Automatic creation of Markov models for reliability assessment of safety instrumented systems

Abstract

After the release of new international functional safety standards like IEC 61508, people care more for the safety and availability of safety instrumented systems. Markov analysis is a powerful and flexible technique to assess the reliability measurements of safety instrumented systems, but it is fallible and time-consuming to create Markov models manually. This paper presents a new technique to automatically create Markov models for reliability assessment of safety instrumented systems. Many safety related factors, such as failure modes, self-diagnostic, restorations, common cause and voting, are included in Markov models. A framework is generated first based on voting, failure modes and self-diagnostic. Then, repairs and common-cause failures are incorporated into the framework to build a complete Markov model. Eventual simplification of Markov models can be done by state merging. Examples given in this paper show how explosively the size of Markov model increases as the system becomes a little more complicated as well as the advancement of automatic creation of Markov models.

Introduction

In accordance with IEC 61508, the new international functional safety standards [1], assessing the reliability measurements of SISs is required in the safety life cycle to assure the safety. The assessments can be done through a number of probabilistic analysis techniques, such as fault tree analysis (FTA) [2], [3], reliability block diagram (RBD) [4], Markov analysis (MA) [3], [5], [6], simplified equations [7], [8] and hybrid method [9]. Hauge et al. introduced a method called PDS [10] to quantify the safety unavailability and loss of production for safety instrumented systems. Availability of SISs can be evaluated as well by probabilistic analysis models. Some compared those techniques and outlined their advantages and disadvantages [11], [12]. MA covers most aspects that affect reliability, shows more flexibility than any other techniques and is the only one that can describe dynamic transitions among different system states. Hokstad questioned whether the Markov chain approach is very appropriate for a system with dormant failures, requiring periodic functional test [13]. He also suggested a “standard” approach, as given e.g. in Chapter 10 of Ref. [14]. Bukowski provided answers to Hokstad's question. She modeled and analyzed the effects of periodic test using Markov models [17]. Markov models can be solved using the methods in Refs. [3], [5], [6], [12], [17]. The numeric technique in Ref. [3] combined with periodic tests modeling [17] can provide a practical and easy way to calculate reliability measures for safety instrumented systems. However, the size of Markov model of SIS increases explosively as the system becomes more complex. It is fallible and time-consuming to create Markov models manually. Those disadvantages may eliminate engineers’ willingness to use MA, though Markov models can be solved by some computer programs.

Compared with manual modeling, automatic Markov modeling is more effective, accurate and convenient, but only a few papers published are focused on that topic. Johnson and Butler developed a high-level abstract language to describe the behavior of the fault-tolerant system to be modeled [15]. Houtermans et al. put forward another method, into which descriptive intermediate models were also incorporated [16]. The intermediate models include an RBD and a voting table, which are used to identify dangerous failures and safe failures, respectively. In the two approaches above, experts are still indispensable for the generation of statements of a high-level abstract language or RBD and voting tables.

Safety instrumented systems are a special kind of fault-tolerant systems, which always consist of three subsystems, the sensor part, the logic part and the final element part. Furthermore, a part can be divided into several independent groups, each of which has its own single channel or redundant channels and the corresponding voting logic. According to such decomposability, this paper presents a new technique that does not use any intermediate model to automatically create Markov models for assessing the reliability measurements of safety instrumented systems. Reparation policies and common-cause failures (CCF) are also introduced into the Markov models.