The Weibull-Geometric (WG) distribution was first introduced by Wagner Barreto-Souzaa, Alice Lemos de Moraisa and Gauss M. Cordeiro in (2011). This distribution generalizes the exponential-geometric distribution proposed by Adamidis and Loukas (1998).It is useful for modeling unimodal failure rates. The WG distribution can be used as a life-time model. In this paper, we deal with the problem of estimating the parameters of the Weibull-Geometric distribution based on progressive first-failure censoring scheme. The maximum likelihood and Bayes methods of estimation are used for this purpose. The Monte Carlo Integration (MCI) technique is used for computing the Bayes estimates. The Bayes estimates of the parameters are compared with their corresponding maximum likelihood estimates via Monte Carlo simulation study.

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The commutative residuated lattices were first introduced by M. Ward and R.P. Dilworth as
generalization of ideal lattices of rings. Complete studies on residuated lattices were developed by H.
Ono, T. Kowalski, P. Jipsen and C. Tsinakis. Also, the concept of lattice implication algebra is due to Y.
Xu. And Luitzen Brouwer founded the mathematical philosophy of intuitionism, which believed that a
statement could only be demonstrated by direct proof. Arend Heyting, a student of Brouwer’s, formalized
this thinking into his namesake algebras. In this paper, we investigate the relationship between implicative
algebras, Heyting algebras and residuated lattices. In fact, we show that implicative algebras and Heyting
algebras can be described as residuated lattices.

The Homrit Waggat granite is a composite granite pluton intruded in metamorphosed
volcano-sedimentary association and the metagabbro-diorite complex to the east and
north and tonalite-granodiorite suite to the south and northeast. Mineralogically and
geochemically the granite phases change from subsolvus peraluminous granodiorite to
hypersolvus metaluminous and highly evolved alkali feldspar granite, passing through
biotite and mylonitized biotite granites. Late to post-magmatic processes are represented
by marginal stockscheider amazonite pegmatite, marginal amazonite albite as well as
greisen zone up to 30 m2. Increasing of SiO2, alkalis, Rb, F, Nb, Ta, Sn, Ga, HREEs and
Y, and decreasing of Fe, Al, Mg, Ca, Mn, Ti, Sr, Ba, Zr, and LREEs from the biotite
granodiorite to hypersolvus alkali feldspar granite reflects magmatic fractionation
processes of Homrit Waggat granite phases. LREEs fractionation patterns as well as
Eu anomalies decrease from granodiorite to the alkali feldspar granite and the latter
displays flat patterns. In the hypersolvus alkali feldspar granite, Ga/Al ratio is
typically of A-type granite, but not their Zr, Y, or Ce enrichments. In addition, the
hypersolvus granite is characterized by low-P2O5 and the LREEs>>HREEs
depletion which reflects the initial undersaturation of accessory mineral assemblage
that resulted from high concentration of volatiles and/or alkali complexes. The
behaviour of REEs and Zr in the mentioned phases is consistent with F- content as
well as accessory minerals in the studied granites. Trace elements pattern in the
spider diagram show significant depletion in Sr, Ba, P and Ti, and enrichment in
Rb, Th and U. The Sr, Ba, P and Ti depletion could be related to fractionation of
plagioclase, apatite and ilmenite. Zircon saturation temperature (Tzr) calculated from
bulk rock composition for Homrit Waggat granites range between 809°C and 765°C.
These values are consistent with low temperature granite which crystallized from a
source melt saturated with zirconium concentrations via partial melting of I- type granite
magma may be granodioritic in composition. The highly evolved alkali feldspar granite
was formed from the initial granodioritic I-type melt via fractional crystallization. F-rich
melt and F-complexing played an important role in the evolution and chemical
characterization of the highly evolved hypersolvus alkali feldspar granite. Four stages of
mineralization were detected in the Homrit Waggat granite. These stages are magmatic,
pegmatitic, metasomatic and veins. Columbite, cassiterite, fluorite as well as
undifferentiated rare earth minerals are detected.

