Phase II Exponential Charts for Monitoring Time Between Events Data: Performance Analysis Using Exact Conditional Average Time to Signal Distribution

Nirpeksh Kumar (1) , Subha Chakraborti (2) , Philippe Castagliola (3)

1 BHU - Banaras Hindu University [Varanasi]
2 UA - University of Alabama [Tuscaloosa]
3 LS2N - équipe CPS3 - Conception, Pilotage, Surveillance et Supervision des systèmes

In this paper, we study the performance properties of the phase II exponential chart with an unknown in-control (IC) rate parameter, used to monitor high-yield processes. The average time to signal (ATS) is used as the chart performance criterion instead of the usual average run length (ARL). Based on the IC conditional ATS (CATS) distribution, we examine the properties of both the equal-tailed and the ATS-unbiased exponential charts with estimated control limits and adjust the limits so that a nominal IC ATS performance is achieved. Two perspectives are investigated: the unconditional, under which the average of IC CATS distribution is set equal to a nominal ATS and, the conditional so that the IC CATS is set to or exceed a nominal ATS with a high probability. It is shown that the ATS-unbiased exponential chart under the conditional perspective has a better IC performance.

Mots clés: Conditional and Unconditional perspectives; Equal-tailed and ATS-unbiased exponential chart; Exact distribution; Guaranteed IC performance; Quality control

Domaines: Statistiques [stat]

Nirpeksh Kumar, Subha Chakraborti, Philippe Castagliola. Phase II Exponential Charts for Monitoring Time Between Events Data: Performance Analysis Using Exact Conditional Average Time to Signal Distribution. Journal of Statistical Computation and Simulation, 2022, 92 (7), pp.1457-1486. ⟨10.1080/00949655.2021.1998501⟩. ⟨hal-03646713⟩