Markov Theory-based Methods For Analysis Of Strategies For Design Tasks Reviewing

As is well-known,new product designs often need to be subdivided into multiple phases and tasks,and managed as projects.On the one hand,the company’s lack of market research or customer fail to identify product requirements,resulting in some design tasks need to be confirmed by the team leaders / design supervisors first or after the customer review has been done.Designers can submit review confirmations for each phase of the design task,or they can proceed directly to the next phase of the design.Each review or confirmation takes a certain amount of time,and the feedback may be a one-time pass,or it may require multiple rework.On the other hand,some adjacent tasks have a certain correlation(coupling)in the design content,so that the rework probability is not independent,which makes it difficult to accurately estimate the probability distribution of the completion time of the design project.In today’s competitive market,companies must not only shorten the design project cycle as much as possible,but also make the fluctuations(variance or risk)of the completion time of the design project as small as possible.In response to this problem,the study has carried out the following work:(1)Analysis of design task review strategy without resource constraints.First,considering the design task’s regular and rework durations are negative exponential distributed.Based on the continuous-time Markov chain(CTMC)model,the project’s completion time expectation value is given to a given review strategy(a scheme for setting the review node is known).A simple design project for a design task illustrates the validity of the method for a computational example.Then,considering the design task’s regular and rework durations are general distributed,the phase-type(PH)distribution is used to approximate the general durations,and the task execution phase is regarded as the virtual task for project network conversion;the execution state transition process of the conversion network is described by a continuous-time Markov chain.And the completion time probability distribution of the project is calculated by using the phase-type distribution.Finally,a typical mold design project design experiment is carried out to analyze the influence of various project environmental parameters on the evaluation strategy’s advantages and disadvantages,and the effectiveness of the model and method is verified.(2)Analysis of design task review strategy under resource constraints.Firstly,the project completion time prediction problem in complex environment is analyzed abstractly,and the simulation model corresponding to different task review strategies is constructed by EM-Plant.Taking a simple design project with six design task nodes as a calculation example,the influence of project environmental parameters such as different scheduling strategies,the reviewing duration(including the duration discount factor and the review fixed time),rework probability and task relevance on the probability distribution of project completion time under resource constraints is analyzed.The simulation obtains the average value of each task waiting time into the Markov chain model,approximates the design task reviewing theory analysis model under resource constraints and makes a concise analysis of the advantages and disadvantages of the simulation model and the numerical model.