The Homrit Waggat granite is a composite granite pluton intruded in metamorphosed
volcano-sedimentary association and the metagabbro-diorite complex to the east and
north and tonalite-granodiorite suite to the south and northeast. Mineralogically and
geochemically the granite phases change from subsolvus peraluminous granodiorite to
hypersolvus metaluminous and highly evolved alkali feldspar granite, passing through
biotite and mylonitized biotite granites. Late to post-magmatic processes are represented
by marginal stockscheider amazonite pegmatite, marginal amazonite albite as well as
greisen zone up to 30 m2. Increasing of SiO2, alkalis, Rb, F, Nb, Ta, Sn, Ga, HREEs and
Y, and decreasing of Fe, Al, Mg, Ca, Mn, Ti, Sr, Ba, Zr, and LREEs from the biotite
granodiorite to hypersolvus alkali feldspar granite reflects magmatic fractionation
processes of Homrit Waggat granite phases. LREEs fractionation patterns as well as
Eu anomalies decrease from granodiorite to the alkali feldspar granite and the latter
displays flat patterns. In the hypersolvus alkali feldspar granite, Ga/Al ratio is
typically of A-type granite, but not their Zr, Y, or Ce enrichments. In addition, the
hypersolvus granite is characterized by low-P2O5 and the LREEs>>HREEs
depletion which reflects the initial undersaturation of accessory mineral assemblage
that resulted from high concentration of volatiles and/or alkali complexes. The
behaviour of REEs and Zr in the mentioned phases is consistent with F- content as
well as accessory minerals in the studied granites. Trace elements pattern in the
spider diagram show significant depletion in Sr, Ba, P and Ti, and enrichment in
Rb, Th and U. The Sr, Ba, P and Ti depletion could be related to fractionation of
plagioclase, apatite and ilmenite. Zircon saturation temperature (Tzr) calculated from
bulk rock composition for Homrit Waggat granites range between 809°C and 765°C.
These values are consistent with low temperature granite which crystallized from a
source melt saturated with zirconium concentrations via partial melting of I- type granite
magma may be granodioritic in composition. The highly evolved alkali feldspar granite
was formed from the initial granodioritic I-type melt via fractional crystallization. F-rich
melt and F-complexing played an important role in the evolution and chemical
characterization of the highly evolved hypersolvus alkali feldspar granite. Four stages of
mineralization were detected in the Homrit Waggat granite. These stages are magmatic,
pegmatitic, metasomatic and veins. Columbite, cassiterite, fluorite as well as
undifferentiated rare earth minerals are detected.

