Np ChartEdit
Np Chart (np chart) is a type of control chart used in quality control to monitor the number of defective items in samples drawn from a production process. Classified as an attributes chart, it tracks outcomes that are either defective or not, rather than measuring a continuous quantity. The chart is defined for a fixed sample size n and uses p, the proportion defective, along with its estimated mean p-bar to determine the upper and lower control limits. The observed number of defectives in each sample forms the np values, which are plotted over time to reveal trends in process performance. For those who study or implement statistical process control, the np chart pairs with other charts to provide a complete picture of process health, and it sits alongside concepts such as control chart and quality control in most practical manuals.
The np chart is particularly common in high‑volume manufacturing where defect rates are low enough that small shifts matter. It complements the p-chart, which tracks the defect rate as a proportion, by presenting the count of defectives in each fixed-size sample. Because the np chart scales the proportion by the fixed sample size n, it yields an integer count and can be easier to interpret in environments where management wants to see concrete defect counts rather than proportions. In practice, the np chart rests on the same probabilistic foundations that underlie the natural variability of a binomial process, and its behavior can be understood through the same families of distributions that include the binomial distribution and, for certain regimes, the Poisson distribution.
Overview
The np chart uses a central line at np-bar, the average number of defectives per sample across an observation window. The control limits are set at np-bar ± 3 sqrt(np-bar(1 − p-bar)), where p-bar is the estimated average defect rate (p-bar = np-bar / n). When the lower control limit would be negative, it is conventionally set to zero, since you cannot observe a negative number of defectives. The resulting chart allows operators and managers to distinguish between common cause variation (normal, expected fluctuations) and special cause variation (unusual events that signal a process change). The np chart assumes that each item within a sample has the same probability of being defective and that observations across samples are independent, conditions often met in well‑controlled manufacturing lines with stable inputs and consistent inspection criteria.
Methodology
Fixed sample size: The chart assumes every sample contains exactly n units. If the process routinely provides samples of different sizes, analysts may prefer alternative charts or adjustments to the limits. See also p-chart for a proportion-based view that can accommodate varying denominators.
Center line: The center line is np-bar, the average number of defectives per sample, computed as the sum of defectives across samples divided by the number of samples, then multiplied by n. This connects the np chart to the underlying proportion defective p-bar.
Control limits: UCL = n p-bar + 3 sqrt(n p-bar (1 − p-bar)) and LCL = max(0, n p-bar − 3 sqrt(n p-bar (1 − p-bar))). These limits derive from the binomial distribution’s standard deviation and the usual approximation that 3-sigma limits capture the majority of expected variation.
Center interpretation: Points falling outside the limits or showing nonrandom patterns (e.g., runs, trends) indicate potential process changes that warrant investigation into material quality, machine settings, or operator practices. See statistical process control for broader methodology and best practices.
Alternatives and extensions: If defect counts are not easily modeled with a fixed n, practitioners may switch to a p-chart or to an extended family of charts such as the c-chart (defects per unit) or the u-chart (defects per unit when units vary in size). Understanding these relationships helps in choosing the most appropriate chart for a given production environment.
Assumptions and limitations
Independence and identical probability: The np chart presumes that each item has the same chance of being defective within a sample and that defects occur independently. Violations—such as assortative mixing, correlated defects, or systematic measurement bias—can distort control limits and lead to false signals.
Fixed sample size: The strongest version of the np chart assumes a constant n. When production or sampling opportunities produce variable sample sizes, analysts may need to normalize the data or switch to p-chart or u-chart variants that handle varying denominators more robustly.
Process stability: The chart assumes a stable process during the observation period. Large, legitimate process changes (such as a deliberate shift in supplier quality or a major equipment upgrade) should be reflected in updated estimates of p-bar and np-bar to maintain meaningful limits.
Applications and practical considerations
In industries with automated inspection and high throughput—such as electronics, automotive components, and consumer goods—np charts provide a clear, auditable record of defect counts over time. They are commonly embedded in broader quality control systems and are used to support decisions on maintenance, supplier management, and production scheduling. Because the metric is a direct count, it can be easier to communicate to nonstatisticians who oversee production lines and budgets. In environments where regulatory regimes require traceable quality metrics, the np chart helps demonstrate control over production quality and facilitates root-cause analysis when anomalies appear.
When adopting an np chart, practitioners often pair it with other charts to capture different dimensions of quality. For example, a p-chart may be used when it is useful to examine defect proportion across samples of varying sizes, while a c-chart or u-chart might be preferred when defects are counted per unit or per batch rather than per fixed-size sample. A well-designed quality program will integrate np charts with process capability analyses, inspection plans, and ongoing process improvement initiatives to reduce variation and improve reliability.