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Fig 1.

The PDF and HRF of IKum distribution for different values of γ and θ.

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Fig 1 Expand

Fig 2.

The process of generating order statistics under Type-I PHCS.

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Fig 2 Expand

Table 1.

Progressive CSs that have been used in the Monte Carlo simulation.

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Table 1 Expand

Table 2.

MSEs for the MLEs and Bayes estimates of (γ, θ, λ) for different schemes with T1 = 0.9, T2 = 0.5.

Prior parameter values are: μ = 2, ν = 1.5, ζ = 1.5, η = 1.5. Population parameter values are: γ = 1.85699, θ = 2.50899, λ = 1.5.

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Table 2 Expand

Table 3.

RABs for the MLEs and Bayes estimates of γ, θ, λ for different schemes with T1 = 0.9, T2 = 0.5.

Prior parameter values are: μ = 2, ν = 1.5, ζ = 1.5, η = 1.5. Population parameter values are: γ = 1.85699, θ = 2.50899, λ = 1.5.

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Table 3 Expand

Table 4.

AILs and CPs of 95% CIs of γ, θ, λ for different schemes with T1 = 0.9, T2 = 0.5.

Prior parameter values are: μ = 2, ν = 1.5, ζ = 1.5, η = 1.5. Population parameter values are: γ = 1.85699, θ = 2.50899, λ = 1.5.

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Table 4 Expand

Table 5.

MSEs for the MLEs and Bayes estimates of γ, θ, λ for different schemes with T1 = 0.9, T2 = 0.5.

Prior parameter values are: μ = 2, ν = 1.5, ζ = 1.5, η = 1.5. Population parameter values are: γ = 1.85699, θ = 2.50899, λ = 1.5.

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Table 5 Expand

Table 6.

RABs for the MLEs and Bayes estimates of γ, θ, λ for different schemes with T1 = 0.9, T2 = 0.5.

Prior parameter values are: μ = 2, ν = 1.5, ζ = 1.5, η = 1.5. Population parameter values are: γ = 1.85699, θ = 2.50899, λ = 1.5.

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Table 6 Expand

Table 7.

AILs and CPs of 95% CIs of γ, θ, λ for different schemes with T1 = 0.9, T2 = 0.5.

Prior parameter values are: μ = 2, ν = 1.5, ζ = 1.5, η = 1.5. Population parameter values are: γ = 1.85699, θ = 2.50899, λ = 1.5.

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Table 7 Expand

Fig 3.

Empirical CDFs against CDFs of the IKum distribution for the given data listed in Table 8, under two the stress levels.

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Fig 3 Expand

Table 8.

Times to breakdown of an insulating fluid.

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Table 8 Expand

Table 9.

MLEs of the parameters, K-S statistic and p-value.

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Table 9 Expand

Table 10.

The three samples under Type-I PHCSs.

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Table 10 Expand

Table 11.

MLEs and Bayes estimates of (γ, θ, λ), MTTF and RF based on the three samples given in Table 10.

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Table 11 Expand

Table 12.

NACIs, LTCIs and credible intervals of the parameters based on the three samples given in Table 10.

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Table 12 Expand