Recommendation

Analysis…Calculations:

     Multiple Linear Regression analysis (utilizing multiple software packages) was then performed on the data set, within the boundaries of the general symbolic model above, to determine the value of each variable coefficient (bi).  Initially using a standard multiple linear regression calculation method and then gravitating to a backward elimination step-wise regression calculation, we came up with the equation coefficient unknowns as detailed in Table 1 (Complete results) in the Figures and Tables section of this report.

     Based on the regression analysis and the preliminary symbolic model equation above, the estimated regression model took the form:

 

Preliminary First-Step Regression Model Equation    yhat = bo + b1x1 + b2x2 + b3x3 + b4x4 + b5x5 + b6x6 + b7x7 = 13.4 - .0122 x1 – 2.62 x2 + .55 x3 + .93 x4 – 2.597 x5 + 19.8 x6 + 32.6 x7  = 13.4 - .0122#FORMS – 2.62#ENG+ .55#DES + .93 ERFORM– …          … - 2.597 RFQFORM+ 19.8 MODCAT + 32.6 CMPLXCAT

In this model estimation, the signs of the coefficient values were as expected except for that of the Number of Designers which was positive, indicating that as the number of designers was increased while holding the number of engineers constant, the resulting duration/lead-time would actually increase.  This could be explained by reviewing the daily interactions between the Engineers and Designers within the department.  After a short while, it became apparent that if the number of designers was increased, while not increasing the number of engineers, the department engineers would spend more of their time supervising and directing the work of the designers and less time on their “value-added” work.  This interaction was a moot point though as will be described when discussing the individual coefficient significance, later in this report.

Analysis…Overall and Individual Model Significance:

     As can be seen from Appendix B: Significance Test Calculations and Table 1: Distilled Regression Analysis Results in the Figures and Tables section of this report, although we had overall model significance, the coefficients b1 (#FORMS), b3 (#DES) and b4 (ERFORM) are dropped out of the estimated regression equation due to lack of individual significance such that resulting regression model became:

 

Final Regression Model Equation       yhat = bo + b2x2 + b5x5 + b6x6 + b7x7              = 14.8 – 2.75 x2  – 3.2 x5 + 19.8 x6 + 32.7 x7         = 14.8 – 2.75#ENG – 3.2RFQFORM* + 19.8MODCAT* + …                     … + 32.7CMPLXCAT*        NOTE: * signifies a dummy variable ( xi = 0 or 1)

 NOTE:

 Other preliminary regression analysis models/evaluations were investigated as follows:

• 9-variable model, with Dummy Variables for all the qualitative variables to try and determine the initial influence of each variable on the model.  Model failed because the statistical software package automatically dropped the Basic Category out of the calculations and DR Form Type caused a “near singularity error” not allowing the calculations to be completed.
• Additional Intermediate Dummy variables were introduced into the model to determine if there was a threshold level for the Number of Projects / Forms where the Dummy variable would become significant.  Could not find a threshold level that gave the new Dummy variable significance.
• Regression calculations were made with 95%, 85% and then finally 70% confidence levels to determine if the overall outcome of the regression models varied.  Not until we ran the analysis at a 70% confidence level did we gain an additional independent variable but only increased the overall fit (R2) by .03%.  Final calculations were kept at the 95% confidence level (alpha=.05).

Analysis…Residual Plots and R2 Review:

     The final step in the regression model analysis was to review and analyze the significance of the R2 value and residual plots for the complete regression model when plotted against the predicted values for the duration/lead-time.

     With a value for R2 of .306 and a standard error of 14.545 days, it became apparent that although this model showed overall significance and had four independent variables with individual significance, the model only explained 30.6% of the variability of the data and therefore represented only a moderately good fit, indicating that there could potentially be a number of variables, related to the duration of projects, that had been overlooked.

     When looking at the residual plots, as detailed in Figure 3 , in the Figures and Tables section of this report, we could also see, specifically from the shape of the Residuals vs the Fitted Values (Predicted Lead-time), that our model possessed a non-constant variance, as indicated by the increasing spread.  This inconsistent and increasing variation in the predicted values and therefore the residual can most likely be attributed to a non-linear relationship within the data set

NOTE: The odd groupings of data are a result of the dummy variables in the model, since each coefficient contributes only when the variable is present.

Recommendation

Data Collection:

The data that has been collected consists of 13 elements, but the data set has been modified to include only the 6 that are pertinent to our investigation:

     1. Form Type (only care about forms that are the direct responsibility of OE
     2. Duration (calendar days … including weekend days)
     3. Category/Difficulty (Basic, Moderate, Complex)
     4. Number of Department Engineers
     5. Number of Department Designers

6th variable not collected but manually calculated based on date and duration data:

     6. Number of Forms (total number of forms already in dept at time new form was received)

The data set is real data collected over the last 2+ years

Has been cleansed of faulted observations created by reopening an already closed observation … the database system cannot handle when a form is reopened and then saved after it has been closed (i.e. the open date is later than closed date)

Consists of the following general “statistics”:
• 997 Total observations (taken from approximately 6000 total recorded observations)
• Observation dates ranging from 07/23/2002 to 11/04/2004
• 622 ER forms, 339 RFQ forms and 36 RFD forms
• 754 Base Category, 214 Moderate Category and 29 Complex Category
• Form durations ranging from 3 minutes up to 107 days

Recommendation

Final Model:

NOTE: * signifies a dummy variable ( = 0 or 1)

Recommendation

Recommendation

Project Environment:

Rite-Hite Products Corporation (RHPC), headquartered in Milwaukee, WI, is a world leader in the manufacture and sale of loading dock and industrial door safety products.  Rite-Hite focuses on providing high-quality, compelling products and complete loading dock solutions that improve both facility safety and overall material handling productivity.  Within RHPC, the Order Engineering (OE) Department is primarily responsible for all of the special “Designed-to-Order” products that flow through RHPC.  These “specials” range from modifications (of widely varying degrees) of standard equipment, to combinations of various standard pieces of RHPC equipment as well as competitive and sister company components, to one-of-a-kind equipment that have never been built before and are often used as loss-leaders, special priced with moderate to deep discounts, to ”steal” business from the RHPC competitors or protect standard RHPC equipment sales from the same competitors.  With a continual increase in new products within RHPC, the workload through the department has increased, from approximately 250 jobs in 1997 to an estimated 500-550 projects this year.  In response to this increase in projects and additional pressures from the RHPC competitors and RHPC sales and customer base, a design-to-order process duration estimation and improvement mandate was handed down.  In late 2002, a special Lotus Notes database system was developed to gather data on each of these projects to help come up with both a baseline for the average special project duration and a means for calculating better estimates for projected completion dates.  Although nothing has been done with this data at this point in time, the system has become the central repository for all information related to every special project that flows through the company.  The system is made up of 10 different “task” forms that each have a specific function, within the department, as described in Appendix A and all involve varying degrees of work based on the project type.  The data that has been collected, within this database, consists of 13 elements, but the data set has been modified to include only those variables that are pertinent to our investigation and are described in detail in the Model section of this report.

The data set is real data collected over the last 2+ years and has been purged of faulted observations created by reopening an already closed observation (i.e. the database system cannot handle when a form is reopened and then saved after it has been closed because the open date will be later than the closed date) and consists of the general “statistics”.