Ms S.Revathi,Published a Paper on the topic "Inequalities on Pwer Series With Real Coefficients and Univalent Function Theory"

 MIXED VARIABLES AND ATTRIBUTES PLAN :THE EXPONENTIONAL CASE

Abstract

             The mixed variables –attributes  test plans for single acceptance sampling are proposed to protect “good lots from” attributes aspect and to optimize sample sizes from variables aspect. For the single and double mixed plans, exact formulas of the operating characteristic and average sample number are developed for exponential distribution. Numerical illustration show that the mixed sampling plan have some advantages over the variables plan or attributes plan alone.

Introduction

                   A lot by lot sampling inspection plan is basis for action. The desired action depends on the defective in the lot. For  instance , if there are “few” defectives, the author wishes to use the lot and if there are “many” defectives, then rework the lot.

(1)   Type of sampling –sampling inspection plans prescribe how the observation , which form the basis for action, should be obtained.

 

a)      Single sampling plans-All the observation are made and then the action is taken. The plans tells how many observation to take.

b)      Multiple sampling plans –A sample of prescribed size is obtained. On the basis  of the data in this first sample a decision is made as to whether an action should be taken disposing of the lot or another fixed size sample should be obtained. If the second sample is obtained, similar process is performed ,etc. The plan specifies the maximum number of samples that can be obtained before a final action is taken.

c)      Sequential sampling plans-Observation are obtained one by one. After each observation is obtained a choice is made :take action for disposal of the lot or obtain another observation. In all cases the observations are made on randomly selected items from the lot.

 

(2)   Type of data – Sampling inspection plans call for collection of data of the following type from the sample items.

a)      Variables- The measurement of one or several characteristics of each item sampled.

b)      Attributes-The determination for each item sampled whether it is defective or not

 

      ( 3)   Number of action- All sampling plans involves at least two possible action, such as accept or reject the lot. But there may be other actions such as screen sell at reduced price, or rework.

The above outline is not complete and does not suggest how a sampling plan is chosen from the many  variable plans. It will, however, allow us to give a compact description of the so called “mixed variables and attributes plans” or simply “mixed plans”. A mixed plan is a double sampling, two action, plan using both variables and attributes data are collected for the first sample. Specifically ,variables and attributes data are collected for the first sample. If these data satisfy some specified condition, the lot is accepted. If that condition is not satisfied, the number of defectives is noted. If there are too many defectives ,the lot is rejected. Otherwise, i.e., the first condition is not satisfied and the number of defectives is not too large, a second sample is finally accepted. From the number of defectives in the first and second sample the lot is finally accepted or rejected. In short, if a lot cannot be accepted on variables or rejected on attributes by a first sample action is finally taken based on attributes information from the first and supplementary sample.

        Mixed plans are found useful  in the following situation: there is evidence suggestion a natural” functional from of the probability distribution  of the variables criteria and all that are unspecified are the values of  parameters of the distribution . Typically , a criterion is assumed to have a normal distribution with unknown mean and variance. In this situation, if  the resulting smaller sample sizes that can be obtained with variables compared to attributes plans more than offset the additional costs of these plans . However, the variables plans have the property that in using them a lot can be rejected even when there are no defectives in the lot. This could happen if the producer screens the lot. Another way that variables plans can give misleading results is that those items which give numerical scores tending to reject the lot may be extreme scores. Thus, the mixed plans have been introduced for situations where departures from “natural” form of the underlying distribution would cause excessive rejection of good lots. The need for  the second sample is that the first sample was for a variables plans ,and hence more data is required to make use of the less efficient attributes technique. Psychologically, these plans give the second chance to safeguard the interest of the producer.