (UCL) and lower control limit (LCL) are calculated as:**

UCL = CL + 3 * sqrt(CL * (1 – CL/n))

LCL = CL – 3 * sqrt(CL * (1 – CL/n))

Where n is the subgroup size.

The control limits are based on the binomial distribution for attribute data. The formulas use 3-sigma limits, which is standard for most control charts in statistical process control. Properly calculating these limits is crucial for accurate control chart interpretation and separating signal from noise.

## Constructing and Interpreting the Charts

Once you have calculated the control limits, you can construct the P chart or NP chart by plotting the fraction of defective/nonconforming (p) or number of nonconforming units (np) on the y-axis against the sample numbers on the x-axis.

The center line represents the average fraction of defective/nonconforming or the average number of defects across all samples.

The upper control limit (UCL) and lower control limit (LCL) are also plotted as horizontal lines spanning the chart. Any points falling outside these control limits indicate the process is out of control and should be investigated for assignable causes of variation.

When interpreting the chart, look for any points beyond the control limits, as well as patterns or trends that could signal an issue. Some examples of patterns to look for include:

- A run of 7 or more points above or below the center line
- 10 out of 11 points on the same side of the center line
- 6 points steadily increasing or decreasing
- 14 or more points alternating up and down

These patterns, even if within the control limits, can indicate the process is not completely stable or in statistical control. Process monitoring with attribute control charts like the P and NP charts allows you to identify issues early before they become bigger problems impacting quality.

## Advantages and Limitations

### Advantages of P Charts and NP Charts

- Simple to construct and interpret compared to other control charts
- Effective for monitoring attribute data like defects, nonconformities, etc.
- Can be used with data from go/no-go inspections or simple pass/fail tests
- Provide a statistically-based method for segregating common vs. assignable causes of variation
- Allow for the early detection of process shifts or trends

### Limitations of P Charts and NP Charts

- Only applicable to attribute data, not variable data like measurements
- Require constant subgroup sizes or areas of opportunity
- Sensitive to changes in sample size that can create false signals
- Don’t provide insight into which specific defects or nonconformities occurred
- Assume that data follows a binomial distribution which may not always be true
- Less sensitive than variable control charts for detecting small process shifts

While P and NP charts have some inherent shortcomings, they are still very useful tools when working with attribute data. Being aware of their advantages and limitations allows users to apply them appropriately within an overall quality control strategy.

For example, they can complement variable control charts by monitoring different aspects of process performance. With proper implementation, P and NP charts enable more effective process monitoring and improvement compared to working without statistical process control methods.

## Case Studies and Examples

To better illustrate the use of P charts and NP charts, let’s look at a couple of case studies and examples.

### Case Study 1: Automobile Defect Tracking

An automotive manufacturer wants to monitor the defect rate of a critical component during the assembly process. They randomly select samples of 50 components from each hour’s production run. The number of defective components in each sample is recorded.

Since the data represents defective or non-defective units, an attributes control chart is appropriate. The subgroup size is 50, so an NP chart tracking the number of defective units would be used.

Control limits are calculated and the chart is constructed. Process analysts can then monitor for any out-of-control signals that may indicate a process issue requiring investigation and correction.

### Case Study 2: Call Center Quality Monitoring

A call center has a team of quality auditors who evaluate recorded customer service calls for adherence to protocols and procedures. Each auditor reviews a random sample of 100 calls per week and records whether each call passed or failed the quality review.

In this case, the quality review data is attribute data (pass/fail), and the subgroup size is constant at 100 calls per auditor per week.

A p-chart monitoring the proportion or fraction of failed calls would allow quality managers to track the defect rate and detect any unusual shifts or trends that may require process improvements.

### Example: Monitoring Packaging Defects

A food manufacturer wants to monitor the fraction of defective units in their packaging process. Samples of 200 units are inspected hourly, and the number of defective units is recorded.

With a constant subgroup size of 200 and attribute data, an NP chart can be used to monitor and control the number of defects. Calculated control limits will allow detection of any out-of-control conditions.

## Best Practices and Tips

When using p charts and np charts, there are several best practices to keep in mind to ensure you get accurate insights:

### Choose the Right Chart

Make sure you select the appropriate chart (p or np) based on your data type and sample size. P charts are used for go/no-go data when the subgroup sample size is constant. Np charts are used when the subgroup sample size varies.

### Proper Sampling

Take random samples that are truly representative of the process you want to monitor. Improper sampling can lead to inaccurate control limits and misleading signals.

### Stratify Data When Needed

If you have different product codes, machines, operators etc., consider stratifying the data into separate charts rather than combining it all. This can reveal sources of variation.

### Examine Patterns

Beyond just points outside the control limits, look for other patterns like runs, trends, or hugging the mean that could indicate an out-of-control process.

### Calculate Capability

Once your process is stable, calculate process capability metrics like Cp/Cpk to see if you are meeting specifications.

### Continual Monitoring

Don’t just create the charts once – keep monitoring and updating them as an ongoing process check.

### Root Cause Analysis

When a chart signals an issue, go through a disciplined root cause analysis to identify and eliminate assignable causes.

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