Question

Discuss with examples Type-I and Type-II errors relative to the SPC theory of control charts.

What practical implication in terms of process operation do these two types of errors have?

Answer 1

Solution:

SPC (Statistical Process Control) is a technique that is widely used in operations management to analyse the processes and determine whether the processes are in control or not depending on the statistical limits that are derived using the statistical information. SPC is very useful in operations management and is considered a crucial element in quality management.

Type-I error is an error where a process which is within statistical control is deemed to be out of control. Such an error is called type-I error because we are stating a perfectly in control process to be out of control. An example will be the process of identifying defects in a process and checking if the defects are within statistical control limits. If the sample consists of observations whose number of defects are within the statistical control limits but we accidently state that process to be out of control. This is an example of Type-I error.

Type-II is an error that occurs when we fail to reject a process that is out of control and deem it to be within control. An example of Type-II error will be when we analyse the process for the number of defects in a sample and accidently fail to state that the process is out of control despite having samples with number of defects that are not within the control limits. This is an example of type-II error.

Type-I and Type-II error have a significant uses in manufacturing and engineering applications. For example, type-II error is often used across in manufacturing for determining an accurate size of the sample. Sample size determination is itself a big topic in statistics and the use of type-II error in determining the sample size is extremely crucial. Similarly we can use type-I error in many engineering applications and use these error as a value against which we can determine many critical parameters of the manufacturing process.

Hence, this is how we can relate the type-I and type-II error to SPC.