An Adaptive Finite Volume Scheme for Solving Nonlinear Diffusion Equations in Image Processing

We propose the coarsening strategy for the finite volume computational method given by K. Mikula and N. Ramarosy (Numer. Math.89, 2001, 561–590) for the numerical solution of the (modified in the sense of F. Catté et al. (SIAM J. Numer. Anal.29, 1992, 182–193)) Perona–Malik nonlinear image selective smoothing equation (called anisotropic diffusion in image processing). The adaptive aproach is directly at hand because a solution tends to be flat in large subregions of the image, and thus it is not necessary to consider the same fine resolution of computations in the whole spatial domain. This access reduces computational effort, because the coarsening of the computational grid rapidly reduces the number of unknowns in the linear systems to be solved at discrete scale steps of the method.     

A translation-invariant wavelet representation algorithm withapplications

We address the time-varying problem of wavelet transforms, and a new translation-invariant wavelet representation algorithm is proposed. Using the algorithm introduced by Beylkin (see SIAM J. Numer. Anal., vol. 29, p.1716-1740, 1992), we compute the wavelet transform for all the circular time shifts of a length-N signal in O(N log N) operations. The wavelet coefficients of the time shift with minimal cost are selected as the best representation of the signal using a binary tree search algorithm with an appropriate cost function. We apply the translation-invariant representation algorithm to a geoacoustic data compression application. The results show that the new algorithm can reduce the distortion (the squared error in our case) substantially, if the input signals are transients that are sensitive to time shifts     

A noise-suppressing and edge-preserving multiframe super-resolution image reconstruction method

Super-resolution technology is an approach that helps to restore high quality images and videos from degraded ones. The method stems from an ill-posed minimization problem, which is usually solved using the L² norm and some regularization techniques. Most of the classical regularizing functionals are based on the Total Variation and the Perona–Malik frameworks, which suffer from undesirable artifacts (blocking and staircasing). To address these problems, we have developed a super-resolution framework that integrates an adaptive diffusion-based regularizer. The model is feature-dependent: linear isotropic in flat regions, a condition that regularizes an image uniformly and removes noise more effectively; and nonlinear anisotropic near boundaries, which helps to preserve important image features, such as edges and contours. Additionally, the new regularizing kernel incorporates a shape-defining parameter that can be automatically updated to ensure convexity and stability of the corresponding energy functional. Comparisons with other methods show that our method is superior and, more importantly, can achieve higher reconstruction factors.     

Applications of Locally Orderless Images

In a recent work, J. J. Koenderink and A. J. Van Doorn considered a family of three intertwined scale-spaces coined the locally orderless image (LOI) (1999, J. Comput. Vision, 31 (2/3), 159–168). The LOI represents the image, observed at inner scale σ, as a local histogram with bin-width β, at each location, with a Gaussian-shape region of interest of extent α. LOIs form a natural and elegant extension of scale-space theory, show causal consistency, and enable the smooth transition between pixels, histograms, and isophotes. The aim of this work is to demonstrate the wide applicability and versatility of LOIs. We present applications for a range of image processing tasks, including new nonlinear diffusion schemes, adaptive histogram equalization and variations, several methods for noise and scratch removal, texture rendering, classification, and segmentation.     

An optimized blockwise nonlocal means denoising filter for 3-D magnetic resonance images

A critical issue in image restoration is the problem of noise removal while keeping the integrity of relevant image information. Denoising is a crucial step to increase image quality and to improve the performance of all the tasks needed for quantitative imaging analysis. The method proposed in this paper is based on a 3-D optimized blockwise version of the nonlocal (NL)-means filter (Buades, , 2005). The NL-means filter uses the redundancy of information in the image under study to remove the noise. The performance of the NL-means filter has been already demonstrated for 2-D images, but reducing the computational burden is a critical aspect to extend the method to 3-D images. To overcome this problem, we propose improvements to reduce the computational complexity. These different improvements allow to drastically divide the computational time while preserving the performances of the NL-means filter. A fully automated and optimized version of the NL-means filter is then presented. Our contributions to the NL-means filter are: 1) an automatic tuning of the smoothing parameter; 2) a selection of the most relevant voxels; 3) a blockwise implementation; and 4) a parallelized computation. Quantitative validation was carried out on synthetic datasets generated with BrainWeb (Collins, , 1998). The results show that our optimized NL-means filter outperforms the classical implementation of the NL-means filter, as well as two other classical denoising methods [anisotropic diffusion (Perona and Malik, 1990)] and total variation minimization process (Rudin, , 1992) in terms of accuracy (measured by the peak signal-to-noise ratio) with low computation time. Finally, qualitative results on real data are presented.     

