Change Point Method with Weibull Distribution

Authors:

D.K. Veersesappa (Rayalaseema University, Kurnool)

K. Sreenivasa Rao (Rayalaseema University, Kurnool)

Y. Raghunatha Reddy (Rayalaseema University, Kurnool)

S.S. Handa (Manav Rachna International University, Faridabad)

Keywords: Cumulative Sum Control Charts, Exponentially Weighted Moving Average Control Charts, Shewart Control Charts, Average Run Length, Statistical Process Control.

Abstract:

The assumption of known in-control mean and SD underlies in all the standard charting methods (Shewart, CUSUM, and EWMA) and change point approach. The values used are generally not exact parameter values, but estimates are obtained in this paper. Using estimated parameters, the ARL behaviour changes randomly from one realization to another, making it impossible to control run length behaviour of any particular chart. The unknown – parameter change point formulation methodology for detecting and diagnosing step changes based on imperfect process knowledge is studied. It is observed that, despite not requiring specification of the post-change process parameter values, its performance is never far short of that of the optimal CUSUM chart which requires this knowledge, and it is far superior for shifts away from the CUSUM shift for which the CUSUM chart is optimal. Also, we observe change point methods are designed for step changes that persist, they are also competitive with the Shewart chart.

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