Transaform a non normal data to normal data which is boundeed to zero
Answers
Most processes, particularly those involving life data and reliability, are not normally distributed. Most Six Sigma and process capability tools, however, assume normality. Only through verifying data normality and selecting the appropriate data analysis method will the results be accurate. This article discusses the non-normality issue and helps the reader understand some options for analyzing non-normal data.
Introduction
Some years ago, some statisticians held the belief that when processes were not normally distributed, there was something “wrong” with the process, or even that the process was “out of control.” In their view, the purpose of the control chart was to determine when processes were non-normal so they could be “corrected,” and returned to normality. Most statisticians and quality practitioners today would recognize that there is nothing inherently normal (pun intended) about the normal distribution, and its use in statistics is only due to its simplicity. It is well defined, so it is convenient to assume normality when errors associated with that assumption would be minor. In fact, most of the efforts done in the interest of quality improvement lead to non-normal processes, since they try to narrow the distribution using process stops. Similarly, nature itself can impose stops to a process, such as a service process whose waiting time is physically bounded at the lower end by zero. The design of a waiting process would move the process as close to zero as economically possible, causing the process mode, median and average to move toward zero. This process would tend towards non-normality, regardless of whether it is stable or non-stable.
Many processes do not follow the normal distributions. Some examples of non-normal distributions include:
Cycle time
Calls per hour
Customer waiting time
Straightness
Perpendicularity
Shrinkage
To help you understand the concept, let us consider a data set of cycle time of a process (Table 1). The lower limit of the process is zero and the upper limit is 30 days. Using the Table 1 data, the process capability can be calculated. The results are displayed in Figure 1.