CMA Intermediate · Operations Management and Strategic Management

Productivity Management and Quality Management: formula sheet

Full chapter guide

Key formulas

Basic productivity: Productivity = Output ÷ Input; Output and input must be in consistent units or values.
Single factor productivity: Single factor productivity = Output ÷ One input (e.g. labour hours, kg of material, machine hours); Also called partial productivity. Result is in units per unit of that input.
Multifactor productivity: Multifactor productivity = Output ÷ (Labour + Material + Energy + any other selected inputs); Inputs must be in the same unit, normally rupees. It leaves out some inputs, such as capital, unless you include them.
Total productivity: Total productivity = Total output ÷ Total input; Both in rupees. Output is value of goods or services produced; input is the sum of all resource costs.
Productivity index: Productivity index = (Current productivity ÷ Base productivity) × 100; Above 100 means improvement over the base period.
Percentage change: % change = (Current − Base) ÷ Base × 100; Use the same type of productivity ratio in both periods.
Productivity: Productivity = Output ÷ Input; Use the same period and consistent units. Output can be units or sales value.
Single-factor (partial) productivity: Labour productivity = Output ÷ Labour hours; Material productivity = Output ÷ Material used; Measures output against one input only.
Total-factor productivity: Total productivity = Total output ÷ Total of all inputs (in rupees); Convert every input to rupees before adding.
Percentage change in productivity: % change = (New productivity − Old productivity) ÷ Old productivity × 100; Always divide by the old figure.
Efficiency: Efficiency % = (Actual output ÷ Standard output) × 100; Equivalent time form: Standard time for actual output ÷ Actual time × 100.
Dimensions of product quality: Performance, Features, Reliability, Conformance, Durability, Serviceability, Aesthetics, Perceived quality; Learn this as a list and give one example for each. Some books use slightly different names, so explain each one you write.
Dimensions of service quality: Reliability, Responsiveness, Assurance, Empathy, Tangibles; Use these when the question is about a bank, hospital, courier or similar service.
Total cost of quality: Cost of quality = Prevention cost + Appraisal cost + Internal failure cost + External failure cost; Cost of good quality is prevention plus appraisal. Cost of poor quality is internal plus external failure.
Control vs assurance: Quality control = detect and correct defects in output; Quality assurance = prevent defects through the system; Control is product-focused and reactive. Assurance is process-focused and proactive.
PDCA cycle: Plan → Do → Check → Act (then repeat); Plan: identify the problem and set the target. Do: implement on a small scale. Check: compare results with the plan. Act: standardise if it worked, otherwise revise.
Crosby's definition of quality: Quality = Conformance to requirements; Linked with Zero Defects and 'do it right the first time'.
Juran's definition of quality: Quality = Fitness for use; Linked with the Quality Trilogy: planning, control, improvement.
Juran's Quality Trilogy: Quality planning + Quality control + Quality improvement; Use it when asked for Juran's contribution.
Deming's main message: Most quality problems are due to the system (management), not the worker; Deming's 14 points are management principles. You do not need to memorise their exact order, but know the key ideas.
Six Sigma defect level: Six Sigma = 3.4 defects per million opportunities (DPMO); Remember it as a target level, not a count for every firm.
DPMO: DPMO = (Number of defects ÷ (Units × Opportunities per unit)) × 10,00,000; Use total opportunities for defects, not just units.
DMAIC: Define → Measure → Analyse → Improve → Control; Keep this order in every answer.
Pareto cumulative %: Cumulative % = (Running total of defects ÷ Total defects) × 100; Arrange causes from largest to smallest before cumulating.
ISO 9000 family roles: ISO 9000 = fundamentals and vocabulary; ISO 9001 = requirements (certifiable); ISO 9004 = guidance for improvement; Only ISO 9001 is certified against. Do not say an organisation is 'ISO 9000 certified' in a precise answer.
PDCA cycle: Plan → Do → Check → Act; The improvement logic behind ISO 9001's process approach.
Certification vs accreditation: Certification = body audits the organisation; Accreditation = authority recognises the certifying body; In India, NABCB (QCI) accredits certification bodies.
ISO vs award: ISO 9001 = conformity to requirements (minimum standard); Award = recognition of excellence (competitive); Use this as the core contrast in any comparison answer.
Typical certification cycle: Certificate valid for three years, with surveillance audits in between, then recertification; This is the usual practice under ISO 9001 certification schemes. State it as 'typically'.

Quick revision

Productivity = Output ÷ Input; the units of output and input must be consistent.
Partial productivity uses one input; multifactor uses several; total productivity uses all inputs.
Always compare productivity with an earlier period or a benchmark, or the number tells you little.
Productivity improves through people, technology, methods and a better working environment.
Quality means fitness for use and meeting customer requirements consistently.
Know each dimension of quality and give a one-line example for it.
TQM is company-wide, customer-focused and built on continuous improvement involving every employee.
Each quality tool has a specific job: know what problem it is used for.
Poor quality raises cost through scrap, rework, returns and lost customers.
ISO standards certify a management system, not that every product is perfect.
Awards recognise performance excellence; learn the names and their focus areas.
Use headings and short points in written answers to earn step marks.

Common mistakes

Adding labour hours to material cost to get total input. Fix: Convert every input to rupees before adding for multifactor or total productivity.
Using total production instead of productivity as the answer. Fix: Always divide output by input. Productivity is a ratio, not a quantity.
Treating productivity and efficiency as the same thing. Fix: Say productivity is output per unit of input, while efficiency compares actual performance with a standard.
Listing government policy or market demand as an internal factor. Fix: Ask if management can change it. If not, it is external.
Treating quality control and quality assurance as the same thing. Fix: Remember control detects defects in output, assurance prevents them through the process. Write at least three points of difference.
Classifying inspection of finished goods as prevention cost. Fix: Inspection and testing find defects, so they are appraisal cost. Prevention happens before defects arise.
Mixing up the definitions of quality: giving 'fitness for use' for Crosby or 'conformance to requirements' for Juran. Fix: Remember Juran = fitness for use (customer view). Crosby = conformance to requirements (specification view).
Writing PDCA stages in the wrong order or calling the last step 'Control' or 'Check' again. Fix: Say Plan, Do, Check, Act. Act means standardise the improvement or revise the plan.
Mixing up the Pareto chart and the histogram. Fix: Pareto bars are categories sorted from highest to lowest with a cumulative line. A histogram shows the spread of a measured variable in ranges.
Drawing a fishbone diagram without a clear problem or cause categories. Fix: Put the effect at the head, draw main bones for categories such as Man, Machine, Material and Method, and add sub-causes on each.

Exam tips

Check units first. If a question mixes units, hours and rupees, convert everything to rupees before adding.
In MCQs, watch for the base period. The percentage change is always on the base.
For written answers, show the formula, the substitution and a closing interpretation to earn step marks.
Be ready to explain in two lines why total productivity is a better measure than a partial ratio.
When comparing plants, use the same ratio for each plant and state which one performs better.
Expect a 'discuss factors' question: structure it as internal and external, then hard and soft, to show clear classification.
For a numerical, always show the ratio, the unit and the percentage change on the old base.
When asked about improving productivity, link each technique to a specific factor and add a manufacturing example.