Reliability tests for Weibull distribution with varying shape-parameter, based on complete data

The Weibull distribution indexed by scale and shape parameters is generally used as a distribution of lifetime. In determining whether or not a production lot is accepted, one wants the most effective sample size and the acceptance criterion for the specified producer and consumer risks. (μ₀ ≡ acceptable MTTF; μ₁ ≡ rejectable MTTF). Decide on the most effective reliability test satisfying both constraints: Pr{reject a lot | MTTF = μ₀} ⩽ α, Pr{accept a lot | MTTF = μ₁ } ⩽ β. α, β are the specified producer, consumer risks. Most reliability tests for assuring MTTF in the Weibull distribution assume that the shape parameter is a known constant. Thus such a reliability test for assuring MTTF in Weibull distribution is concerned only with the scale parameter. However, this paper assumes that there can be a difference between the shape parameter in the acceptable distribution and in the rejectable distribution, and that both the shape parameters are respectively specified as interval estimates. This paper proposes a procedure for designing the most effective reliability test, considering the specified producer and consumer risks for assuring MTTF when the shape parameters do not necessarily coincide with the acceptable distribution and the rejectable distribution, and are specified with the range. This paper assumes that α < 0.5 and β < 0.5. This paper confirms that the procedure for designing the reliability test proposed here applies is practical