A theoretical study of phosphorescent Cu(I) complexes with 2-(2'quinolyl)imidazole and POP mixed ligands

We herein report a theoretical study using density functional theory (DFT) and time-dependent DFT (TD-DFT) methods to investigate Cu(I) complexes with 2-(2′-pyridyl/quinolyl)imidazole and bis[2-(diphenylphosphino)phenyl]ether mixed ligands. Based on the experimental data for complexes 1 and 2, we first benchmarked different functionals with different HF% and found B3PW91 to be the optimal functional for this system. The computational results indicate that complex 1, with a pyridyl unit, has a much larger radiative decay rate (k_r) than complex 2, which has a quinolyl unit. This difference is presumably due to higher HOMO electronic distribution in the d_x²-_y² orbital, which leads to a markedly shortened CuN₂ bond, enhancing the metal-ligand interaction. However, a much smaller experimental value was found for the non-radiative decay rate (k_nr) in complex 2, rendering 1 a slightly weaker emitter than 2. We conclude that the difference is due to more effective suppression of deformation when the quinolyl unit is used instead of pyridyl. We sought to increase the photoluminescence quantum yield (PLQY) through modifying the ligand on complex 2, with the goal being to keep the small k_nr value while simultaneously increasing k_r. The computational results indicate that our designed complexes 2a-2c, which possess modified ligands with electron-donating or withdrawing alkyl substituents on N₃, increased the distributions of d_x²-_y² and decreased that of the d_yz compared to 2. Their coordinating abilities were therefore enhanced, with the k_r values being 1.34, 22.70, and 0.16 times that of 2 for 2a, 2b and 2c, respectively. Higher PLQYs were achieved in 2a and 2b with the addition of electron-donating alkyl substituents on the ligands, which yielded complexes with significantly shortened CuN₂ bonds and enhanced metal-ligand interaction. This investigation on the microscopic mechanism of the photoluminescent properties of these complexes can provide useful knowledge for experimentalists.     

Image selective restoration using multi-scale variational decomposition

In this paper we propose a multi-scale variational decomposition model for image selective restoration. Firstly, we introduce a single-parameter (BV, G, L²) variational decomposition functional and theoretically analyze the relationship between the parameter and the scale of image features. And then, by replacing the fixed scale parameter with a varying sequence in the single-parameter decomposition functional, we obtain the multi-scale variational decomposition which can decompose the input image into a series of image slices of different scales. Furthermore, we show some properties and prove the convergence of the multi-scale decomposition. Finally, we introduce an alternating and iterative method based on Chambolle’s projection algorithm to numerically solve the multi-scale variational decomposition model. Experiments are conducted on both synthetic and real images to demonstrate the effectiveness of the proposed multi-scale variational decomposition. In addition, we use the multi-scale variational decomposition to achieve image selective restoration, and compare it with several state-of-the-art models in denoising application. The numerical results show that our model has better performance in terms of PSNR and SSIM indexes.     

A Bayesian estimation of reliability model using the linex loss function

In this paper the problem of Bayes estimation of the reliability and the shape parameter p of a finite range failure time model is considered (assuming scale parameter θ is known). Following Zellner [A. Zellner, J. Am. Statist. Assoc. 81, 446–451 (1986)] the asymmetric loss function is used to obtain the Bayes estimators. Efficiencies of the proposed Bayes estimators are obtained with respect to the ordinary Bayes estimators and it was found that the proposed Bayes estimators are better than the ordinary Bayes estimators for quite a wide range of parameters.     

