six sigma-based x-bar control chart for continuous quality improvement

Introduced by Shewhart, the traditional variable control chart for mean (X-bar Chart) is an effective tool for controlling and monitoring processes. Notwithstanding, the main disadvantage of X-bar chart is that the population standard deviation is unknown though the sample mean is an unbiased estimator of the population mean. There are many approaches to estimating the unknown standard deviation with the expertise available with the researchers and practitioners that may lead to varying conclusions. In this paper, an innovative approach is introduced to estimate the population standard deviation from the perspective of Six Sigma quality for the construction of the proposed control chart for mean called Six Sigma-based X-bar control chart. Under the assumption that the process is normal, in the proposed chart the population mean and standard deviation are drawn from the process specification from the perspective of Six Sigma quality. After discussing the aspects of the traditional X-bar control chart, the procedure for the construction of the proposed new Six Sigma-based X-bar control chart is presented. The new chart is capable of maintaining the process mean close to the target by variance reduction resulting in quality improvement. Also, it may be noted that at a point of time, the process, though under statistical control, may be maintaining a particular sigma quality level only while the goal is Six Sigma quality level of just 3.4 defects per million opportunities. Hence, as a practice of continuous quality improvement, it is suggested to use the proposed control chart every time with improvement till the goal of Six Sigma with 3.4 defects per million opportunities is achieved. An innovative cyclic approach for performing the continuous quality improvement activity is also presented. The construction of the proposed Six Sigma-based X-bar control chart is demonstrated using an illustrative example.