Process time is a central factor in the management and control of systems delivering products and services. Occasionally, process time varies between cycles. Therefore, predictions of process performance, accounting for observed variation, are desirable. A historically-proven good method to generate predictions for process-time is modelling its statistical distribution. This would allow answering such questions like, “what is the most likely process time?” (“what is the mode?”), “what is its highest value so that the probability of exceeding it is less than 10%?” (“what is the 90% percentile of the distribution?”).
A question often asked is “why process time varies?”. Two answers have traditionally been given:
- “Because of error” (caused by multiple occasional factors, each marginally contributing to observed process-time random variation);
- “Because of covariates” (delivering systematic variation plus error to process time, thus increasing its variation).
A third possible source of variation, which to date has been much neglected or ignored, is process work-content variation, namely, work-content becoming random, partially (semi-repetitive processes), or completely (non-repetitive, memory-less, processes). This paper addresses distributional effects that random work-content exerts on shape characteristics of process-time distribution.
To demonstrate what a “semi-repetitive process” implies, consider a certain category of surgeries, open-heart surgery. Let us first address a subcategory including single-bypass surgeries. While some variation between patients undergoing surgery certainly do exist, work-content essentially remain the same so that we may characterize surgeries belonging to this subcategory “repetitive processes”. However, consider all open-heart surgeries. Since the number of bypasses randomly varies between patients, yet most other work elements of surgery remain the same (including those consuming most of surgery-time), this surgery category comprises “semi-repetitive processes”.
A most dramatic effect on the shape of the time-distribution of semi-repetitive or non-repetitive processes is the departure of the mode from the mean. This causes the distribution to become positively skewed (long right tail). Quantifying appropriately the mean-mode distance forms a basis for a new Repetitiveness Measure (RM), developed in the new article. This measure makes possible future development of SPC control scheme for work-content stability. A new bi-variate model, describing process-time variation in terms of work-content variation and error variation, is introduced. Two scenarios are addressed therein — a multiplicative error and an additive error. For the former, a newly defined extended exponential is used to model work-content variation. A generalized gamma is used for the latter.
Using a database of 10K surgeries and a sample of theoretical distributions, a comprehensive study of the effects on shape characteristics of process time-distribution, exercised by work-content variation, is explored and demonstrated. Finally, a model for the distribution of the sample mean is developed.