OPS.18:5.1 - A process signal calls for containment and investigation

In this constructed recurring inspection operation, the supplied stable reference proportion of nonconforming items is p₀ = 0.02. Samples contain n = 200 independent, comparable items under the stated binomial basis. The local monitoring policy uses a three-standard-deviation p-chart rule and calls for segregation of the affected output and investigation when the upper limit is exceeded.

The upper limit is p₀ + 3√(p₀(1 − p₀)/n) = 0.02 + 3√(0.02 × 0.98 / 200), approximately 0.0497, or 4.97%. The corresponding lower value is negative and is truncated to zero.

The next sample contains twelve nonconforming items: 12 / 200 = 0.06, or 6%. This exceeds the specified upper limit. The practitioner applies the policy’s containment and investigation response and identifies the sampled output, source process and current configuration.

The arithmetic establishes the signal under that rule. It does not identify why the items failed, determine another lot’s disposition or show that the process is capable of meeting a product specification. The three-standard-deviation calculation defines the limit for this rule; it does not supply an exact confidence or false-alarm probability. With this low reference rate, a claim about false-alarm or missed-detection probability needs an appropriately qualified binomial or other statistical design.

Suppose the investigation finds a changed setup condition. Returning to the earlier setup and obtaining the required process and output evidence can support restart under the responsible authority. A single subsequent point below the limit is insufficient to establish every one of those claims. A persistent smaller shift may call for a monitor such as an exponentially weighted moving average (EWMA), which retains information from successive observations, if its detection properties fit the need.