The Homrit Waggat granite is a composite granite pluton intruded in metamorphosed
volcano-sedimentary association and the metagabbro-diorite complex to the east and
north and tonalite-granodiorite suite to the south and northeast. Mineralogically and
geochemically the granite phases change from subsolvus peraluminous granodiorite to
hypersolvus metaluminous and highly evolved alkali feldspar granite, passing through
biotite and mylonitized biotite granites. Late to post-magmatic processes are represented
by marginal stockscheider amazonite pegmatite, marginal amazonite albite as well as
greisen zone up to 30 m2. Increasing of SiO2, alkalis, Rb, F, Nb, Ta, Sn, Ga, HREEs and
Y, and decreasing of Fe, Al, Mg, Ca, Mn, Ti, Sr, Ba, Zr, and LREEs from the biotite
granodiorite to hypersolvus alkali feldspar granite reflects magmatic fractionation
processes of Homrit Waggat granite phases. LREEs fractionation patterns as well as
Eu anomalies decrease from granodiorite to the alkali feldspar granite and the latter
displays flat patterns. In the hypersolvus alkali feldspar granite, Ga/Al ratio is
typically of A-type granite, but not their Zr, Y, or Ce enrichments. In addition, the
hypersolvus granite is characterized by low-P2O5 and the LREEs>>HREEs
depletion which reflects the initial undersaturation of accessory mineral assemblage
that resulted from high concentration of volatiles and/or alkali complexes. The
behaviour of REEs and Zr in the mentioned phases is consistent with F- content as
well as accessory minerals in the studied granites. Trace elements pattern in the
spider diagram show significant depletion in Sr, Ba, P and Ti, and enrichment in
Rb, Th and U. The Sr, Ba, P and Ti depletion could be related to fractionation of
plagioclase, apatite and ilmenite. Zircon saturation temperature (Tzr) calculated from
bulk rock composition for Homrit Waggat granites range between 809°C and 765°C.
These values are consistent with low temperature granite which crystallized from a
source melt saturated with zirconium concentrations via partial melting of I- type granite
magma may be granodioritic in composition. The highly evolved alkali feldspar granite
was formed from the initial granodioritic I-type melt via fractional crystallization. F-rich
melt and F-complexing played an important role in the evolution and chemical
characterization of the highly evolved hypersolvus alkali feldspar granite. Four stages of
mineralization were detected in the Homrit Waggat granite. These stages are magmatic,
pegmatitic, metasomatic and veins. Columbite, cassiterite, fluorite as well as
undifferentiated rare earth minerals are detected.

The Homrit Waggat granite is a composite granite pluton intruded in metamorphosed
volcano-sedimentary association and the metagabbro-diorite complex to the east and
north and tonalite-granodiorite suite to the south and northeast. Mineralogically and
geochemically the granite phases change from subsolvus peraluminous granodiorite to
hypersolvus metaluminous and highly evolved alkali feldspar granite, passing through
biotite and mylonitized biotite granites. Late to post-magmatic processes are represented
by marginal stockscheider amazonite pegmatite, marginal amazonite albite as well as
greisen zone up to 30 m2. Increasing of SiO2, alkalis, Rb, F, Nb, Ta, Sn, Ga, HREEs and
Y, and decreasing of Fe, Al, Mg, Ca, Mn, Ti, Sr, Ba, Zr, and LREEs from the biotite
granodiorite to hypersolvus alkali feldspar granite reflects magmatic fractionation
processes of Homrit Waggat granite phases. LREEs fractionation patterns as well as
Eu anomalies decrease from granodiorite to the alkali feldspar granite and the latter
displays flat patterns. In the hypersolvus alkali feldspar granite, Ga/Al ratio is
typically of A-type granite, but not their Zr, Y, or Ce enrichments. In addition, the
hypersolvus granite is characterized by low-P2O5 and the LREEs>>HREEs
depletion which reflects the initial undersaturation of accessory mineral assemblage
that resulted from high concentration of volatiles and/or alkali complexes. The
behaviour of REEs and Zr in the mentioned phases is consistent with F- content as
well as accessory minerals in the studied granites. Trace elements pattern in the
spider diagram show significant depletion in Sr, Ba, P and Ti, and enrichment in
Rb, Th and U. The Sr, Ba, P and Ti depletion could be related to fractionation of
plagioclase, apatite and ilmenite. Zircon saturation temperature (Tzr) calculated from
bulk rock composition for Homrit Waggat granites range between 809°C and 765°C.
These values are consistent with low temperature granite which crystallized from a
source melt saturated with zirconium concentrations via partial melting of I- type granite
magma may be granodioritic in composition. The highly evolved alkali feldspar granite
was formed from the initial granodioritic I-type melt via fractional crystallization. F-rich
melt and F-complexing played an important role in the evolution and chemical
characterization of the highly evolved hypersolvus alkali feldspar granite. Four stages of
mineralization were detected in the Homrit Waggat granite. These stages are magmatic,
pegmatitic, metasomatic and veins. Columbite, cassiterite, fluorite as well as
undifferentiated rare earth minerals are detected.