Synthesis and correlation between structure and photovoltaic performance of two-dimensional BDT-TPD polymers

Four BDT-TPD polymers (PA–PD) were synthesized by modifying the alkylthienyl chains on BDT, placing spacer group between BDT and TPD, and installing extended conjugated side chains on the BDT of the polymer to investigate the correlation between structure and photovoltaic performance for these polymers. The molecular weight of PA–PD polymers ranged from the highest (Mn = 80 kDa for PA) to the lowest (Mn = 7.9 kDa for PD), and their decomposition temperatures at 5% weight loss were in the range 401–435 °C. PA, PB, and PC showed similar UV–vis absorption spectra; however, PD showed much broader absorption spectrum in the entire UV–vis region, because of the extended conjugated side chains. The HOMO levels of the polymers were −5.72, −5.63, −5.48, and −5.61 eV for PA, PB, PC, and PD, respectively, indicating very low-lying HOMO energy levels. The bandgaps of these polymers were calculated and found to be in the range 1.85–1.88 eV. The theoretical calculations clearly show that the torsional angles between the alkylthienyl group and BDT unit of the simplified dimer correlated to the π-orbital delocalization, suggesting that the HOMO π-electrons of vertically aligned conjugated side chains do not delocalize well in the polymers such as PA, PB, and PC bearing high torsional angles. The optimized weight ratios of the polymer to PC₆₁BM were determined to be 1:1, 1:1.5, and 1:1 for PA, PC, and PD, respectively, and the average PCEs of the devices were 5.36%, 4.62%, and 2.74% for PA, PC, and PD, respectively, after optimization with 1,8-diiodooctane (DIO). A relatively small amount of DIO as an additive was necessary to reach the optimal PCEs of the devices, and the device incorporating PC needed only 0.5% DIO to obtain the best PCE. The AFM study reveals that the blend films after adding DIO showed much smooth morphologies, and the blend film of PA exhibited more crystalline property, as shown by the XRD analysis.     

Side chain effect on photovoltaic properties of dibenzo[a,c]phenazine based donor–acceptor polymers

The electron–donor polymers containing dibenzo[a,c]phenazine (BPz) derivatives with 2,7-alkyl and 11,12-alkoxy substituted, PBDT-BPzC and PBDT-OBPz, respectively, were synthesized to investigate the photovoltaic effect of different side chain substitutions. The polymers exhibit similar physical properties, except the HOMO and LUMO of PBDT-BPzC are 0.18 and 0.15 eV deeper than PBDT-OBPz, resulting in the V_oc of polymer solar cells (PSCs) based on PBDT-BPzC are above 0.1 V higher than that of PBDT-OBPz. With the contribution of the superior V_oc, polymer PBDT-BPzC showed preferable photovoltaic performances, and the PCE reached 4.44%, which is 0.49% higher than PBDT-OBPz. This research reveals a preferred side chain substituted way to modify BPz unit, and gives an optimally developing the dibenzo[a,c]phenazine derivatives based electron–donor polymers.     

Thiophene-2,5-diesters as electrochromic materials: The effect of ester groups on the device performance and stability

A series of thiophene-2,5-dicarboxylic acid diesters (R–Th, compounds 3–9) with linear and branched alkyl (3–7) and benzyl (8,9) ester groups have been synthesized and characterized by ¹H/¹³C NMR and MS. Their electrochemical reduction in cyclic voltammetry experiments proceed as two-step single-electron transfer process to form radical anions R–Th^•– (at −1.87 … −2.00 V vs Ag/Ag⁺) and dianions R–Th^2– (at −2.48 … −2.68 V vs Ag/Ag⁺). In spectroelectrochemical experiments in Bu₄NClO₄/N,N-dimethylformamide electrolyte solution, all compounds exhibit reversible color changes from colorless in their neutral state to blue colors in the reduced state, with two characteristic absorptions of radical anions R–Th^•– in the short-wavelength (ca. 406–420 nm) and long-wavelength regions (ca. 610–655 nm). The L*a*b* CIE color coordinates of th e sandwich-type electrochromic devices have been evaluated by colorimetry measurements and the devices demonstrated good coloration efficiency of up to 512 cm² C⁻¹. The cycling stability of the materials on electrochromic coloring/bleaching substantially depends on the structure of the R ester groups and increased with increasing the steric hindrances in the R. In the series of seven studies compounds, the best cycling stability was observed for R = 2-ethylhexyl and benzyl. The degradation mechanism during electrochromic cycling in an inert atmosphere (under nitrogen) and in air is discussed.     

