PLM Maturity Evaluation and Prediction Based on a Maturity Assessment and Fuzzy Sets Theory

: Companies adopt PLM maturity models to evaluate PLM implementation and recognize relative positions in PLM selection to better harness PLM benefits. However, the majority traditional PLM maturity models are relative time-consuming and energy-consuming. This work focuses on proposing a fuzzy extended PCMA ( P LM C omponents M aturity A ssessment) maturity model to brightly evaluate the gradual process of PLM maturity accompaniment with time changes, which aims to reduce the efforts spent on maturity evaluation. The proposed PCMA uses triangular fuzzy elements to express maturity levels that can solve vague and complexity issues in PLM evaluation. The proposed fuzzy PCMA is tested by two Chinese firms. The first evaluation uses PCMA maturity model to obtain the maturity levels for a Chengdu company in 2010. The PLM maturity for this company from 2011 to 2013 is conducted by the fuzzy extended PCMA maturity model through inputting the KPIs‟ value. Fuzzy extended PCMA is also used to predict the maturity level for a Shanghai company. A comparison of the results obtained by fuzzy extended PCMA model and the real-life situation verify the effectiveness of the proposed model.


Introduction
Product Lifecycle Management (PLM ) manages a company's product from its early conception stages to the final disposal stages. PLM drives cost reductions, facilitates reducing lead time, and imp roves product quality [1,13]. To pave the way toward obtaining the true benefits of PLM, the users should have a clear Assessment), need to be integrated and collaborated with PLM to satisfy performance requirements. Thus zhang et al. [3][4] extends the TIFO framewo rk into TIFOS framework by adding a new dimension called SustainWare in consideration of sustainability.
Several basic co mponents construct PLM functionalities. Stark et al. [5] state that PLM is a holistic approach and PLM contains nine PLM co mponents , which consist of products, data, applications, processes, people, work methods, and equip ment. Abramovici et al. [6] define five PLM levels, and each PLM level has several concrete PLM co mponents that can have interdependencies with other co mponents .
Fifteen different types of PLM co mponents in TIFOS framework is collected and described by zhang et al. [3], which include techniques & practices, PLM software & applications, strategy & supervision, quality management, business management, maintenance management, BOM management, PDM, financial management, people, distributed collaboration management, workflow & process management, eco-friendly & innovation, life cycle assessment, and green conception. This work will adopt these fifteen PLM components to analyze PLM implementation.
Many co mpanies start to enlarge investment of PLM to reap PLM benefits. Decision-makers have yet to clarify PLM adoption and imp lementation, because of PLM being large and co mplex. Measuring PLM components adoption, running condition, and maturity situation, can reflex imp lementation of PLM and provide guidelines for decision-makers in a co mpany. Th is work aims to solve the following research questions: To solve the two questions we study literature works as well as experimental research. In literature studies, PLM maturity models [1,[7][8][9][10][11][12] identify different maturity growth stages that can evaluate PLM adoption; but these maturity models are still weaker to aid co mpanies in self-evaluation PLM and to recognize the gradual process of PLM acco mpaniment through time changes. Most of the PLM maturity models define several maturity levels and describe the differences between each level by using linguistic terms. The linguistic terms have a feature of uncertainty and vagueness, which makes the decision-makers, not able to input accurate values for each maturity level. The third research question is:

How can companies maximally keep and express decision-makers' intentions, while evaluating PLM implementation by using PLM maturity models?
A fuzzy extended PCMA maturity model is proposed to be able to resolve these research questions.
This model is used to evaluate and predict the gradual process of PLM maturity by using the first year's evaluation results and the KPIs values to reduce the efforts spen t on PLM evaluation. The proposed maturity model is examined by a structured survey. The experimental research is conducted to validate the survey and the fuzzy extended PCMA maturity model. The survey was conducted in two Chinese firms in 2013. The work is structured as follows: section 2 gives the literature view of PLM maturity models and fuzzy sets theory; section 3 describes the running mechanis m of PCMA maturity model; section 4 proposes a fuzzy extended PCMA maturity model to automatically evaluate PLM maturity; section 5 examines the proposed fuzzy extended PCMA by two case studies; section 6 concludes our work.

