On testing of parameters in modulated power law process

Abstract

The modulated power law process (MPLP) is often used to model failure data from repairable system, when both renewal type behaviour and time trends are present. The MPLP allows for the failure rate of a system to be affected by the failure and repair. Since the MLEs of the estimates do not have closed form expressions, they have to be approximated, and hence deriving a test procedure will be difficult. Black and Rigdon (1996) have proposed asymptotic MLEs and asymptotic likelihood ratio tests for the parameters which also do not have closed form expressions and hence are not easy for application. In this paper, we derive a closed form expression for the test statistics which is simple and easy to apply for testing (i) H0: β = 1 versus H1: β ≠ 1 when κ is known and (ii) H0: (β = 1 and κ = 1) versus H1: (β ≠ 1 or κ ≠ 1). The simulation study for percentiles and powers are given. We also compare the performance of the test with that of Black and Rigdon's (1996) test. Some numerical examples are also provided to illustrate the testing procedures. Copyright © 2001 John Wiley & Sons, Ltd.