Np chart

Np chart, also known as a number nonconforming control chart, is a tool used in statistical quality control used to monitor the amount of nonconforming units in a sample.

Usage of Np chart

Control charts are powerful tools for constructing and sustaining the statistical control of a producing process. Classic control charts are audited by taking random, n-sized samples from the running procedure for a h times. After inspecting the items in the sample and recording measurements of interest, computed data (regarding the appropriate time order) are presented on a graphical visualization. To compare the results with predetermined values of control limits two limit controls are necessary: an upper control limit (UCL) and a lower control limit (LCL). If the plotted calculated statistic marks between them it is considered that the process is in the in-control state. In another case that may be a signal that some process shift has appeared and a rectifying actions should be taken immediately to eliminate the cause of the discrepancy and bring this process back into control.

The fraction nonconforming is usually understood as the ratio of the number of nonconforming items in a population to the total number of items in that population. The items usually have a number of quality characteristics that are examined at the same time by the inspector. If the item does not accommodate to standard on one or more of these attributes, it is classified as nonconforming. An np control chart make it possible to look at variation in yes/no type attributes data. There are only two possible results: either the item is defective or it is not defective.

The np Control Chart is an adaptation of the p chart but it bases on the number nonconforming rather than the fraction nonconforming. It is helpful in situations when it is easier for someone to interpret process performance in terms of concrete numbers of units in place of the somehow more abstract proportion.

The np-chart is used with data compiled in subgroups that are the same size. Np charts present how the process which is measured by the number of nonconforming items, fluctuates over time. Usage of np-charts is convenient for determining if the process is stable and foreseeable, likewise to observe the effects of process improvement approaches.

Designing Np chart

Designing a control chart means making the choices of n, h, UCL and LCL to be used during the process monitoring.

Gathering the data

Gather the data:

1. Select the subgroup size (n) - this size must be constant.
2. Choose the frequency with which you will collect the data.
3. Select the number of subgroups (k).
4. Check out every item in the subgroup and mark it as defective or non-defective.
5. Establish np (number of defective items) for each subgroup.

Mapping out the data

Map out the data:

1. Choose the scales for the chart.
2. Mark the values of the nps for every subgroup on the chart.
3. Draw straight lines between consecutive points.

Computing the CL, UCL and LCL

Compute the center line, upper control line and lower control line:

1. Calculate the center line (CL). $n{\bar {p}}={\frac {\sum np}{k}}$
2. Draw the CL on the control chart as a solid line.
3. Compute the control limits for the np chart. Upper control limit: $UCL=n{\bar {p}}+3{\sqrt {n{\bar {p}}(1-(n{\bar {p}}/n))}}$ Lower control limit: $LCL=n{\bar {p}}-3{\sqrt {n{\bar {p}}(1-(n{\bar {p}}/n))}}$.
4. Mark the control limits on the chart as dashed lines.

Interpreting the results

Use those tests for statistical control:

• Points beyond the control limits,
• Length of runs test,
• Number of runs test.

Examples of Np chart

• An Np chart may be used to monitor the production of a manufacturing process. For example, a manufacturer may use an Np chart to monitor the number of defective items produced during each production batch. The chart can be used to identify any patterns or trends in the number of defects, and to ensure that the number of defects is within acceptable limits.
• An Np chart may also be used to monitor the quality of customer service. For example, a company may use an Np chart to track the number of customer complaints received each week. The chart can be used to identify any patterns of customer dissatisfaction, and to ensure that customer service is meeting acceptable standards.
• An Np chart may also be used to monitor the quality of a hospital's patient care. For example, a hospital may use an Np chart to track the number of medical errors made each month. The chart can be used to identify any patterns of medical errors, and to ensure that the patient care is meeting acceptable standards.

