Statistics

This paper proposes, with justification, a class of product-cum-dual to product estimators for estimating the population mean in systematic sampling using auxiliary information. The bias and variance of the proposed class of estimators have been derived under large sample approximation. Asymptotic optimum estimator (AOE) and its approximate variance estimator are derived and efficiency comparisons made with existing related estimators in theory. Analytical and numerical results show that at optimal conditions, the proposed class of estimators is always more efficient than all existing estimators under review.

This paper proposed a modified ratio-cum-product estimators of finite population mean using information on coefficient of variation and co-efficient of kurtosis of auxiliary variable in Stratified Ranked Set Sampling (SRSS). It has been shown that this method is highly beneficial to the estimation based on Stratified Simple Random Sampling (SSRS). The bias and mean squared error of the proposed estimators are derived. Theoretically, it is shown that these suggested estimators are more efficient than the estimators in Stratified simple random sampling. The results have been illustrated by numerical examples.

In this study, a comparison of performance among four different methods (Probability Weighted Moments (PWM), Maximum Likelihood Methods (MLM), the Methods of Moments (MOM), and the least Square Method (LSM)) of estimating the parameters of the Weibull distribution was done, using different values of ? and ?. This study contains two different experiments; experiment I and experiment II. Values of ? > ?, ? < ?, ? = ? were used in experiment I, and another varied values of ? < ?, ? < ?, ? = ? in line with some modeled distribution of the Weibull distribution, were used in experiment II. These values were generated by simulation. The aim is to find the best methods of estimating the two-parameter Weibull distribution. Based on the sample sizes and parameters considered, the method which gave the best estimate for the two-parameter Weibull distribution, is the method of Moments (MOM), taking into consideration the total deviation as a measurement for comparison. This study will help to estimate parameters associated with various models of a component or system such as reliability problems, maintainability and predictions such as MTTF, MTTFF, MTTR, MTBF, Hazard Rate etc.

In the present paper the system considered consists of two subsystems A and B. Subsystem A consists of identical operating and warm standby units. While subsystem B has two dissimilar units: main unit and a unit in cold standby. Main unit of subsystem B is assumed to be more efficient than the standby unit so when the main unit fails the system goes to the state of low efficiency. Main unit is connected to cold standby unit with a switching over device. Further, whenever there is a failure in one of the units of A and in the main unit of subsystem B, the system goes to critical state where system has to stop functioning to avoid the further failures. Also we have considered that the company providing repair facility has appointed a repairman. The repairman repairs the system in case of minor failures but when the system fails completely he has to take it to the nearest service station of the company for repair. By applying Supplementary variable technique, Laplace transformations and copula methodology transition state probabilities, asymptotic behaviour, reliability, availability, M.T.T.F., cost effectiveness and sensitivity of the system have been determined. Particular cases corresponding to the situations when the standby unit of subsystem A is in cold standby and in hot standby have also been considered. At last some numerical examples have been taken to illustrate the model.

Livestock industry in Nigeria is ridden with myriad of problems, which have resulted to a gross shortage of meat and other animal products. The growth rate of agriculture sector in Nigeria is still below the potentials of the natural and human resources due to high cost of agricultural inputs. To increase protein intake in Nigeria, there is urgent need to increase broiler production at household and commercial holdings. This research was conducted to assess the weight gained by the broiler chickens served fluted pumpkin leaves extract and also to examine the possible combination of number of weeks and  quantity of fluted pumpkin leaves extract that can result in maximum weight of the broiler chickens. The data were collected as a secondary data from the Federal College of Animal Health and Production Technology (I.A.R & T), Ibadan. An 8-weeks experiment was conducted to assess the weight gained by the broiler chickens served with fluted pumpkin leaves extract (FPLE). Forty day old Anak 2000 broiler chicks were randomly distributed to 5 treatments which contained 0, 30, 60, 90 and 120 ml of FPLE per litre of water for A, B, C, D and E, respectively, in a completely randomized design. Each treatment was replicated four times with two birds per replicate. The birds were fed with the same starter and finisher diets. The feed and water were served. Factorial design was used to study the main and interaction effects of number of weeks and quantity of FPLE on the weight of broiler chickens. Response surface model was fitted and subjected to canonical analysis to the characterization of the nature of its turning point and to capture the combination of number of weeks and quantity of FPLE that brings maximum weight of the broiler chickens. The results showed that the average body weight gained was significant (P<0.05). It was least in control compared to the birds served with 30-120 ml of FPLE. Factorial Design revealed that birds served with FPLE gained more weight than those in control. The birds served 120 ml of FPLE per litre of water for 8 weeks had the best performance in terms of weight gain. The use of FPLE in broiler chickens production is most effective from five weeks of age. The fitted Response Surface Model indicated that number of weeks and quantity of FPLE together with their mutual interaction significantly (P<0.05) determined the weight of broiler chickens. The maximum weight was achieved when number of week was ten with 100ml of FPLE. Number of weeks, FPLE and their mutual interaction play a key role in obtaining maximum weight of broiler chickens. These factors should be put into consideration in making of feed for broiler chickens.

In this paper an attempt has been made to study the efficiency of randomized block designs with two missing values. Consequently, we have obtained explicit expressions for the variances of the elementary treatment contrasts, average variance and the loss of efficiency in randomized block designs due to two missing values. Further we have also tabulated the loss of efficiency for various values of and where are respectively representing the number of treatments and the number of blocks in the randomized block designs.

A step-by-step analysis of means (ANOM) procedure has been extended to analyze the data from orthogonal array experiments. The procedure is also illustrated with the help of a numerical example.

Acceptance sampling plans developed relating to groups of items on testers are called the group acceptance sampling plan (GASP). In this scheme, a sample of items is distributed into different groups and a lot of product is rejected if more than a specified number of failures are recorded in any group. A group ac¬ceptance sampling schedule can be used to save the time and cost in inspection as compared with classical acceptance sampling. In this paper, a procedure for constructing a group acceptance sampling plan (GASP) indexed through indifference quality level (IQL) and Inverse Rayleigh distribution is proposed. Suitable tables and examples are also provided for easy selection of the plans.

The present paper deals with estimation of the population mean of the study variable when the information on the auxiliary variable is known and their population parameters are known. In the past, a number of modified ratio estimators are suggested with known values for the Co-efficient of Variation, Co-efficient of Kurtosis, Co-efficient of Skewness, Population Correlation Coefficient etc. However all these modified ratio estimators are biased but with less mean squared errors compared to the usual ratio estimator. In this paper some strategies have been suggested to improve the performance of the existing modified ratio estimators, which lead to a class of almost unbiased modified ratio estimators; and their performances are better than the modified ratio estimators. These are explained with the help of numerical examples.

This paper investigates a two multi-component unit parallel system model with imperfect detection and common cause failure. A single repair facility is always available with the system but whenever a regular detector fails in detection of the failure cause, then the unit goes for replacement for which a single replacement facility is always available. Using regenerative point technique various measure of system effectiveness are obtained. The behaviour of MTSF and profit function have been studied in a particular case.