Synthesis,optical and electrochemical properties of pyridal[2,1,3]thiadiazole based organic dyes for dye sensitized solar cells

The asymmetric nature of pyridal[2,1,3]thiadiazole (PyT), allows the synthesis of two isomers, series SC-PyTNn (n = 1–4) and SC-NPyTn (n = 1–6), where the nitrogen atom of PyT is positioned closer to the arylamine donor and the anchoring group, respectively. PyT derivatives have significant bathochromic shift of the electronic absorption compared to their 2,1,3-benzothiadiazole congeners. The short-circuit photocurrent density, open-circuit voltage and fill factor of DSSCs using the dyes as the sensitizers are in the range of 0.68–9.47 mA/cm⁻², 0.43–0.61 V and 0.59–0.72, respectively. SC-NPyTn (n = 1–6) exhibited higher cell efficiencies than SC-PyTNn (n = 1–4). Power conversion efficiency of up to 4.24% was observed for SC-NPyT3.     

Two new A-D-A type small molecule acceptors based on C2v-symmetric dithienocyclopentaspiro[fluorene-9,9′-xanthene] core for polymer solar cells

A C_2v-symmetric core, dithienocyclopentaspiro[fluorene-9,9′-xanthene], was used as the central block for the first time to design and synthesize A-D-A type small molecule acceptors for nonfullerene polymer solar cells (PSCs), and two new small molecule acceptors of TSFX-2F and TSFX-4F were synthesized based on the C_2v-symmetric core. The two TSFX-based acceptors show high thermal stability, strong absorption in the wavelength region of 550–750 nm and appropriate energy levels. The PSCs with the broad bandgap polymer J71 as donor and TSFX-2F as acceptor demonstrated power conversion efficiency (PCE) of 9.42% with open circuit voltage (V_oc) of 0.89 V, short circuit current density (J_sc) of 15.27 mA cm⁻² and fill factor (FF) of 69.30%, while the PSC based on J71:TSFX-4F shows a PCE of 8.47% with V_oc of 0.83 V, J_sc of 15.48 mA cm⁻² and FF of 66.16%. The higher V_oc of the PSC based on J71: TSFX-2F is benefitted from the up-shifted LUMO energy level of the TSFX-2F acceptor, and its higher FF can be ascribed to the higher and more balanced hole and electron mobilities of the J71: TSFX-2F active layer. This work demonstrates that the new C_2v-symmetric building block is a promising central D-unit for the design and synthesis of new structured norfullerene acceptors for high-performance PSCs.     

Highly phosphorescent platinum(II) complexes based on rigid unsymmetric tetradentate ligands

A new class of highly phosphorescent Pt(II) complexes (Pt1–Pt3) based on rigid unsymmetric tetradentate ligands (L1-L3) were designed and synthesized. L1-L3 ligands are an analogue to N,N-di(2-phenylpyrid-6-yl)aniline (L) except that one coordination phenyl group in L is replaced by other motifs with different electron donating/accepting capabilities. The effect associated with the modulation of a single coordination group within each ligand on the photophysical and electroluminescent properties of Pt1–Pt3 was investigated systematically. Among Pt1–Pt3, Pt1 has the highest HOMO due to the presence of a strong electron-donating group (3-methylindole), and exhibits the narrowest bandgap; Pt2 has the lowest HOMO due to the lack of strong donor group within the structure, and shows the widest bandgap. Organic light-emitting diodes (OLEDs) based on these three complexes showed yellowish green to greenish yellow electroluminescence with high efficiency. Notably, the device based on Pt1 at the doping level of 10 wt% achieved a maximum efficiency of 53.0 cd A⁻¹, 35.9 lm W⁻¹ and 16.3% with CIE coordinates of (0.44, 0.53).     

First-Principles Study of Structural,Electronic, Optical,and Thermal Properties of BeSiSb<Subscript>2</Subscript> and MgSiSb<Subscript>2</Subscript>

Structural, electronic, optical, and thermal properties of ternary II–IV–V₂ (BeSiSb₂ and MgSiSb₂) chalcopyrite semiconductors have been calculated using the full-potential linearized augmented plane wave scheme?in the generalized gradient approximation. The optimized equilibrium structural parameters (a, c, and u) are in good agreement with theoretical results obtained using other methods. The band structure and density of states reveal that BeSiSb₂ has an indirect (Γ–Z) bandgap of about 0.61 eV, whereas MgSiSb₂ has a direct (Γ–Γ) bandgap of 0.80 eV. The dielectric function, refractive index, and extinction coefficient were calculated to investigate the optical properties, revealing that BeSiSb₂ and MgSiSb₂ present very weak birefringence. The temperature dependence of the volume, bulk modulus, Debye temperature, and heat capacities (C _v and C _p) was predicted using the quasiharmonic Debye model at different pressures. Significant differences in properties are observed at high pressure and high temperature. We predict that, at 300 K and 0 GPa, the heat capacity at constant volume C _v, heat capacity at constant pressure C _P, Debye temperature θ _D, and Grüneisen parameter γ will be about 94.91 J/mol K, 98.52 J/mol K, 301.30 K, and 2.11 for BeSiSb₂ and about 96.08 J/mol K, 100.47 J/mol K, 261.38 K, and 2.20 for MgSiSb₂, respectively.     

