In order to compare Shewhart, CUSUM, and EWMA control charts, consider simulated data for the tensile strength of a phenolic resin. It is assumed that the tensile strength x is normally distributed with a mean of μ = 70 MPa and a standard deviation of σ = 3 MPa. A single measurement is available at

Question

In order to compare Shewhart, CUSUM, and EWMA control charts, consider simulated data for the tensile strength of a phenolic resin. It is assumed that the tensile strength x is normally distributed with a mean of [latex]μ = 70 MPa[/latex] and a standard deviation of [latex]σ = 3 MPa[/latex]. A single measurement is available at each sampling instant. A constant [latex](δ = 0.5σ = 1.5)[/latex] was added to [latex]x(k) for k ≥ 10[/latex] in order to evaluate each chart’s ability to detect a small process shift. The CUSUM chart was designed using [latex]K = 0.5σ[/latex] and [latex]H = 5σ[/latex], while the EWMA parameter was specified as [latex]λ = 0.25.[/latex]

Accepted Answer

The relative performance of the Shewhart, CUSUM, and EWMA control charts is compared in Fig. 21.6. The Shewhart chart fails to detect the 0.5σ shift in x. However, both the CUSUM andEWMAcharts quickly detect this change, because limit violations occur about 10 samples after the shift occurs (at k = 20 and k = 21, respectively). The mean shift can also be detected by applying the Western Electric Rules in the previous section.

Question 21.3: In order to compare Shewhart, CUSUM, and EWMA control charts...

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