# Sampling plans

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### DIFFERENT TYPES OF sampling plan used in industries

### Acceptance Sampling

Acceptance sampling refers to the application of specific sampling plans to a designated lot or sequence of lots. Acceptance sampling procedures can, however, be used in a program of acceptance control to achieve better quality at lower cost, improved control, and increased productivity. This involves the selection of sampling procedures to continually match operating conditions in terms of quality history and sampling results. In this way the plans and procedures of acceptance sampling can be used in an evolutionary manner to supplement each other in a continuing program of acceptance control for quality improvement with reduced inspection. It is the objective of acceptance control in any application to eventually phase out acceptance sampling in favor of supplier certification and process control. After explaining a variety of specific sampling procedures, this section concludes with suggestions on how and when to progress from sampling inspection toward reliance on process control and check inspection and eventually to no inspection at all, depending on the stage of the life cycle of the product and the state of control.

Statistical quality control technique, where a random sample is taken from a lot, and upon the results of the sample taken the lot will either be rejected or accepted.

Accept lot

Ready for customers

Reject lot

Not suitable for customers

Statistical process control

determine if in acceptable limits

### Purposes

Determine the quality level of an incoming shipment or, at the end production

Ensure that the quality level is within the level that has been predetermined.

### ADVANTAGES OF ACCEPTANCE SAMPLING

1. Economy due to inspecting only part of the product

2. Less handling damage during inspection

3. Fewer inspectors, thereby simplifying the recruiting and training problem

4. Upgrading the inspection job from piece-by-piece decisions to lot-by lot decisions

5. Applicability to destructive testing, with a quantified level of assurance of lot quality

6. Rejections of entire lots rather than mere return of the defectives, thereby providing stronger motivation for improvement.

### DISADVANTAGES OF ACCEPTANCE SAMPLING

1. There are risks of accepting “bad” lots and of rejecting “good” lots.

2. There is added planning and documentation.

3. The sample usually provides less information about the product than does 100 percent inspection.

### Sampling

Samplingis that part ofstatisticalpractice concerned with the selection of an unbiased orrandomsubset of individual observations within a population of individuals intended to yield some knowledge about thepopulationof concern, especially for the purposes of making predictions based onstatistical inference. Sampling is an important aspect ofdata collection.

Researchers rarely survey the entire population for two reasons , the cost is too high, and the population is dynamic in that the individuals making up the population may change over time. The three main advantages of sampling are that the cost is lower, data collection is faster, and since the data set is smaller it is possible to ensure homogeneity and to improve the accuracy and quality of the data.

### Process

* Specifying asampling frame, asetof items or events possible to measure

* Specifying asampling methodfor selecting items or events from the frame

* Determining the sample size

* Implementing the sampling plan

* Sampling and data collecting

* Reviewing the sampling process

* Defining the population of concern

### PROBABILITY AND NON PROBABILITY SAMPLIMG

Aprobability samplingscheme is one in which every unit in the population has a chance (greater than zero) of being selected in the sample, and this probability can be accurately determined. The combination of these traits makes it possible to produce unbiased estimates of population totals, by weighting sampled units according to their probability of selection.

Probability sampling includes: Simple Random Sampling, Systematic Sampling, Stratified Sampling, Probability Proportional to Size Sampling, and Cluster or Multistage Sampling. These various ways of probability sampling have two things in common:

1. Every element has a known nonzero probability of being sampled and

2. involves random selection at some point.

Nonprobability samplingis any sampling method where some elements of the population havenochance of selection (these are sometimes referred to as 'out of coverage'/'undercovered'), or where the probability of selection can't be accurately determined. It involves the selection of elements based on assumptions regarding the population of interest, which forms the criteria for selection. Hence, because the selection of elements is nonrandom, nonprobability sampling does not allow the estimation of sampling errors. These conditions place limits on how much information a sample can provide about the population. Information about the relationship between sample and population is limited, making it difficult to extrapolate from the sample to the population.

Nonprobability Sampling includes:Accidental Sampling,Quota SamplingandPurposive Sampling. In addition, nonresponse effects may turnanyprobability design into a nonprobability design if the characteristics of nonresponse are not well understood, since nonresponse effectively modifies each element's probability of being sampled.

### SAMPLING METHODS

Within any of the types of frame identified above, a variety of sampling methods can be employed, individually or in combination. Factors commonly influencing the choice between these designs include:

§ Nature and quality of the frame

§ Availability of auxiliary information about units on the frame

§ Accuracy requirements, and the need to measure accuracy

§ Whether detailed analysis of the sample is expected

§ Cost/operational concerns

### Simple random sampling

In asimple random sample('SRS') of a given size, all such subsets of the frame are given an equal probability. Each element of the frame thus has an equal probability of selection: the frame is not subdivided or partitioned. Furthermore, any givenpairof elements has the same chance of selection as any other such pair (and similarly for triples, and so on). This minimises bias and simplifies analysis of results. In particular, the variance between individual results within the sample is a good indicator of variance in the overall population, which makes it relatively easy to estimate the accuracy of results.

However, SRS can be vulnerable to sampling error because the randomness of the selection may result in a sample that doesn't reflect the makeup of the population. For instance, a simple random sample of ten people from a given country willon averageproduce five men and five women, but any given trial is likely to overrepresent one sex and underrepresent the other. Systematic and stratified techniques, discussed below, attempt to overcome this problem by using information about the population to choose a more representative sample.