Investigations into inward positioned 3,3′-Dihexylditheinylbenzothiadiazole (DTBTh)-Benzodithiophene (BDT) based polymer solar cells by controlling molecular weight and alkyl side chain

In previous studies, PSCs based on polymers with an inward alkyl positioned DTBT unit showed poor power conversion efficiency mainly due to the greatly distorted polymer backbone structure caused by severe steric hindrance between the alkyl groups on the flanking thiophene of DTBT and the BT unit. In this study, PSCs based on polymers with an inward alkyl positioned DTBT unit are markedly improved by controlling the molecular weight and alkyl chain length. Two BDT-DTBTs and one BDT-BT polymers were synthesized by engineering alkylthienyl chains on BDT and by installing these with a short alkyl chain on the inward alkyl positioned DTBT. Extraordinary bathochromic shifts in the absorption maxima at 146 nm for PA and 165 nm for PB were observed going from solution to a solid film state, suggesting great differences in the polymer structures of the two states. Optical and electrochemical measurements were taken, and the HOMO levels of PA, PB, and PC were determined to be −5.76, −5.66, and −5.71 eV, respectively, indicating very low-lying HOMO energy levels. The optimized PSCs based on PA, PB, and PC exhibit power conversion efficiencies (PCEs) of 3.75%, 2.42%, and 2.30%, respectively, with V_oc (0.77–0.86 V), J_sc (6.9–8.7 mA/cm²), and FF (38–52%). We believe that the highest PCE for the PSCs based on PA may be attributed to the high molecular weight and improved processability relative to those of PB and PC. A theoretical study suggests that the polymer backbones of PA and PB are highly distorted between the donor unit and the acceptor unit, by as much as 49°, possibly by the steric hindrance between BT and the inward positioned methyl group on the flanking thiophene. Therefore, the conjugations for the HOMO p-orbitals of PA and PB are highly localized throughout the backbone while the conjugations for the HOMO p-orbitals of PC are well delocalized. The AFM study revealed that DIO additive greatly changed the morphology of the polymer blend from an amorphous state into distinct nanoscale phase separated states, leading to a great improvement in PCEs. The XRD study revealed that all polymers are amorphous.     

Tetrasubstituted adamantane derivatives with arylamine groups: Solution-processable hole-transporting and host materials with high triplet energy and good thermal stability for organic light-emitting devices

Four new host/hole-transporting materials, namely 4,4′,4″,4‴-(adamantane-1,3,5,7-tetrayl)tetrakis(N,N-diphenylaniline) (4TPA-Ad, 1),4,4′,4″,4‴-(adamantane-1,3,5,7-tetrayl)tetrakis(N,N-di-p-tolylaniline) (4MTPA-Ad, 2), 1,3,5,7-tetrakis(4-(9H-carbazol-9-yl)phenyl)adamantane (4Cz-Ad, 3) and 1,3,5,7-tetrakis(4-(3,6-di-tert-butyl-9H-carbazol-9-yl)phenyl)adamantane (4tBuCz-Ad, 4), were designed and synthesized by incorporating four electron-donating arylamine units into the rigid adamantane skeleton via a simple C–N coupling reaction. Their thermal, photophysical and electrochemical properties were investigated. The molecular design endows the materials with high triplet energies of ∼3.0 eV, good solution processability, high thermal stability and appropriate HOMO levels. Two types of electroluminescent devices using 1–4 as hole-transporting or host materials were fabricated. The device based on 2 as solution-processed hole-transporting material and tris(quinolin-8-yloxy)aluminum as an emitter revealed a maximum current efficiency of 4.2 cd A⁻¹, which was comparable with the TAPC-based control device. The sky-blue device employing 2 as solution-processed host material and 4,6-(difluorophenyl)pyridine-N,C^2′)picolinate (FIrpic) as an emitter showed a maximum current efficiency of 16.6 cd A⁻¹ with Commission Internationale de I’Eclairage (CIE) coordinates of (0.16, 0.32).     