PLM maturity models
PLM maturity models provide guidelines to PLM implementation for any given company. CMMI (Capability Maturity Model Integration) [7][8][9] has the potential to significantly improve the organization "s profitability, because it has the abilities to evaluate an organization"s maturity and process area capability.
CMMI defines multiple process areas, and provides the goals for each level of implementation. Yet it has not proposed a roadmap to implementati on or identification of key process improvement areas . A company usually needs to prepare lots of documents to suit CMMI assessment in China . These prepared documents are specially used for one-time assessments. Strategies have not been given to analyze the weaker items obtained from the assessments, which makes the companies cannot receive the true benefits of maturity assessments. Besides the whole assessment process is quite time-consuming and energy-consuming. Stark [1] proposes a PDM (product data management) maturity model with four stages of evaluation, and defines the activities that a company needs to carry out at each stage. Batenburg [10] develops a PLM framework to assess and guide PLM implementations for organizations in terms of five dimensions: Strategy and policy, Monitoring and control, Organisation and processes , People and culture, and Information technology. Henk and Kees [11] apply Batenburg model in 20 companies to analyze PLM implementation of these companies . Sääksvuori Model [12] determines the maturity of a large international corporation for a corporate-wide PLM development program and develops business and PLM related issues. Yet, it should be mentioned that most of these maturity models are qualitative analysis, which cannot give a satisfactory impression of companies" relative position, and cannot solve research questions mentioned in introduction.

Applying fuzzy sets theory to describe maturity levels
Maturity models adopt linguistic terms to exp ress the content of maturity levels. The linguistic terms have to be changed into numbers to make the maturity results easier understand. Crisp numbers cannot precisely exp ress maturity results due to complex and vague features of linguistic terms. Fuzzy set theory is proposed by Zadeh [14] and this theory is a revolutionary way of solving the vagueness issues. Fuzzy sets theory allows objects to exist in more than one set. The membership function is proposed to demonstrate how much degree of an element belongs in a set, which means that the associated membership function of an object is mu ltivalued. Fu zzy triangular elements and the corresponding membership function of fuzzy sets theory is used to express performance evaluation of maturity levels , because the advantages of fuzzy triangular numbers in fuzzy sets [15].

The running mechanism of PCMA Maturity Model
The goal of PCMA maturity model is to measure and monitor PLM dimensions. Key performance indicators (KPIs) are used to help define concrete actions in evaluation [16][17]. An example of outcome of PLM maturity evaluation is shown in Table 1. The evaluation concerns a PLM dimension called 'FunctionWare' in TIFOS framework. Five maturity levels are defined, based on 'standard' scale in PLMIG [19] and CMMI scale [7][8][9]. The maturity score on each KPI is represented by a black rectangle. The maturity level of this dimension of the company is determined by the average score of all related KPIs. The relative weights among each KPI will be discussed in the future.  Table 2. Similarly, we can obtain the maturity score of every PLM dimension.  Table 3.

Fuzzy extended PCMA maturity model
Fuzzy sets is adapted to address PLM maturity levels to better express decision-makers' intentions in PLM maturity evaluation. Five out of nine level fundamental scales of judgments are described via the triangular fuzzy numbers to express the relative difference among maturity levels in Table 4. The    Table 5. can be gotten from the ratio of the j year to the x year for the same KPI. The formula to get the maturity level in x year is shown in the following: To be more precise, the formula (1) can be replaced by formula (2): The sign f(k i ) shows that formula (3)   The second example is the second KPI value in 2010 and 2013 in Table 5. The maturity level in 2013 for the second KPI in cost category is calculated by formula (2) in the following: The sign f(k i ) shows that formula (5)

Conclusion and Future Work
This work analyzes PLM co mponents that can fulfill PLM functionalit ies. To better handle PLM implementation, a PCMA maturity model is used to evaluate the maturity of PLM co mponents. PCMA maturity model first gives the maturity level, then proposes the detail description of each maturity level, and collects the corresponding KPIs based on the content of each maturity level; finally obtaining the values of KPIs through a survey. A fuzzy extended PCMA maturity model is proposed to reduce the energy that spends on maturity evaluation. This model builds the relationship between the ratio for a pair of maturity levels and the ratio for the corresponding KPIs in two selected years in formu la 2. A coefficient in formu la 2 can determine how to get the changing degree and changing range for an unknown maturity level. The co mparison results show that the proposed model can be used in real-life cases and can efficiently reduce the use of human resources, time, and expense in maturity evaluation.
The restrict ion of the proposed model is that the selected years must be in the same stage of the company. The results of the proposed model should be recalculated when the company has significant decisions changes. The future work will use more realistic data to examine the effectiveness of the proposed fuzzy extended PCMA maturity model. The realistic data that extracted fro m social med ia are diversity and comp lexity. Therefore, strategies will be g iven to demystify Big Data based on data structures (structured data, semi-structured data and non-structured data) that enhancing the credibility of the proposed PLM maturity model.