Advantages of Np chart

A Np chart provides several advantages for organizations looking to monitor the amount of nonconforming units in a sample. These advantages include:

• The ability to quickly identify process changes and take action when necessary. This allows organizations to reduce the risk of producing nonconforming units and maintain quality standards.
• The chart is easy to read and understand, making it accessible for all users.
• The Np chart provides a visual representation of process performance, enabling users to easily identify trends and outliers.
• The chart can help identify areas of improvement and can be used to ensure consistent levels of quality over time.
• The Np chart is a valuable tool for organizations looking to optimize their processes and ensure quality standards are met.

Limitations of Np chart

Np chart is a useful tool for monitoring the amount of nonconforming units in a sample, but it has some limitations. These limitations include:

• It is not suitable for processes with small sample size. This is because it may not provide an accurate representation of the process.
• It is sensitive to outliers and extreme values, which can lead to inaccurate results.
• It is difficult to interpret as it requires special calculations to determine the process performance.
• It is not suitable for processes with multiple outputs, as it cannot track the performance of each output.
• It relies on assumptions of randomness and normality of the data, which may not always be the case.
• It does not provide information on the causes of nonconforming units, so it may not be helpful in improving the process.

Other approaches related to Np chart

An introduction to the other approaches related to Np chart is that these approaches can be used to compare different samples for quality control. Here is a list of other approaches related to Np chart:

• Control charts: Control charts allow for the monitoring of processes over time, which can be used to identify process changes and determine whether the process is in control.
• Run charts: Run charts can be used to analyze process performance over time and to identify trends in the data.
• Pareto charts: Pareto charts are used to visually display data in order to identify the most significant factors that are contributing to a problem.
• Cause-and-effect diagrams: Cause-and-effect diagrams can be used to identify the root causes of a problem, which can then be used to develop corrective actions.

In summary, the Np chart is a tool used in statistical quality control to monitor the amount of nonconforming units in a sample. Other approaches related to Np chart include control charts, run charts, Pareto charts, and cause-and-effect diagrams, which all can be used in different ways to analyze different aspects of process performance.

Footnotes

Np chart — recommended articles

P chart — Control chart — Attribute control chart — Statistical process control — Quality control — CUSUM chart — Process capability — Overall equipment effectiveness — Analytical sheet

References

• Bashiri, M., Amiri, A., Asgari, A., Doroudyan, M. H. (2013), Multi-objective efficient design of np control chart using data envelopment analysis, "International Journal of Engineering", Vol. 26, Nr 6
• Chong, Z. L., Khoo, M. B., Castagliola, P. (2014), Synthetic double sampling np control chart for attributes, "Computers & Industrial Engineering", Vol. 75
• Faraz, A., Heuchenne, C., Saniga, E. (2017), The np Chart with Guaranteed In‐control Average Run Lengths, "Quality and Reliability Engineering International', Vol. 33 Issue: 5, pp. 1057-1066
• Hashemian S.M., Noorossana R., Keyvandarian A., Shekary A.M. (2016), Performance of adaptive np-chart with estimated parameter, "International Journal of Quality & Reliability Management", Vol. 33 Issue: 6, pp. 769
• Ho, L. L., Costa, A. F. B. (2011), Monitoring a wandering mean with an np chart, "Production", Vol. 21, Nr 2
• Kooli I., Limamb M. (2015), Economic design of attribute np control charts using a variable sampling policy "Applied Stochastic Models in Business and Industry", Vol. 31, pp. 483
• McNeese B. (2009), np Control Charts, "SPC for Excel"
• Montgomery D.C. (2012), Introduction To Statistical Quality Control, 7th Edition, Wiley, Arizona State University, pp. 316-330
• Morais M.C. (2016), An ARL-Unbiased np-Chart, "Economic Quality Control", Vol. 31 Issue: 1, pp. 11-21
• Ye ZS, Xie M. (2015), Stochastic modelling and analysis of degradation for highly reliable products, "Applied Stochastic Models in Business and Industry", Vol. 31 Issue: 1, pp. 16-36

Author: Anna Kasprzyk