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Business Analytics. MEAN STANDARD DEVIATION NORMAL CURVE DISTRIBUTION RAND. back2basics. HANDS ON. Process Capability. Product Specifications Preset product or service dimensions, tolerances e.g. bottle fill might be 16 oz. ±.2 oz. (15.8oz.-16.2oz.)

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  • RAND
process capability
Process Capability
  • Product Specifications
    • Preset product or service dimensions, tolerances
    • e.g. bottle fill might be 16 oz. ±.2 oz. (15.8oz.-16.2oz.)
    • Based on how product is to be used or what the customer expects
  • Process Capability – Cp and Cpk
    • Assessing capability involves evaluating process variability relative to preset product or service specifications
    • Cp assumes that the process is centered in the specification range
relationship between process variability and specification width
Three possible ranges for Cp

Cp = 1, as in Fig. (a), process

variability just meets specifications

Cp ≤ 1, as in Fig. (b), process not capable of producing within specifications

Cp ≥ 1, as in Fig. (c), process

exceeds minimal specifications

One shortcoming, Cpassumes that the process is centered on the specification range

Relationship between Process Variability and Specification Width
computing the c pk value at cocoa fizz
Computing the Cpk Value at Cocoa Fizz
  • Design specifications call for a target value of 16.0 ±0.2 OZ.

(USL = 16.2 & LSL = 15.8)

  • Observed process output has now shifted and has a µ of 15.9 and a

σ of 0.1 oz.

  • Cpkis less than 1, revealing that the process is not capable
6 sigma versus 3 sigma
Motorola coined “six-sigma” to describe their higher quality efforts back in 1980’s

Six-sigma quality standard is now a benchmark in many industries

Before design, marketing ensures customer product characteristics

Operations ensures that product design characteristics can be met by controlling materials and processes to 6σ levels

Other functions like finance and accounting use 6σ concepts to control all of their processes

±6 Sigma versus ± 3 Sigma

Product Quality


Background & Objectives

Modeling Techniques

  • FRED is the world’s leading ERP Systems company but Doors 5000 failed severely on fundamentals* perception, MS was anxious that Doors 7000 might suffer because of this
  • FRED would like to know following the huge investments made to improve Doors 7000 fundamentals, in which areas they excelled
  • FRED wants to Identify any perception issues with Doors 7000 fundamentals, with enough precision to understand root cause(s) and find out if there is still a need for fundamentals marketing of Doors

Hypotheses generation


To understand which fundamentals drive outcomes like satisfaction, favorability etc.


  • A set of hypotheses were formulated to form the basis for further analysis
  • Total Potential Value (TPV) should align with Fred H2 Target segments*
  • Communication on improved Doors fundamentals has resonated across segments
  • Doors 7000 fundamentals have shown improvement over its predecessors Vista and XP
  • Better perceptions of Doors fundamentals can help reduce the bleed to Max among currently dissatisfied users

* Fundamentals consists of Speed/ Performance, Security, Reliability, Navigation/Ux, Software Compatibility, Hardware Compatibility, Battery Life

**H2 Target Segments: Extreme Enthusiasts, Go Getters, Savvy Socials



  • Y=mx+c
  • Difference between Correlation and regression ????
  • Benefits of finding out Regression coefficient Vis a Vis Correlation Coefficient???
  • Y=Mx+C+E

ILLUSTRATION: Yogurt Filling Operation

An industrial engineer has suspected that the filling volume variability could be caused by three main factors;

feed rate of containers, temperature of yogurt, and the length in time the machine has been in operation since the start of the shift.

The industrial engineer suspects that there could be other factors affecting the filling volume; but only the stated factors can be easily controlled.


He understands that the filling volume will not be the same if it is repeated with the same values of feed rate, temperature, and operation duration.

The variability in the filling volume is caused by a random error, that for practical purposes is not important. But, he knows very well that, in regression analysis, the error is supposed to be normally distributed with mean zero and constant variance.

This error includes the effects of factors that are not included in the analysis; such as the age of the machine, viscosity of the liquid, etc.


This first step in the analysis is to collect data. What he has done was to observe the filling operation at different values of the control variables


To make scientifically based conclusions, he has to test some relevant hypotheses, like

1. how the feed rate, temperature, and operation duration collectively contribute to the variability or change in the filling volume.

2. how the filling volume is affected by the individual control variables.

3. how good the regression model in its entirety.