An effective joint X-bar and R chart to monitor the process mean and variance

Abstract

When the shift occurs in both sample mean and standard deviation of a process, a joint X-bar and R charts can be used to monitor the process mean and variance. This paper deals with very simple and effective design of proposed X-bar and R charts to monitor the process mean and standard deviation. The concept of the proposed chart is based upon the sum of chi-square (χ) to compute and compare Average Run Length values (ARLs). Although Variable Sample Size (VSS), Variable Sampling Interval (VSI) and Variable Sample Size and Sampling Interval (VSSI) joint charts are very useful to catch the small shifts in the mean or standard deviation, they make the chart more complex and very difficult to use at shop-floor level. The performance of the proposed chart has been compared with VSS, VSI and VSSI joint schemes proposed by Costa (1999).

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