(X)over-bar Charts with Variable Sample Size, Sampling Interval, and Warning Limits

作者：Mahadik Shashibhushan B^*

来源：Quality and Reliability Engineering International, 2013, 29(4): 535-544.

DOI：10.1002/qre.1403

• adaptive control chart
• average number of samples to signal
• average number of observations to signal
• average number of switches to signal
• statistical process control
• steady-state average time to signal

The notion of variable warning limits is proposed for variable sample size and sampling interval (VSSI) (X)over-bar charts. The basic purpose is to lower down the frequency of switches between the pairs of values of the sample sizes and sampling interval lengths of VSSI (X)over-bar charts during their implementations. Expressions for performance measures for the variable sample size, sampling interval, and warning limits (VSSIWL) (X)over-bar charts are developed. The performances of these charts are compared numerically with that of VSSI and VSSI (1, 3) (X)over-bar charts, where VSSI (1, 3) (X)over-bar charts are the VSSI (X)over-bar charts with runs rule (1, 3) for switching between the pairs of values of sample sizes and sampling interval lengths. Runs rule (1, 3) greatly reduces the frequency of the switches; however, it slightly worsens the statistical performances of the VSSI (X)over-bar charts in detecting moderate shifts in the process mean. It is observed that the out-of-control statistical performance and overall switching rate of VSSIWL (X)over-bar charts are adaptive for the same in-control statistical performances. These charts can be set to yield exactly similar performances as that of VSSI (1, 3) (X)over-bar charts, to yield tradeoff performances between that of VSSI (1, 3) and VSSI (X)over-bar charts, or to yield significantly lower switching rate than even that of VSSI (1, 3) (X)over-bar charts at the cost of slightly inferior statistical performances than that of VSSI (1, 3) (X)over-bar charts.

• 出版日期2013-6