Six Sigma Process Capability Analysis When the Process Measurements do not follow a Normal Distribution: A Case Study

Most Six Sigma process capability analyses are based on the assumption that the process data are normally distributed. However, many processes, particularly those involving life and reliability data, do not follow normal distribution. Evaluating Process Capability using the assumptions of normality in such cases may lead to erroneous evaluation and wrong conclusions. In cases, where the process measurements do not follow a normal distribution, special techniques are required to deal with non-normality. This paper examines the evaluation techniques for non-normal process data, and provides cases and analysis techniques for such data. In the first part of the paper, the probability plot is used to fit an appropriate distribution. Then that distribution is used to determine the nonconformance rate or the process capability. In the second part of the paper, the following non-normal process capability techniques are used to evaluate non-normal data: (1) the distribution fit approach, (2) Box-Cox Transformation, and (3) Johnson Transformation. These methods provided almost identical process capability for the same data. The paper also examined the most common methods for handling non-normal data including sub group averaging, segmenting data, transforming data, using other distributions (Wiebull Distributions, Log Normal, Exponential, Extreme value , and Logistic), and using the non-parametric methods. Determining the correct process capability in Six Sigma is critical to assessing the current and improved process performance of any process. During a Six Sigma project, the process capability is evaluated twice; first during the measure phase to show the impact of the problem and again after the improvement phase to show how the process has improved. This paper addresses the importance and evaluation techniques of process capability involving non-normal data.