Detection of shift in process mean withX¯chart for autocorrelated data

Abstract

Purpose -The purpose of this paper is to study the performance of the X-bar chart on the basis of average run lengths (ARLs) for the positively correlated data. The ARLs at various sets of parameters of the X-bar chart are computed by simulation. The performance of the chart at the various shifts in the process mean is compared with the X-bar chart suggested by Zang and residual chart proposed by Zang. The optimal schemes suggested in this paper are also compared with variable parameters (VP) chart and double sampling (DS) X-bar chart suggested by Costa and Machado. Design/methodology/approach -Positively correlated observations having normal distribution are generated with the help of the MATLAB software. The performance of the X-bar chart in terms of ARLs at the various shifts in the process mean is compared with the X-bar chart suggested by Zang and residual chart proposed by Zang. The optimal schemes are also compared with VP X-bar chart and DS X-bar chart suggested by Costa and Machado. Findings -The suggested optimal schemes of X-bar chart perform better at the various shifts in the process mean than the X-bar chart suggested by Zang and residual chart suggested by Zang. It was concluded that, although the suggested schemes for X-bar chart detect shifts later than the VP and DS X-bar charts proposed by Costa and Machado, they involved a much smaller number of parameters that are to be adjusted. So the time required for adjustment in case of optimal scheme is very small compared to the VP and DS charts.Research limitations/implications -The optimal schemes of X-bar chart are developed for the normally distributed autocorrelated data. But this assumption may also be relaxed to design these schemes for autocorrelated data. Moreover, the optimal schemes for chart can be developed for variable sample size and for variable sampling intervals. Originality/value -Although it is the extension of previous work, it can be applied to various manufacturing industries as well as service industries where the data is positively correlated and normally distributed.

Bayesian networks for statistical process control with attribute data

“…The idea is to establish an upper warning limit below the upper control limit (UCL), and adjust the sample size or sampling interval when sample results fall between the warning and control limits. Hashemian et al (2016) Variable data Attribute data Static control charts Duncan (1956Duncan ( , 1971, Cowden (1957), Gibra (1967Gibra ( , 1971, Goel et al (1968), Taylor (1968), Knappenberger and Grandage (1969), Baker (1971), Saniga (1977Saniga ( , 1979, Saniga and Montgomery (1981), Lorenzen and Vance (1986), Costa (1993Costa ( , 1998Costa ( , 1999, Singh and Prajapati (2013), Oprime andMendes (2017) Ladany (1973), Chiu (1975Chiu ( , 1976, Ladany and Alperovitch (1975), Montgomery et al (1975), Alperovitch and Friedman (1976), Sculli and Woo (1976), Duncan (1978), Gibra (1978), Saniga and Montgomery (1981), von Collani (1989), Darestani et al (2014) Adaptive control charts Reynolds et al (1988), Runger and Pignatiello (1991), Prabhu et al (1993Prabhu et al ( , 1994, Park and Reynolds (1994), , , Bai and Lee (1998), Zimmer et al (1998),…”

Cost comparisons of modifiedX̅chart for autocorrelated observations

“…The comparison of performance on the basis of average run lengths (ARLs) of the modified X chart with the Shewhart X chart for correlated data has already been given in Singh and Prajapati [5].…”

“…They observed that by implementing same, the cost of quality reduces significantly in the chosen industry. Singh and Prajapati [5] suggested the optimal schemes of X chart and compared with VP X chart and DS X chart, suggested by Costa and Machado [18]. Mitra and Clark [23] focused on determining changes in process variability of multivariate processes.…”

“…Thus the process may be assumed out of control. The detailed procedure is shown in Singh and Prajapati [5].…”