سارہ برنہارڈ
گذشتہ مارچ میں دنیا کی سب سے مشہور ایکٹرس سارہ برنہارڈ کی ۷۴ سال کی عمر میں موت ہوئی۔ مرتے وقت اس نے اپنے کفن کے متعلق بھی دریافت کیا جو ۴۰ سال سے ہر وقت اس کے پاس رہتا تھا۔ (مئی ۱۹۲۳ء)
‘Adl and Qisṭ is indeed a manifestation of God’s mercy, rather, it may also be seen as a principal objective of Shariʿah. The origin or sources of administration of justice in Islām are the Quran, Sunnah of the holy Prophet, consensus of opinions of the jurists of Islamic jurisprudence and Analogy (Qiyās). Justice is a sacred obligation of supererogatory. It is obligatory upon the Muslim rulers to appoint judges for the dispensation of justice to attain equality, to protect the human rights from their violation, to safeguard the lives and properties, and to maintain law and order in society. As a judge is supposed to accomplish a very important and noble task being a regent of Allāh, hence, some vital merits and criteria regarding the conditions and qualifications for the appointment of the Qāḍī or judge in the light of the Qur’ān, Sunnah and Islamic jurisprudence and the code of conduct for the Pakistani judges must be observed at all costs. The author of this paper has discussed these conditions and qualifications in this article. There are some unanimous conditions for the appointment of judges, while some others are not agreed upon. While presenting the difference of opinions of the Islamic jurists, the author tried to explain, reconcile the opinions and at some places presented her own view in the light of her analysis and arguments. These conditions are around thirty, but the author according to her own discretion chose some of the most important ones to discuss in this paper.
Most popular statistical process control (SPC) technique is control charting and control charts are used for monitoring the process and detection the unusual variations in the process parameters. Now, control charts have also been developed under Bayesian perspectives. In this study, we have suggested some Bayesian memory control charts for efficient monitoring the process parameters under different loss functions. We have considered squared error loss function (SELF), linex loss function (LLF), precautionary loss function (PLF) and general entropy loss function (GELF) in this study. Exponentially weighted moving average (EWMA) control chart is used for monitoring the mean and dispersion of the process in separate chapters while double EWMA (DEWMA) control chart and cumulative sum (CUSUM) control chart are also used for monitoring the mean of the process. Using Bayesian inference, two types of priors (informative and non-informative) are used for the construction of control charts. Sensitivity analysis for hyperparameters has also performed. Monte Carlo simulations are used to compute ARL and SDRL as performance measures of the control charts. It is shown that the proposed control charts under square error loss function are more efficient for detection of smaller shifts in the process parameters than the proposed control charts under other loss functions considered in this study. This thesis, in general, will help quality practitioners to use Bayesian methods for the monitoring of process location and dispersion under different loss functions.