Ever wondered why there's a difference in the number of samples needed when doing medical device Process Validation compared to QC inspection?
Typically, several times more samples are needed in the former than in the latter. The differences result from their radically different 𝒂𝒊𝒎𝒔 and 𝒂𝒔𝒔𝒖𝒎𝒑𝒕𝒊𝒐𝒏𝒔 about the process or lot/batch:
📌 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 #1 - 𝑷𝒖𝒓𝒑𝒐𝒔𝒆
In 𝑷𝒓𝒐𝒄𝒆𝒔𝒔 𝑽𝒂𝒍𝒊𝒅𝒂𝒕𝒊𝒐𝒏 the purpose is 𝑨𝒏𝒂𝒍𝒚𝒕𝒊𝒄: to study the performance of the constant-cause system that produced the product under study (i.e., the manufacturing process).
In 𝑸𝑪 𝑰𝒏𝒔𝒑𝒆𝒄𝒕𝒊𝒐𝒏 the purpose is 𝑬𝒏𝒖𝒎𝒆𝒓𝒂𝒕𝒊𝒗𝒆: to estimate how many units (%) are defective in the lot/batch to determine if we'll accept it, reject it, or re-work it.
📌 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 #2 - 𝑺𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄𝒂𝒍 𝑫𝒊𝒔𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏
In 𝑷𝒓𝒐𝒄𝒆𝒔𝒔 𝑽𝒂𝒍𝒊𝒅𝒂𝒕𝒊𝒐𝒏 with attribute data (good/bad units), the 𝑩𝒊𝒏𝒐𝒎𝒊𝒂𝒍 distribution is the correct one to use as there are potentially an infinite number of units that could be produced by the process now and in the future.
In 𝑸𝑪 𝑰𝒏𝒔𝒑𝒆𝒄𝒕𝒊𝒐𝒏 with attribute data, the 𝑯𝒚𝒑𝒆𝒓𝒈𝒆𝒐𝒎𝒆𝒕𝒓𝒊𝒄 distribution is the exact one to use as the lot/batch size is finite. The Binomial approximation can be used when Lot Size >> Sample Size.
📌 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 #3 - 𝑷𝒓𝒆𝒔𝒖𝒎𝒑𝒕𝒊𝒐𝒏
In 𝑷𝒓𝒐𝒄𝒆𝒔𝒔 𝑽𝒂𝒍𝒊𝒅𝒂𝒕𝒊𝒐𝒏 the manufacturing process is presumed non-conforming ("guilty") until it is proven conforming ("not guilty" or "innocent").
In 𝑸𝑪 𝑰𝒏𝒔𝒑𝒆𝒄𝒕𝒊𝒐𝒏, 𝘢𝘴𝘴𝘶𝘮𝘪𝘯𝘨 𝘵𝘩𝘦 𝘮𝘢𝘯𝘶𝘧𝘢𝘤𝘵𝘶𝘳𝘪𝘯𝘨 𝘱𝘳𝘰𝘤𝘦𝘴𝘴 𝘩𝘢𝘴 𝘢𝘭𝘳𝘦𝘢𝘥𝘺 𝘣𝘦𝘦𝘯 𝘷𝘢𝘭𝘪𝘥𝘢𝘵𝘦𝘥, the lot/batch is presumed conforming ("innocent") until it is proven non-conforming ("guilty") [the asumption of an already validated process is key here.]
📌 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 #4 - 𝑸𝒖𝒂𝒍𝒊𝒕𝒚 𝑳𝒊𝒎𝒊𝒕
In 𝑷𝒓𝒐𝒄𝒆𝒔𝒔 𝑽𝒂𝒍𝒊𝒅𝒂𝒕𝒊𝒐𝒏 the parameter used is the 𝑹𝒆𝒋𝒆𝒄𝒕𝒊𝒐𝒏 𝑸𝒖𝒂𝒍𝒊𝒕𝒚 𝑳𝒊𝒎𝒊𝒕 (RQL; equal to 100% - % Reliability). The concern is to reject, with a high probability, lots with % defectives greater than the RQL (i.e., a process that makes an unacceptably large number of defective units).
In 𝑸𝑪 𝑰𝒏𝒔𝒑𝒆𝒄𝒕𝒊𝒐𝒏, the parameter most commonly used is the 𝑨𝒄𝒄𝒆𝒑𝒕𝒂𝒏𝒄𝒆 𝑸𝒖𝒂𝒍𝒊𝒕𝒚 𝑳𝒊𝒎𝒊𝒕 (AQL). Per the definition of AQL, the concern is to accept - with a high probability - lots with % defectives at or below the AQL.
📌 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 #5 - 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝑳𝒐𝒕𝒔 & 𝑺𝒂𝒎𝒑𝒍𝒆 𝑺𝒊𝒛𝒆
This is the result of all the other differences above and provides the answer to our original question.
In 𝑷𝒓𝒐𝒄𝒆𝒔𝒔 𝑽𝒂𝒍𝒊𝒅𝒂𝒕𝒊𝒐𝒏 we seek to establish consistency (typ. requiring >= 3 lots) and, since the process must be proven conforming, we generally need 𝒎𝒂𝒏𝒚 𝒔𝒂𝒎𝒑𝒍𝒆𝒔 to establish this statistically.
In 𝑸𝑪 𝑰𝒏𝒔𝒑𝒆𝒄𝒕𝒊𝒐𝒏, since the purpose is to disposition one lot, a 𝒔𝒎𝒂𝒍𝒍𝒆𝒓 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒔𝒂𝒎𝒑𝒍𝒆𝒔 needed since the lot is presumed conforming.