SRS may also be cumbersome and tedious when sampling from an unusually large target population. In some cases, investigators are interested in research questions specific to subgroups of the population. For example, researchers might be interested in examining whether cognitive ability as a predictor of job performance is equally applicable across racial groups. SRS cannot accommodate the needs of researchers in this situation because it does not provide subsamples of the population. Stratified sampling, which is discussed below, addresses this weakness of SRS.

Simple random sampling is always an EPS design, but not all EPS designs are simple random sampling.

### Systematic sampling:-

Systematic samplingrelies on arranging the target population according to some ordering scheme and then selecting elements at regular intervals through that ordered list. Systematic sampling involves a random start and then proceeds with the selection of everykth element from then onwards. In this case,k=(population size/sample size). It is important that the starting point is not automatically the first in the list, but is instead randomly chosen from within the first to thekth element in the list. A simple example would be to select every 10th name from the telephone directory (an 'every 10th' sample, also referred to as 'sampling with a skip of 10').

As long as the starting point israndomized, systematic sampling is a type ofprobability sampling. It is easy to implement and thestratificationinduced can make it efficient,ifthe variable by which the list is ordered is correlated with the variable of interest. 'Every 10th' sampling is especially useful for efficient sampling fromdatabases.

Example: Suppose we wish to sample people from a long street that starts in a poor district (house #1) and ends in an expensive district (house #1000). A simple random selection of addresses from this street could easily end up with too many from the high end and too few from the low end (or vice versa), leading to an unrepresentative sample. Selecting (e.g.) every 10th street number along the street ensures that the sample is spread evenly along the length of the street, representing all of these districts. (Note that if we always start at house #1 and end at #991, the sample is slightly biased towards the low end; by randomly selecting the start between #1 and #10, this bias is eliminated.)

However, systematic sampling is especially vulnerable to periodicities in the list. If periodicity is present and the period is a multiple or factor of the interval used, the sample is especially likely to beunrepresentative of the overall population, making the scheme less accurate than simple random sampling.

Example: Consider a street where the odd-numbered houses are all on the north (expensive) side of the road, and the even-numbered houses are all on the south (cheap) side. Under the sampling scheme given above, it is impossible' to get a representative sample; either the houses sampled willallbe from the odd-numbered, expensive side, or they willallbe from the even-numbered, cheap side.

Another drawback of systematic sampling is that even in scenarios where it is more accurate than SRS, its theoretical properties make it difficult toquantifythat accuracy. (In the two examples of systematic sampling that are given above, much of the potential sampling error is due to variation between neighbouring houses - but because this method never selects two neighbouring houses, the sample will not give us any information on that variation.)

As described above, systematic sampling is an EPS method, because all elements have the same probability of selection (in the example given, one in ten). It isnot'simple random sampling' because different subsets of the same size have different selection probabilities - e.g. the set {4,14,24,...,994} has a one-in-ten probability of selection, but the set {4,13,24,34,...} has zero probability of selection.

Systematic sampling can also be adapted to a non-EPS approach; for an example, see discussion of PPS samples below.

### Quota sampling:-

Inquota sampling, the population is first segmented intomutually exclusivesub-groups, just as instratified sampling. Then judgment is used to select the subjects or units from each segment based on a specified proportion. For example, an interviewer may be told to sample 200 females and 300 males between the age of 45 and 60.

It is this second step which makes the technique one of non-probability sampling. In quota sampling the selection of the sample is non-random. For example interviewers might be tempted to interview those who look most helpful. The problem is that these samples may be biased because not everyone gets a chance of selection. This random element is its greatest weakness and quota versus probability has been a matter of controversy for many years

### Convenience sampling:-

Convenience sampling(sometimes known asgraboropportunity sampling) is a type of nonprobability sampling which involves the sample being drawn from that part of the population which is close to hand. That is, a sample population selected because it is readily available and convenient. The researcher using such a sample cannot scientifically make generalizations about the total population from this sample because it would not be representative enough. For example, if the interviewer was to conduct such a survey at a shopping center early in the morning on a given day, the people that he/she could interview would be limited to those given there at that given time, which would not represent the views of other members of society in such an area, if the survey was to be conducted at different times of day and several times per week. This type of sampling is most useful for pilot testing. Several important considerations for researchers using convenience samples include:

1. Are there controls within the research design or experiment which can serve to lessen the impact of a non-random, convenience sample whereby ensuring the results will be more representative of the population?

2. Is there good reason to believe that a particular convenience sample would or should respond or behave differently than a random sample from the same population?

3. Is the question being asked by the research one that can adequately be answered using a convenience sample?

In social science research,snowball samplingis a similar technique, where existing study subjects are used to recruit more subjects into the sample.

### Sampling and data collection:-

### Good data collection involves:

§ Following the defined sampling process

§ Keeping the data in time order

§ Noting comments and other contextual events

§ Recording non-responses

Most sampling books and papers written by non-statisticians focus only in the data collection aspect, which is just a small though important part of the sampling process.

### Sampling error

Sampling errors are caused by sampling design. It includes:

(1)Selection error: Incorrect selection probabilities are used.

(2)Estimation error: Biased parameter estimate because of the elements in these samples.

### Non-sampling error

Non-sampling errors are caused by the mistakes in data processing. It includes:

(1)Overcoverage: Inclusion of data from outside of the population.

(2)Undercoverage: Sampling frame does not include elements in the population.

(3)Measurement error: The respondent misunderstand the question.

(4)Processing error: Mistakes in data coding.

(5)Non-response: