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Concurrent design and manufacturing involves simultaneously completing design and manufacturing stages of production. By completing the design and manufacturing stages at the same time, products are produced in less time while lowering cost. Although concurrent design and manufacturing requires extensive communication and coordination between disciplines, the benefits can increase the profit of a business and lead to a sustainable environment for product development. Concurrent design and manufacturing can lead to a competitive advantage over other businesses as the product maybe produced and marketed in less time.^[1]

• 3Business benefits

Introduction[edit]

The success behind concurrent design and manufacturing lies within completing processes at the same time while involving all disciplines. As product development has become more cost and time efficient over the years, elements of concurrent engineering have been present in product development approaches. The elements of concurrent engineering that were utilized were cross-functional teams as well as fast time-to-market and considering manufacturing processes when designing.^[2] By involving multiple disciplines in decision making and planning, concurrent engineering has made product development more cost and time efficient. The fact that concurrent engineering could result in faster time-to-market is already an important advantage in terms of a competitive edge over other producers. Concurrent engineering has provided a structure and concept for product development that can be implemented for future success.

Concurrent vs sequential engineering[edit]

Concurrent and Sequential engineering cover the same stages of design and manufacturing, however, the two approaches vary widely in terms of productivity, cost, development and efficiency. The 'Sequential Engineering vs Concurrent Design and Manufacturing' figure shows sequential engineering on the left and concurrent design and manufacturing on the right. As seen in the figure, sequential engineering begins with customer requirements and then progresses to design, implementation, verification and maintenance. The approach for sequential engineering results in large amounts of time devoted to product development. Due to large amounts of time allocated towards all stages of product development, sequential engineering is associated with high cost and is less efficient as products can not be made quickly. Concurrent engineering, on the other hand, allows for all stages of product development to occur essentially at the same time. As seen in the 'Sequential Engineering vs Concurrent Design and Manufacturing' figure, initial planning is the only requirement before the process can occur including planning design, implementation, testing and evaluation. The concurrent design and manufacturing approach allows for shortening of product development time, higher efficiency in developing and producing parts earlier and lower production costs.

Concurrent and Sequential Engineering may also be compared using a relay race analogy.^[3] Sequential engineering is compared to the standard approach of running a relay race, where each runner must run a set distance and then pass the baton to the next runner and so on until the race is completed. Concurrent engineering is compared to running a relay race where two runners will run at the same time during certain points of the race. In the analogy, each runner will cover the same set distance as the sequential approach but the time to complete the race using the concurrent approach is significantly less. When thinking of the various runners in the relay race as stages in product development, the correlation between the two approaches in the relay race to the same approaches in engineering is vastly similar. Although there are more complex and numerous processes involved in product development, the concept that the analogy provides is enough to understand the benefits that come with concurrent design and manufacturing.

Business benefits[edit]

Using concurrent engineering, businesses can cut down on the time it takes to go from idea to product. The time savings come from designing with all the steps of the process in mind, eliminating any potential changes that have to be made to a design after a part has gone all the way to production before realizing that it is difficult or impossible to machine. Reducing or eliminating these extra steps means the product will be completed sooner and with less wasted material in the process. During the design and prototyping process, potential issues in the design can be corrected earlier in the product development stages to further reduce the production time frame.

The benefits of concurrent design and manufacturing can be sorted in to short term and long term.

Short term benefits[edit]

• Competitive advantage with implementing part into market quickly
• Large amounts of same part produced in a shorter amount of time
• Allows for early correction of part
• Less material wasted
• Less time spent on multiple iterations of essentially the same part

Long term benefits[edit]

• More cost efficient over several parts produced and several years
• Large amounts of different parts produced in a shorter total amount of time
• Better communication between disciplines in company
• Ability to leverage teamwork and make informed decisions^[3]

See also[edit]

References[edit]

1. ^Partner, Concurrent Engineering PTC. 'What is Concurrent Engineering?'. www.concurrent-engineering.co.uk. Retrieved 2016-02-16.
2. ^Loch, Terwiesch (1998). 'Product Development and Concurrent Engineering'. INSEAD. Retrieved March 8, 2016.
3. ^ ^ab'Sequential versus Concurrent Engineering—An Analogy'. ResearchGate. doi:10.1177/1063293X9500300401. Retrieved 2016-03-04.

In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data are evaluated as they are collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results are observed. Thus a conclusion may sometimes be reached at a much earlier stage than would be possible with more classical hypothesis testing or estimation, at consequently lower financial and/or human cost.

• 3Applications of sequential analysis

History[edit]

The method of sequential analysis is first attributed to Abraham Wald^[1] with Jacob Wolfowitz, W. Allen Wallis, and Milton Friedman^[2] while at Columbia University'sStatistical Research Group as a tool for more efficient industrial quality control during World War II. Its value to the war effort was immediately recognised, and led to its receiving a 'restricted' classification.^[3] At the same time, George Barnard led a group working on optional stopping in Great Britain. Another early contribution to the method was made by K.J. Arrow with D. Blackwell and M.A. Girshick.^[4]

A similar approach was independently developed from first principles at about the same time by Alan Turing, as part of the Banburismus technique used at Bletchley Park, to test hypotheses about whether different messages coded by German Enigma machines should be connected and analysed together. This work remained secret until the early 1980s.^[5]

Peter Armitage introduced the use of sequential analysis in medical research, especially in the area of clinical trials. Sequential methods became increasingly popular in medicine following Stuart Pocock's work that provided clear recommendations on how to control Type 1 error rates in sequential designs.^[6]

Alpha spending functions[edit]

When researchers repeatedly analyze data as more observations are added, the probability of a Type 1 error increases. Therefore, it is important to adjust the alpha level at each interim analysis, such that the overall Type 1 error rate remains at the desired level. This is conceptually similar to using the Bonferroni correction, but because the repeated looks at the data are dependent, more efficient corrections for the alpha level can be used. Among the earliest proposals is the Pocock boundary. Alternative ways to control the Type 1 error rate exist, such as the Haybittle-Peto bounds, and additional work on determining the boundaries for interim analyses has been done by O’Brien & Fleming^[7] and Wang & Tsiatis.^[8]

A limitation of corrections such as the Pocock boundary is that the number of looks at the data must be determined before the data is collected, and that the looks at the data should be equally spaced (e.g., after 50, 100, 150, and 200 patients). The alpha spending function approach developed by Demets & Lan^[9] does not have these restrictions, and depending on the parameters chosen for the spending function, can be very similar to Pocock boundaries or the corrections proposed by O'Brien and Fleming.

Applications of sequential analysis[edit]

Clinical trials[edit]

In a randomized trial with two treatment groups, group sequential testing may for example be conducted in the following manner: After n subjects in each group are available an interim analysis is conducted. A statistical test is performed to compare the two groups and if the null hypothesis is rejected the trial is terminated; otherwise, the trial continues, another n subjects per group are recruited, and the statistical test is performed again, including all subjects. If the null is rejected, the trial is terminated, and otherwise it continues with periodic evaluations until a maximum number of interim analyses have been performed, at which point the last statistical test is conducted and the trial is discontinued.^[10]

Other applications[edit]

Sequential analysis also has a connection to the problem of gambler's ruin that has been studied by, among others, Huygens in 1657.^[11]

Step detection is the process of finding abrupt changes in the mean level of a time series or signal. It is usually considered as a special kind of statistical method known as change point detection. Often, the step is small and the time series is corrupted by some kind of noise, and this makes the problem challenging because the step may be hidden by the noise. Therefore, statistical and/or signal processing algorithms are often required. When the algorithms are run online as the data is coming in, especially with the aim of producing an alert, this is an application of sequential analysis.

Bias[edit]

Trials that are terminated early because they reject the null hypothesis typically overestimate the true effect size.^[12] This is because in small samples, only large effect size estimates will lead to a significant effect, and the subsequent termination of a trial. Methods to correct effect size estimates in single trials have been proposed.^[13] Note that this bias is mainly problematic when interpreting single studies. In meta-analyses, overestimated effect sizes due to early stopping are balanced by underestimation in trials that stop late, leading Schou & Marschner to conclude that 'early stopping of clinical trials is not a substantive source of bias in meta-analyses'.^[14]

The meaning of p-values in sequential analyses also changes, because when using sequential analyses, more than one analysis is performed, and the typical definition of a p-value as the data “at least as extreme” as is observed needs to be redefined. One solution is to order the p-values of a series of sequential tests based on the time of stopping and how high the test statistic was at a given look, which is known as stagewise ordering,^[15] first proposed by Armitage.

See also[edit]

Notes[edit]

1. ^Wald, Abraham (June 1945). 'Sequential Tests of Statistical Hypotheses'. The Annals of Mathematical Statistics. 16 (2): 117–186. doi:10.1214/aoms/1177731118. JSTOR2235829.
2. ^Berger, James (2008). Sequential Analysis. The New Palgrave Dictionary of Economics, 2nd Ed. pp. 438–439. doi:10.1057/9780230226203.1513. ISBN978-0-333-78676-5.
3. ^[1]
4. ^Kenneth J. Arrow, David Blackwell and M.A. Girshick (1949). 'Bayes and minimax solutions of sequential decision problems'. Econometrica. 17 (3/4): 213–244. doi:10.2307/1905525. JSTOR1905525.
5. ^Randell, Brian (1980), 'The Colossus', A History of Computing in the Twentieth Century, p. 30
6. ^W., Turnbull, Bruce (2000-01-01). Group sequential methods with applications to clinical trials. Chapman & Hall. ISBN9780849303166. OCLC900071609.
7. ^O'Brien, Peter C.; Fleming, Thomas R. (1979-01-01). 'A Multiple Testing Procedure for Clinical Trials'. Biometrics. 35 (3): 549–556. doi:10.2307/2530245. JSTOR2530245.
8. ^Wang, Samuel K.; Tsiatis, Anastasios A. (1987-01-01). 'Approximately Optimal One-Parameter Boundaries for Group Sequential Trials'. Biometrics. 43 (1): 193–199. doi:10.2307/2531959. JSTOR2531959.
9. ^Demets, David L.; Lan, K. K. Gordon (1994-07-15). 'Interim analysis: The alpha spending function approach'. Statistics in Medicine. 13 (13–14): 1341–1352. doi:10.1002/sim.4780131308. ISSN1097-0258.
10. ^Korosteleva, Olga (2008). Clinical Statistics: Introducing Clinical Trials, Survival Analysis, and Longitudinal Data Analysis (First ed.). Jones and Bartlett Publishers. ISBN978-0-7637-5850-9.
11. ^Ghosh, B. K.; Sen, P. K. (1991). Handbook of Sequential Analysis. New York: Marcel Dekker. ISBN9780824784089.^{[page needed]}
12. ^Proschan, Michael A.; Lan, K. K. Gordan; Wittes, Janet Turk (2006). Statistical monitoring of clinical trials : a unified approach. Springer. ISBN9780387300597. OCLC553888945.
13. ^Liu, A.; Hall, W. J. (1999-03-01). 'Unbiased estimation following a group sequential test'. Biometrika. 86 (1): 71–78. doi:10.1093/biomet/86.1.71. ISSN0006-3444.
14. ^Schou, I. Manjula; Marschner, Ian C. (2013-12-10). 'Meta-analysis of clinical trials with early stopping: an investigation of potential bias'. Statistics in Medicine. 32 (28): 4859–4874. doi:10.1002/sim.5893. ISSN1097-0258. PMID23824994.
15. ^Gordan., Lan, K. K.; Turk., Wittes, Janet (2007-01-01). Statistical monitoring of clinical trials : a unified approach. Springer. ISBN9780387300597. OCLC553888945.

References[edit]

• Wald, Abraham (1947). Sequential Analysis. New York: John Wiley and Sons.
• Bartroff, J., Lai T.L., and Shih, M.-C. (2013) Sequential Experimentation in Clinical Trials: Design and Analysis. Springer.
• Ghosh, Bhaskar Kumar (1970). Sequential Tests of Statistical Hypotheses. Reading: Addison-Wesley.
• Chernoff, Herman (1972). Sequential Analysis and Optimal Design. SIAM.
• Siegmund, David (1985). Sequential Analysis. Springer Series in Statistics. New York: Springer-Verlag. ISBN978-0-387-96134-7.
• Bakeman, R., Gottman, J.M., (1997) Observing Interaction: An Introduction to Sequential Analysis, Cambridge: Cambridge University Press
• Jennison, C. and Turnbull, B.W (2000) Group Sequential Methods With Applications to Clinical Trials. Chapman & Hall/CRC.
• Whitehead, J. (1997). The Design and Analysis of Sequential Clinical Trials, 2nd Edition. John Wiley & Sons.

External links[edit]

• R Package: Wald's Sequential Probability Ratio Test by OnlineMarketr.com
• Software for conducting sequential analysis and applications of sequential analysis in the study of group interaction in computer-mediated communication by Dr. Allan Jeong at Florida State University

Commercial

• PASS Sample Size Software includes features for the setup of group sequential designs.