Variability as a Cause of Production Inefficiency: 23-Ind-A4 Production Management, December 2015, Q5

Question 5: Variability as a Cause of Production Inefficiency (20 marks)

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(a) Example: Variability's Effect on Productivity, and a Way to Reduce It

Consider a single machine feeding a downstream assembly station, where the machine's processing time is not constant but varies randomly around its average (due to tool wear, operator technique, or intermittent minor jams). Queueing theory shows that as this processing-time variability increases — holding average utilization fixed — the average queue of parts waiting in front of the downstream station grows sharply and nonlinearly (the Kingman/VUT relation: waiting time scales with a variability term times a utilization term that explodes as utilization approaches 100%). The productivity impact is direct: the downstream station experiences unplanned idle time whenever its input buffer empties between arrivals, so its actual output per hour falls below what its rated capacity could achieve, even though no equipment or labour was added or removed — the lost output is purely a consequence of unpredictable timing, not insufficient capacity. To protect against this, the plant is typically forced to carry either extra WIP buffer (tying up capital and space, since by Little's law $L=\lambda W$, buffering variability adds to flow time $W$ without adding to the useful throughput $\lambda$) or accept the periodic idle time and its lost output outright. A concrete way to reduce this variability is to implement statistical process control (SPC) on the upstream machine's cycle time and standardize its operating procedure (tooling, changeover method, preventive-maintenance schedule) — converting an erratic, operator-dependent process into one with a tight, predictable distribution of processing times, which directly raises the downstream station's achievable productivity without adding any capacity.

(b) Principles for Reducing Variability

A useful, general set of principles (synthesizing the standard "factory physics" and lean perspectives) is:

Standardize the work. Document and enforce a single best method for each task (standardized work instructions, jigs/fixtures, SOPs) so that operator-to-operator and cycle-to-cycle differences shrink; this attacks the largest and most controllable source of variability in most manual or semi-manual operations.
Maintain equipment proactively. Total productive maintenance (TPM) and condition-based maintenance prevent the gradual drift and sudden breakdowns that inject variability into machine cycle times and availability, rather than reacting to failures after they occur.
Control and monitor with data. Use SPC (control charts) to distinguish common-cause variability (inherent to the process, requiring a process change to fix) from special-cause variability (an assignable, fixable event), and act on out-of-control signals immediately before they propagate downstream.
Reduce setup/changeover variability. Apply SMED (single-minute exchange of die) principles so changeovers are fast and consistent in duration, since an unpredictable changeover time is often a bigger driver of downstream variability than the changeover's average length.
Improve supplier and input consistency. Work upstream with suppliers on incoming-material quality and delivery reliability, since variable input quality (dimensions, defect rate) forces variability into every downstream process that consumes it.
Buffer deliberately where variability cannot be eliminated. Where a source of variability is irreducible (e.g., genuine demand randomness), use capacity, inventory, or time buffers consciously and size them analytically (via queueing/Little's-law relationships) rather than by ad hoc padding, so the buffer is neither starving the line nor tying up excess capital.

Concept & Theory

Topic. Variability as a driver of both cost and productivity loss in a production system, and the standard toolkit (SPC, TPM, SMED, standardized work) for reducing it.

Key relations. Kingman/VUT approximation for expected queue-wait: $W_q\approx\left(\dfrac{c_a^2+c_s^2}{2}\right)\left(\dfrac{\rho}{1-\rho}\right)t_s$, where $c_a^2,c_s^2$ are squared coefficients of variation of arrivals and service and $\rho$ is utilization; Little's law $L=\lambda W$.

Why this works. A production system with zero variability could, in principle, run at 100% utilization with zero buffer and zero idle time — the entire reason plants lose productivity (and carry WIP, safety stock, and slack capacity) is to absorb variability. Every principle above works by either removing a source of variability at its origin (standardized work, TPM, supplier quality) or by making the residual variability manageable with a properly-sized buffer, which recovers more of the system's rated productivity than an unmanaged buffer would.

Common pitfall. Treating "add more buffer/inventory" as the default fix for lost productivity — it hides the underlying problem and adds carrying cost without raising true capacity, whereas removing the root cause of the variability (a specific machine, a specific operator step, a specific supplier) recovers productivity directly and is almost always cheaper in the long run.

Source. Hopp & Spearman, Factory Physics, Ch. 8–9 (variability laws, buffering); Montgomery, Introduction to Statistical Quality Control, Ch. 1–5 (SPC and common vs. special-cause variation).

Question 5 of 7: Variability as a Cause of Production Inefficiency

Question 5: Variability as a Cause of Production Inefficiency (20 marks)

(a) Example: Variability's Effect on Productivity, and a Way to Reduce It

(b) Principles for Reducing Variability