Desktop version

Home arrow Mathematics

  • Increase font
  • Decrease font

<<   CONTENTS   >>


Sampling is defined as a systematic statistical method for obtaining information about some of the characteristics of a community, by studying a part which represents the whole. Different methods are employed for sampling:

  • • Random sampling
  • • Systematic sampling
  • • Sampling successively

The way a method is chosen is determined by the purpose and conditions of the research. Applications

Sampling can be divided into two general categories:

  • • Sampling for acceptance (inspection)
  • • Sampling for review

In sampling to accept or reject a group of items based on the results of the sample(s), the industry application is to provide certain levels of assurance and information about whether the inputs of a product or process can meet the necessary requirements or not. In a sample for review, a numerical or analytic study is used to estimate the values of one or more characteristics of a community. At this stage, we often deal with surveys in which information is collected on a particular topic (e.g., measuring customer satisfaction). Also, the method is used to determine the number of samples needed to measure one or more characteristics of the statistical community. Other aspects of the application of sampling through this method are

  • • Estimation of the proportion of a community that might purchase a particular product
  • • Estimation of the percentage of items that provide a measure for certain criteria
  • • Control of a production process involving operators, machines, and products for monitoring variability and determining corrective and preventive measures
  • Advantages

An appropriate sampling plan, compared to a census of the entire community or a 100% inspection, can certainly save time, cost, and labor. Additionally, sampling is the only way to obtain the right information when the product inspection involves destructive tests. Disadvantages

In designing a sampling process, the following should be considered:

  • • How to select the sample size
  • • Sampling time
  • • Sampling method
  • • Basis for sub-grouping

However, failure to pay attention to any of the above factors, which are mostly disregarded, gives rise to error rates.


Simulation is an execution method through which a system (theoretical or empirical) is mathematically presented in the form of a computer program so that it can solve a problem. If the method of presenting includes concepts of probability theory, especially random variables, the designation Monte Carlo method simulation is used. Applications

In the field of theoretical sciences, this technique is used when no comprehensive theory of problem solving is known, or if one is known, it cannot be applied to strengthen this technique (space programs or advanced missile defense projects can be cited as an example). In the field of empirical sciences, the technique is used when a system or a process can be properly described with the help of a computer program. The following are some of the more specific uses of the technique:

  • • Modeling oscillation in advanced mechanical parts
  • • Modeling oscillation of component profiles in complex assemblies
  • • Determining optimal timing for preventive maintenance
  • • Cost analysis and other analyses in design and production areas for resource allocation
  • Advantages

In the field of theoretical sciences, simulation (especially the Monte Carlo method) provides an appropriate tool for solving problems, especially in cases where direct and straightforward computations might be very difficult to accomplish. In the field of empirical science, simulations are used for a variety of tests found to be experimentally impossible or very costly to conduct. Hence, simulation has the advantage of offering the best solution at the shortest time and lowest costs. Disadvantages

Note that in the field of theoretical sciences, evidence based on conceptual reasoning is more useful than simulation techniques since the technique often does not show the reasons for the outcome result. In the field of empirical sciences, there might exist some limitations where the simulated model does not fit. For this reason, the method is not to be used as a suitable substitute for reviews and evaluations.

Statistical Process Control Charts

Process control charts—a graphic representation of the data—are drawn from the samples gathered periodically from a process and displayed on the graph in the time order they were collected in. The control limits in these charts show the intrinsic variability of a process in a stable state as the role of control charts is to help to assess the stability of a process carried out by examining punctuated data relative to the control limits. In the case of variable data, a control diagram is used to monitor the changes of the process centre and a separate control diagram is used to monitor the process fluctuations. For descriptive data, control charts typically represent the number or ratio of non-conforming items or the number of observed non-conformities in the samples taken from the process. The general pattern of these charts is Shewhart model variables. There are other examples of control charts that have specific features (such as moving average charts). Applications

These charts are used to specify changes in a process where the recorded data is compared with the control limits. In the simplest possible way, a point outside of the control limits indicates a change in the process which might be attributed to some specific causes. These causes need to be analyzed and determined for the observation task outside of the control limits. Many organizations such as automotive, electronic, and defense industries often use this technique to meet two purposes:

  • • To prove the sustainability of a production process and its continuous sustainability
  • • To determine the risk and the scope of corrective actions

This useful technique is exploited in the machining industry to reduce unnecessary interferences in a process. Another aspect of this technique is the control of such typical features as average response time, error rate, and the frequency of complaints for measuring, complicating, and improving the performance in the service industry. Advantages

Besides showing the data, the process control charts have uses in helping to find the right answer for the reason behind process fluctuations. The crucial point is to distinguish between randomized (inherent) fluctuations and fluctuations in certain cases. The following can be mentioned as important benefits of these graphs:

  • • Process control
  • • Process capability analysis
  • • Measurement system analysis
  • • Cause and effect analysis
  • • Continuous improvement
  • Disadvantages

The most important point in the useful application of these charts is the selection of logical sub-groups that form the basis for the effective use of the charts. The interpretation of these charts in identifying the sources of a process variability is also very important an in some cases it is overlooked. Thus, the outcome results might be misleading. Further, there are some short-term processes that have scant data for determining appropriate control limits. Another setback is the existence of alpha and beta errors that never approximate zero.

<<   CONTENTS   >>

Related topics