1,2-diphenylbenzimidazole-triarylamine hybrided bipolar host materials employing fluorene as bridge for RYB and white electrophosphorescent devices

Four novel bipolar hosts (DTAFNBI, m-DTAFNBI, DTAFCBI and m-DTAFCBI) comprising a hole-transport ditolylphenylamino donor and an electron-transport 1,2-diphenylbenzimidazole acceptor connected via a fluorene spacer were synthesized and characterized. Through the different linkage topologies of phenylbenzimidazole, the thermal, photophysical, and electrochemical properties can be fine-tuned. The saturated fluorene spacer along with the ditolylphenylamino donor and the phenylbenzimidazole acceptor endowed high triplet energies (E_T = 2.47–2.62 eV, recorded in neat film at 20 K) and bipolar transporting abilities. Furthermore, the tetragonal geometry given by the sp³-hybridized C9 of fluorene encumbered intermolecular packing and led to excellent thermal and morphological stabilities (T_d = 379–392 °C, corresponding 5% weight loss; T_g = 148–162 °C). As a result, these bipolar materials were utilized as universal hosts for red, yellow, and blue (RYB) phosphorescent OLEDs, showing maximum external quantum efficiencies (η_ext) of 9.6%, 14.7%, and 18.9% for blue (FIrpic), yellow (m-(Tpm)₂Ir(acac) and red [Os(bpftz)₂(PPhMe₂)₂, OS1], respectively. In addition, white organic light-emitting diodes combining a blue emitter (FIrpic) and yellow emitter m-(Tpm)₂Ir(acac) and a red emitter (OS1) within a single emitting layer were also fabricated which also exhibited good efficiencies (9.5–13.7%, 15.1–23.5 cd A⁻¹, 13.3–23.9 lm W⁻¹) with relatively low efficiency roll off.     

Silicon-based carbazole and oxadiazole hybrid as a bipolar host material for phosphorescent organic light-emitting diodes

A silicon-based bipolar compound, 2-(4-((4-(9H-carbazol-9-yl)phenyl)dimethylsilyl)phenyl)-5-phenyl-1,3,4-oxadiazole (COHS), was designed and prepared as a host material for phosphorescent organic light-emitting diodes (OLEDs). The conjugated analogue of COHS, 2-(4′-(9H-carbazol-9-yl)biphenyl-4-yl)-5-phenyl-1,3,4-oxadiazole (COH), was also prepared to investigate their structure–property relationships. Thermal-, photophysical- and electrochemical properties as well as their single-crystal X-ray structures were studied for COHS and COH. The central silicon atom in COHS successfully disconnected the electronic communication between the carbazole and oxadiazole groups, resulting in relatively high triplet energy of ca. 2.71 eV, which were capable of hosting green phosphorescent emitters. DFT calculations were conducted to investigate the electronic structures of COHS and COH, and the results showed good correlation to experimental results. Finally, COHS and COH were used as a bipolar host material for a green phosphorescence organic light-emitting diode (PHOLED) devices with Ir(ppy)₃ (tris[2-phenylpyridinato-C²,N]iridium(III)) as a dopant. The resulting device with COHS (device I) showed higher performance than the device with COH (device II), exhibiting high efficiencies and low-efficiency roll-off. Device I achieved maximum external quantum efficiencies (EQE) of 15.8%, whereas device II exhibited a relatively lower EQE of 13.0%.     

Bayesian shrinkage estimation of reliability in parallel system with exponential failure of the components

The paper presents a Bayesian shrinkage method of estimating the reliability of a parallel system with identical exponential distribution of failure times. Data is available from type II censored samples. Thompson (J. Am. Statist. Ass.63, 113–123, 1968) proposed the ordinary shrunken estimator ?θ + (1-?)θ₀, with ? a constant (0 ? ? ? 1) and θ₀ the prior or guess value of θ, which is more efficient than the unbiased estimator θ if θ is close to θ₀ and is less efficient otherwise. Here we postulate a prior distribution of θ around θ₀ and use an ordinary Bayes estimator of θ instead of θ₀ in the ordinary shrunken estimator. The Bayesian shrinkage estimator of parallel system reliability has thus been obtained and Monte Carlo study of its efficiency with respect to unbiased and maximum likelihood estimators (mles) was conducted. It was found that the proposed estimator is better.